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Course name, topic name, question and instructions were posted individually in the document.

1.one main topic above 400 words and 2 references 

2. Two replies each 250 words.(my classmate replies are posted in the document.

3. APA format

4. Assignment must needed as per instructions, as mentioned in attached document.(Must follow the highlighted instructions in the document whihc is indicating to complete the discussion.)

Please ping me if there is any question/confusion. Must follow instructions.

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Lesson 6 Discussion Forum

Discussion assignments will be graded based upon the criteria and rubric specified in the Syllabus.

For this Discussion Question, complete the following.

Question

Review the two articles about bank failures and bank diversification that are found below this. Economic history assures us that the health of the banking industry is directly related to the health of the economy. Moreover, recessions, when combined with banking crisis, will result in longer and deeper recessions versus recessions that do occur with a healthy banking industry.

Instructions:

1. Locate one journal article for each of your two chosen economic types. You need to focus on the Abstract, Introduction, Results, and Conclusion. For our purposes, you are not expected to fully understand the Data and Methodology.  

2. Summarize these journal articles. Please use your own words. No copy-and-paste. Cite your sources.

3. During the second week of the Module, you will need to reply to the posts of two of your peers. Your replies must focus on increasing knowledge of the class and must advance the discussion further. Simply affirming your peers does not count as a substantive reply. 

4.Please post (in APA format) your article citation.

5. Please provide 3 references under the discussion.

6. Please post replies to 2 of my classmates each 250 words and their discussions are provided below.

Supplemental Resources: – Material Chapter 9 and 10:

Reading Assignment:

Please read Chapters 11 & 12  from the Managerial Economics and Strategy textbook

https://www.richmondfed.org/~/media/richmondfedorg/publications/research/economic_quarterly/2005/winter/pdf/walter.pdf

Classmate post 1

Banking Failures and Diversification: Journal articles review

Review of the two articles – Walter (2005) and Strahan (2006) on bank failures and bank diversification establishes that economic history and the health of the banking industry are dependent on the health of economy.  In comparison two latest articles by Banwo et.al., (2019) and Wu et.al., (2020) are reviewed to identify the impact of economic factors, banking industry and its diversification.

Banking Failures during Depression

Walter (2005) economic diversification exposes question on whether the diversification of banks is actually the diversification of the economy in the United States was topped the evaluation of this article should be in the light of global financial crisis of 2008 to 2009. The authors suggest that the 1977 major backing changes at this value to the net effect of bank diversification has meant that the lower levels of volatile conditions of the state level are reduced. Hence the link between local economy and the local banking system is also well balanced. The state economies become less volatile after these interstate banking reforms.

Bank Diversification, Economic Diversification

Strahan (2006) diversification and expansion for channel in respect to data and the relationship between the late 1990 and early 2008 shows that the banking have also dramatically changed in this period regulatory changes are in the individual States have been predominant and made it easier for banks to ensure that the capital is well protected and profits and gains from local and micro environment is much easier because of the diversification.

Diversification, efficiency and risks of banks

In the article by Wu, Chen, Chen & Jeon (2020) the impact of diversification of banks is studied. Their research of three dozen and more emerging economies showed that diversification brings stability in the banks. However, the counter-effect of such diversification is increased exposure to risks. Hence, diversification of banks leads to competing effects on banking risks.

Consequences of Diversification and financial Stability

In this article by authors, Banwo Harrald and Medda (2018) explore the consequences of diversification and financial stability. Their use of agent-based model uses real economy and financial systems. Their model validates (1) single banks will fail less if they diversify (2) joint-ventures increase systemic risks and diversification will result in downturn. They also recommend that regulations should encourage credit transactions which lower similarity in bank to bring about financial stability to permit diversification.

Conclusion

Hence, the inference from the original two articles Walter (2005) and Strahan (2006) is that the economic history and the health of the banking industry are dependent on the health of economy.  In the latest chosen articles by Banwo et.al., (2019) and Wu(2020) for review, diversification and efficiency in banks was directly related to risk with increased diversification leading to stabilization but was associated with risk of lowered efficiency. Higher diversifications lead to complexity of risks. Hence, despite benefitting from diversification of banks, it eventually leads to instability in banks. 

————————————————————————————————————————————-

Classmate post2:

Failures in Banks and Bank Diversification

Abstract

The term Bank is placing a significant role in the economy and also this is providing various services for the individuals so that they can be more able to save their money. This banking sector will also have to provide another service that is financial services by which people can make investments.

Introduction

In the article 1, the growth of the economy, savings, and investments will be more helpful. There are some of the features that are existed in the financial services and that feature is that the rate percent will be less (Audrino et al., 2019). The main reason under the failure of the banks is that if the activities of the bankers for crediting and debiting were not done then banks will have a failure. Besides this diversification is that enabling capital to particular assets so that there will be a minimization of exposure and this is known as diversification.

In the article 2, it is also explained that if there is a failure observed in the banks then bank authorities will be considered by the FDIC. All the risks that are occurring in the banks can be minimized with the help of bank diversification. But there are also risks observed in the diversification and these diversification risks will be in large-sized banks and medium-sized banks (Gunji et al., 2018). Shutting down the bank’s currency controller will have the main authority and value of assets that are owned by the banks and are minimized below the levels of the market.

Results

If there is a lack of liquidity then that can result in the less apt for money lending to the firms and needed customers (Ozdemir et al., 2018). Results that are obtained are that the investments that are made by the firms and banks will be minimized. Hence by this companies will hire fewer employees.

Conclusion

From various banks, more money will be asked by the failed banks so that that will be paid for the customers (Audrino et al., 2019). Bank failures are also resulting in reducing the reputation of the banks due to which most of the customers are facing many difficulties.

Managerial Economics and Strategy

Third Edition

Chapter 12

Game Theory and Business Strategy

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Managerial Problem

Dying to Work

If the firm knows how dangerous a job is but potential employees do not, does it cause the firm to underinvest in safety? Can the government intervene to improve this situation?

Solution Approach

We need to focus on game theory, a set of tools used to analyze strategic decision making. In deciding how much to invest in safety, firms take into account the safety investments of rivals.

Empirical Methods

Oligopoly firms interact within a game as players that follow the rules of the game. Games can be static or dynamic.

Players decide their strategies based on payoffs, level of information, and their rationality.

The game optimal solution is a Nash Equilibrium and depends on information and rationality.

Players determine transaction prices in bargaining and auction mechanisms.

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Learning Objectives (1 of 2)

12.1 Oligopoly Games

Use payoff matrices to analyze oligopoly markets

12.2 Types of Nash Equilibria

Describe the different types of Nash equilibria

12.3 Information and Rationality

Explain the role of information and rationality in game theory

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Learning Objectives (2 of 2)

12.4 Bargaining

Derive the outcome of a bargaining game

12.5 Auctions

Determine the optimal bidding strategy in an auction

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12.1 Oligopoly Games (1 of 8)

A Game Between American and United Airlines

Players and Rules

Two players, American and United, play a static game (only once) to decide how many passengers per quarter to fly. Their objective is to maximize profit.

Rules: Other than announcing their output levels simultaneously, firms cannot communicate (no side deals or coordination allowed).

Complete information: Firms know all strategies and payoffs.

Strategies

Each firm’s strategy is to take one of the two actions, choosing either a low output (48 k passengers per quarter) or a high output (64 k).

Payoff Matrix or Profit Matrix

Both firms know all strategies and corresponding payoffs for each firm.

Table 12.1 summarizes this information. For instance, if American chooses high output (q A=64) and United low output (q U=48), American’s profit is $5.1 million and United’s profit is $3.8 million.

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Table 12.1 Dominant Strategies in a Quantity-Setting Game

Note: Quantities are in thousands of passengers per quarter; (rounded) profits are in millions of dollars per quarter. The payoff to American Airlines is in the upper-right corner of each cell and the payoff to United Airlines is in the lower left.

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12.1 Oligopoly Games (2 of 8)

Dominant Strategies

If one is available, a rational player always uses a dominant strategy: A strategy that produces a higher profit than any other strategy the player can use no matter what its rivals do.

Dominant strategies and game solution in Table 12.1

If United chooses the high-output strategy (q U = 64), American’s high-output strategy maximizes its profit.

If United chooses the low-output strategy (q U = 48), American’s high-output strategy maximizes its profit.

Thus, the high-output strategy is American’s dominant strategy.

Similarly, United’s high-output strategy is also a dominant strategy.

Because the high-output strategy is a dominant strategy for both firms, we can predict the dominant strategy solution of this game is q A = q U = 64.

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12.1 Oligopoly Games (3 of 8)

Dominant Strategies

Dominant strategy solution is not the best solution

A striking feature of this game is that the players choose strategies that do not maximize their joint or combined profit.

In Table 12.1, each firm could earn $4.6 million if each chose low output (q A = q U = 48) rather than the $4.1 million they actually earn by setting q A = q U = 64.

Common Confusion: Rival firms always choose a set of strategies that benefits all of them. This is not true in the Prisoner’s Dilemma game.

Prisoner’s Dilemma game

Prisoners’ dilemma game: All players have dominant strategies that lead to a profit that is inferior to what they could achieve if they cooperated.

Given that the players must act independently and simultaneously in this static game, their individual incentives cause them to choose strategies that do not maximize their joint profits.

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12.1 Oligopoly Games (4 of 8)

Best Responses

Many games do not have a dominant strategy solution. So, we use the approach of best response: The strategy that maximizes a player’s profit given its beliefs about its rivals’ strategies.

A dominant strategy is a strategy that is a best response to all possible strategies that a rival might use. In the absence of one, each firm can determine its best response to any possible strategy chosen by its rivals.

Best response is the basis for a Nash equilibrium: A set of strategies if, when all other players use these strategies, no player can obtain a higher profit by choosing a different strategy.

A Nash equilibrium is self-enforcing.

There are two steps to find a Nash equilibrium:

First step: Determine each firm’s best response to any given strategy of the other firm.

Second step: Check whether there are any pairs of strategies (a cell in profit matrix) that are best responses for both firms, so the strategies are a Nash equilibrium in the cell.

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12.1 Oligopoly Games (5 of 8)

A more complicated game between American and United to illustrate best responses

Now both American and United can choose from three strategies: 96, 64, or 48 passengers. The profit matrix in Table 12.2 has nine cells (3×3).

Same rules as before: Static simultaneous game, perfect information

First Step: Best Responses in Table 12.2

If United chooses q U = 96, American’s best response is q A = 48; if q U = 64, American’s best response is q A = 64; and if q U = 48, q A = 64.

If American chooses q A = 96, United’s best response is q U = 48; if q A = 64, United’s best response is q U = 64; and if q A = 48, q U = 64.

Second Step: Nash Equilibrium in Table 12.2

There is only one cell for it (both parts green): q A = q U = 64.

This is a Nash Equilibrium: Neither firm wants to deviate from its strategy. But, equilibrium does not maximize joint profits.

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Table 12.2 Best Responses in a Quantity Setting Game

Note: Quantities are in thousands of passengers per quarter; (rounded) profits are in millions of dollars per quarter.

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12.1 Oligopoly Games (6 of 8)

Failure to Maximize Joint Profits

Common Confusion: If firms in a market decide to advertise, doing so raises their profits. We’ll show that, for some profit matrices, all the firms would benefit if they could agree not to advertise.

In panel a of Table 12.3, two firms play a static game where a firm’s advertising does not bring new customers into the market but only has the effect of stealing business from the rival firm.

Firms decide simultaneously to “advertise” or “do not advertise.” Advertising is a dominant strategy for both firms. In the resulting dominant strategy solution and Nash equilibrium, each firm earns 1 but would make 2 if neither firm advertised. Solution does not maximize joint profits.

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12.1 Oligopoly Games (7 of 8)

Failure to Maximize Joint Profits

In panel b of Table 12.3, firms play a static game in which advertising by a firm brings new customers to the market and helps both firms.

Firms decide simultaneously to “advertise” or “does not advertise.” Advertising is a dominant strategy for both firms. In the resulting dominant strategy solution and Nash equilibrium, each firm earns 4. Solution does maximize joint profits.

Whether a Nash equilibrium maximizes the combined profit for the players depends on the profit matrix.

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Table 12.3 Advertising Games: Prisoners’ Dilemma or Joint-Profit Maximizing Outcome?

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12.1 Oligopoly Games (8 of 8)

Pricing Games in Two-Sided Markets

A two-sided market is an economic platform that has two or more user groups that provide each other with network externalities (Chapter 9).

MasterCard and Visa connect merchants and consumers. The more consumers who use a card, the more attractive accepting that card is to merchants. The more merchants who accept the card, the more likely consumers want to use it.

Prisoner’s Dilemma game in Table 12.4. MasterCard and Visa are rivals, their pricing strategies are balanced pricing (both merchants and consumers pay fees), or unbalanced pricing (only merchants pay). Unbalanced pricing is the dominant strategy for each firm, and the Nash Equilibria gives 4 each. Firms would earn more if they used balanced pricing, 7 each.

eHarmony and Match.com connect the two sides of a date.

Non-Prisoner’s Dilemma game in Table 12.5. eHarmony and Match.com are dating platforms, their pricing strategies are balanced pricing (men and women pay), or unbalanced pricing (only one group pays). Balanced pricing is the dominant strategy for each firm. The solution maximizes the joint payoffs to the firms.

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Table 12.4 Unbalanced Pricing in a Two-Sided Market

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Table 12.5 Balanced Pricing in a Two-Sided Market

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12.2 Types of Nash Equilibria (1 of 8)

There are three types of Nash equilibria

Unique Nash equilibrium

Only one combination of strategies is each firm’s strategy a best response to its rival’s strategy.

Examples are the Bertrand and Cournot models, and all games played so far.

Multiple Nash equilibria

Many oligopoly games have more than one Nash equilibrium.

To predict the likely outcome of multiple equilibria, we may use additional criteria.

Mixed strategy Nash equilibria

In the games we played so far, players were certain about what action to take at each rival’s decision (pure strategy).

When players are not certain, they use a mixed strategy: A rule telling the player how to randomly choose among possible pure strategies.

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12.2 Types of Nash Equilibria (2 of 8)

Multiple Equilibria

Coordination Game: In Table 12.6, two network firms play a static game. Each firm chooses simultaneously and independently to schedule a show on Wednesday or Thursday.

If firms schedule it on different days, both earn 10. Otherwise, each loses 10.

Best Responses: Neither network has a dominant strategy. For each network, its best choice depends on the choice of its rival.

In Table 12.6, if Network 1 opts for Wednesday, then Network 2 prefers Thursday. But, if Network 1 chooses Thursday, then Network 2 prefers Wednesday. Best responses are colored green.

Two Nash equilibrium solutions: There are two cells with both firms’ best responses (green cells)

These Nash equilibria have one firm broadcast on Wednesday and the other on Thursday.

We predict the networks would schedule shows on different nights. But, we cannot forecast which night each network will choose.

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Table 12.6 Network Scheduling: A Coordination Game

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12.2 Types of Nash Equilibria (3 of 8)

Cheap Talk

Firms can engage in credible cheap talk if they communicate before the game and both have an incentive to be truthful (higher profits).

If Network 1 announces in advance that it will broadcast on Wednesday, Network 2 will choose Thursday and both networks will benefit. The game becomes a coordination game.

The Pareto Criterion

If cheap talk is not allowed or is not credible, it may be that one of the Nash equilibria provides a higher profit to all players than the other Nash equilibria.

If so, we expect firms acting independently to select a solution that is better for all parties (Pareto Criterion), even without communicating. In Table 12.7, there are two Nash equilibria, but we expect firms to choose the one with the higher profits.

Unfortunately, we cannot always use cheap talk or the Pareto criterion to predict the outcome in a game with multiple equilibria.

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Table 12.7 The Pareto Criterion in a Network Scheduling Coordination Game

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12.2 Types of Nash Equilibria (4 of 8)

Mixed Strategy Equilibria

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12.2 Types of Nash Equilibria (5 of 8)

Mixed Strategy Equilibria

So far, we assumed that each firm uses a pure strategy: An action that a player takes in every possible situation in a game.

A pure strategy is a rule telling the player with certainty what action to take at each decision point in a game.

In the following games, a firm uses a mixed strategy: A player chooses among possible pure strategies according to probabilities that the player sets.

A mixed strategy is a rule telling the player which method to use to randomly choose among possible pure strategies. The method could be a dice to throw or a coin to flip.

A pure strategy can be viewed as a special case of a mixed strategy: A player assigns a probability of one to a single pure strategy and zero to all other possible pure strategies.

A mixed strategy that assigns positive probabilities to two or more actions is called non-pure mixed strategy.

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12.2 Types of Nash Equilibria (6 of 8)

Only Mixed-Strategy Equilibria

Design Competition Game: Two firms, upstart and established, compete for an architectural contract and simultaneously decide if their proposed designs are traditional or modern.

The profit matrix is in Table 12.8. If both firms adopt the same design, then the established firm wins. However, if the firms adopt different designs, the upstart firm wins the contract.

The best responses for the upstart are a modern design if the established firm uses a traditional design, and a traditional design if the rival picks modern.

The best responses for the established are a modern design if the upstart firm uses a modern design, and a traditional design if the rival picks traditional.

Pure strategies have no Nash equilibrium

Given the best responses, for each cell, one firm or the other regrets their design choices.

Thus, if both firms use pure strategies, this game has no Nash equilibrium.

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Table 12.8 Mixed Strategies in a Design Competition

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12.2 Types of Nash Equilibria (7 of 8)

Only Mixed-Strategy Equilibria

Mixed strategy Nash equilibrium: If each firm chooses a traditional design with probability ½, this design game has a mixed-strategy Nash equilibrium.

The probability that a firm chooses a given style is ½ and the probability that both firms choose the same cell is ¼. Each of the four cells in Table 12.6 is equally likely to be chosen with probability ¼.

The established firm’s expected profit—the firm’s profit in each possible outcome times the probability of that outcome—is 9, the highest possible. The firm just flips a coin to chose between its two possible actions.

Similarly, the upstart’s expected profit is 9 and flips a coin too.

Why would each firm use a mixed strategy of ½ ?

Because it is in their best interest to flip a coin.

If the upstart firm knows the established firm will choose traditional design with probability > ½ or 1, then the upstart picks modern for certain and wins the contract. So, it is best for the traditional firm to flip a coin (probability = ½).

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12.2 Types of Nash Equilibria (8 of 8)

Both Pure- and Mixed-Strategy Equilibria

Two firms are considering opening gas stations at the same location but only one station would operate profitably (small demand). If both firms enter, each loses 2.

The profit matrix is in Table 12.9. Neither firm has a dominant strategy. Each firm’s best action depends on what the other firm does. There are 3 Nash Equilibria.

Three Nash equilibria in total

Two Nash equilibria with pure strategies: Firm 1 enters and Firm 2 does not enter, or Firm 2 enters and Firm 1 does not enter.

How do the players know which outcome will arise? They don’t know. Cheap talk is no help.

One mixed-strategy Nash equilibrium: Each firm enters with probability

No firm could raise its expected profit by changing its mixed strategy.

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Table 12.9 Nash Equilibria in an Entry Game

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12.3 Information and Rationality (1 of 5)

The Logic of Incomplete Information and Rationality

We have assumed so far firms have complete information: Know all strategies and profits.

However, in more complex games, firms have incomplete information.

Incomplete information may occur because of private information or high transaction costs.

We have assumed so far players act rationally: They use all their available information to determine their best strategies (maximizing profit strategies).

However, players may have limited powers of calculation, or be unable to determine their best strategies (bounded rationality).

When firms have incomplete information or bounded rationality, the Nash equilibria are different from games with full information and rationality.

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12.3 Information and Rationality (2 of 5)

Incomplete Information

Investment game: Google and Samsung must decide “to invest” or “do not invest” in complementary products that “go together.” (Chrome O S and Chromebook, respectively)

In Table 12.10, there is a profit asymmetry: A Chromebook with no Chrome O S has no value at all, but Chrome O S with no Chromebook still has value.

Assume complete information in Table 12.10

If each firm has full information, Google’s dominant strategy is “to invest” and Samsung’s best response to it is “to invest.”

The solution is a unique Nash equilbrium with both firms investing.

Assume incomplete information in Table 12.10

With private information, Samsung does not know Google’s dominant strategy is always “to invest.”

Given its limited information, Samsung weights a modest gain versus a big loss. If it thinks it is likely Google will not invest (big loss), then Samsung does not invest.

Samsung and Google fail to coordinate their strategies.

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Table 12.10 Complementary Investment Game

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12.3 Information and Rationality (3 of 5)

Managerial Implication: Solving Coordination Problems

Managers often worry about whether their products will work with other products.

For example, it is important for smartphones to work with headphones, with car audio systems, and with hearing aids produced by other companies.

To work together, each of these products must use the same technical standard.

Managers may be reluctant to invest in adopting a particular technical standard unless they are confident other companies will use the same standard.

Smartphones use the Bluetooth standard, as do many car audio systems, headphones, and hearing aids. How did so many different companies agree to coordinate on the Bluetooth standard?

This coordination is handled by the Bluetooth Special Interest Group, a not-for-profit standard setting organization (S S O) with over 33,000 member companies who use the Bluetooth standard as of 2018.

S S Os look for patent-holders to agree to license the technology on a “fair, reasonable, and nondiscriminatory” basis.

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12.3 Information and Rationality (4 of 5)

Rationality

We normally assume that rational players consistently choose actions that are in their best interests given the information they have. They are able to choose profit-maximizing strategies.

Bounded Rationality

However, actual games are more complex. Managers with limited powers of calculation or logical inference (bounded rationality) try to maximize profits. But, due to their cognitive limitations, do not always succeed.

Maximin Strategies

In very complex games, a manager with bounded rationality may use a rule of thumb approach, perhaps using a rule that has worked in the past.

A maximin strategy maximizes the minimum profit. This approach ensures the best possible profit if your rival takes the action that is worst for you.

The maximin solution for the game in Table 12.10 is for Google to invest and for Samsung not to invest.

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12.3 Information and Rationality (5 of 5)

Managerial Implication: Using Game Theory to Make Business Decisions

When making strategic decisions, managers should consider five principles based on game theory:

Dominance. A manager who has a dominant strategy—a strategy that is always best no matter what rivals do—should use it.

Best Response. A manager who does not have a dominant strategy should determine the best responses to the strategies that rivals might use.

Point of View. A manager should consider possible strategies from the rival’s vantage point, try to predict which strategy the rival will choose, and select the best response to that strategy.

Coordination. When doing so increases profit, a manager should coordinate with other firms through pre-play communication (cheap talk) or by using legal contracts.

Randomize. A manager may be able to earn a higher profit by using a mixed strategy to keep rivals guessing.

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12.4 Bargaining (1 of 4)

Bargaining is important in our personal lives. Car buyers bargain with car dealers, married couples and roommates bargain over responsibility for household chores, and teenagers bargain with their parents over anything.

Bargaining is also common in business situations. Managers and employees bargain over wages and working conditions, firms bargain downstream with suppliers and bargain upstream with distributors.

Bargaining Games

Bargaining games: Any situation in which two or more parties with different interests or objectives negotiate voluntarily over the terms of some interaction, such as the transfer of a good from one party to another.

For simplicity, we will focus on two-person bargaining games.

The solution for bargaining games is called Nash Bargaining Solution.

Nash Bargaining solution ≠ Nash Equilibrium. The Nash equilibrium is for noncooperative games where players do not negotiate quantities or prices.

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12.4 Bargaining (2 of 4)

The Nash Bargaining Solution

The Nash bargaining solution to a cooperative game is efficient in the sense that there is no alternative outcome that would be better for both parties or strictly better for one party and no worse for the other.

The game in Table 12.1 (American Versus United) becomes a bargaining game if rules allow firms to bargain over their output levels and reach a binding agreement.

Follow three steps to find a Nash bargaining solution:

First, find the profit at the disagreement point: The outcome that arises if no agreement is reached, call it d. In Table 12.1, d A = d U = 4.1.

Second, if a proposed agreement is reached, the firm earns a profit of π and a net surplus, π − d. In Table 12.1, π A − d A and π U − d U

Third, the Nash bargaining solution is the outcome in which each firm receives a nonnegative surplus and in which the product of the net surplus of the two firms

(called the Nash product, N P) is maximized. In Table 12.1,

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12.4 Bargaining (3 of 4)

The Nash Bargaining Solution

Maximize

There are four possible outcomes in Table 12.1. In the upper left cell, in which each firm produces the large output, the N P = 0 because each firm has zero net surplus. In the lower left cell and in the upper right cell, N P < 0. In the lower right cell, where each firm produces the small output and earns 4.6,

maximum N P.

So, the Nash bargaining equilibrium predicts both American and United fly 48 thousand passengers.

If the firms could bargain about how they set their output levels in an oligopoly game, they could reach an efficient outcome that maximizes the Nash product.

Such an agreement creates a cartel and raises the firms’ profits. The gain to firms from such a cartel agreement is more than offset by lost surplus for consumers (Chapter 11). Consequently, such agreements are illegal in most developed countries under antitrust or competition laws.

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12.4 Bargaining (4 of 4)

Inefficiency in Bargaining

The Nash bargaining solution presumes that the parties achieve an efficient outcome where neither party could be made better off without harming the other party.

However in the real world, bargaining frequently yields inefficient outcomes.

Reasons for Inefficient Outcomes

The bargaining process takes time, which delays the start of the benefit flow and therefore reduces the value of benefits overall, for instance a strike.

Usually in a strike, negotiators fail to quickly reach an agreement due to bounded rationality or incomplete information about the other side’s profits. The parties do the best they can but are unable to determine the best possible strategies and therefore they make mistakes that are costly to both parties.

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12.5 Auctions (1 of 8)

An auction is a sale in which a good or service is sold to the highest bidder.

In auction games, players called bidders devise bidding strategies without knowing other players’ payoff functions.

A bidder needs to know the rules of the game: The number of units being sold, the format of the bidding, and the value that potential bidders place on the good.

Real Scenarios for Auction Games

Government-related games: Government procurement auctions; auctions for electricity and transport markets; auctions to concede portions of the airwaves for radio stations, mobile phones, and wireless internet access.

Market transaction games: Goods commonly sold at auction are natural resources such as timber and drilling rights for oil, as well as houses, cars, agricultural produce, horses, antiques, and art. And of course, goods online in sites like eBay.

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12.5 Auctions (2 of 8)

Elements of Auctions

Number of units

Auctions can be used to sell one or many units of a good.

Format of bidding

English auction: Ascending-bid auction process where the good is sold to the last bidder for the highest bid. Common to sell antiques.

Dutch auction: Descending-bid auction process where the seller reduces the price until someone accepts it and buys at that price.

Sealed-bid auction: Bidders submit a bid simultaneously without seeing anyone else’s bid and the highest bidder wins. In a first-price auction, the winner pays its own, highest bid. In a second-price auction, the winner pays the amount bid by the second-highest bidder.

Double auction: All potential buyers and sellers make public offers stating prices at which they are willing to buy or sell.

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12.5 Auctions (3 of 8)

Elements of Auctions

Value

Private value: Individual bidders know how much the good is worth to them but not how much other bidders value it.

Common value: The good has the same value to everyone, but no bidder knows exactly what that value is.

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12.5 Auctions (4 of 8)

Bidding Strategies in Private-Value Auctions

Second-Price Auction Strategies

Second-Price Auction Game Rules: Traditional sealed-bid, second-price auction. Each bidder places a different private value on a single, indivisible good.

The amount that you bid affects whether you win, but it does not affect how much you pay if you win, which equals the second-highest bid.

Bidding your highest value is your best strategy (weakly dominates all others).

Suppose that you value a folk art carving at $100. If you bid $100 and win, your C S = 100—second price. If you bid less than $100, your risk not winning. If you bid more than $100, your risk ending up with a negative C S.

So, bidding $100 leaves you as well off as, or better off than, bidding any other value.

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12.5 Auctions (5 of 8)

English Auction Strategy

English Auction Game Rules: Ascending-bid auction process where the good is sold to the last bidder for the highest bid. Each bidder has a private value for a single, indivisible good.

The amount that you bid affects whether you win and pay.

Your best strategy is to raise the current highest bid as long as your bid is less than the value you place on the good.

Suppose that you value a folk art carving at $100. If you bid an amount b and win, your surplus is $100 − b. Your surplus is positive or zero for b ≤ 100. But, negative if b > 100. So, it is best to raise bids up to $100 and stop there.

If all participants bid up to their value, the winner will pay slightly more than the value of the second-highest bidder. Thus, the outcome is essentially the same as in the sealed-bid, second-price auction.

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12.5 Auctions (6 of 8)

Equivalence of Auction Outcomes

Dutch auction rules: Descending-bid auction process where the seller reduces the price until someone accepts the offered price and buys at that price.

Sealed-bid rules: Bidders submit a bid simultaneously without seeing anyone else’s bid, the highest bidder wins and pays its own bid.

In both games, each bidder has a private value for a single, indivisible good.

The amount that you bid affects whether you win and pay.

The best strategy for both games is to bid an amount that is equal to or slightly greater than what you expect will be the second-highest bid, given that your value is the highest.

Bidders shave their bids to less than their value to balance the effect of decreasing the probability of winning and increasing C S. The bid depends on the beliefs about the strategies of rivals.

Thus, the expected outcome is the same under each format for private-value auctions: The winner is the person with the highest value, and the winner pays roughly the second-highest value.

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12.5 Auctions (7 of 8)

The Winner’s Curse

The winner’s curse occurs in common-value auctions: The winner’s bid exceeds the common-value item’s value. So, the winner ends up paying too much.

The overbidding occurs when there is uncertainty about the true value of the good, as is in timber land auctions.

Best strategy to avoid the winner’s curse

Rational bidders shade or reduce their bids below their estimates.

The amount of reduction depends on the number of other bidders, because the more bidders, the more likely that the winning bid is an overestimate.

Bounded rationality and the winner’s curse

Although rational managers should avoid the winner’s curse, there is strong empirical evidence for the winner’s curse (corporate acquisition market).

One explanation is bounded rationality.

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12.5 Auctions (8 of 8)

Managerial Implication: Auction Design

Managers who sell assets using auctions need to understand how an auction’s design affects bidders’ behavior.

Because intelligent bidders shade their bids, sellers of common-value goods can do better with an English auction than with a sealed-bid auction. In an English auction, bidders may revise their views about the object’s value as they watch others bid.

Many sellers have learned this lesson. For example, online auction sites such as eBay do not use sealed-bid auctions, choosing modified English auctions or other types of auctions instead.

Many governments have failed to learn it. They continue to rely heavily on sealed-bid auctions even though it is likely they would earn more money if they used an English auction to sell lumber, rights to airwaves, and other property.

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Managerial Solution

Dying to Work

If the firm knows how dangerous a job is but potential employees do not, does it cause the firm to underinvest in safety? Can the government intervene to improve this situation?

Solution

The firms are engaged in a prisoners’ dilemma game.

The firms underinvest in safety because each firm bears the full cost of its safety investments but derives only some of the benefits.

This outcome results because workers cannot tell which firm is safer.

If the government or a union were to collect and provide workers with firm-specific safety information at relatively low costs, the firms might opt to invest.

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Copyright

This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

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Managerial Economics and Strategy

Third Edition

Chapter 11

Oligopoly and Monopolistic Competition

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Managerial Problem

Gaining an Edge from Government Aircraft Subsidies

Airbus and Boeing are the only manufacturers of large commercial planes.

If only one firm receives a subsidy, how can it gain competitive advantage? What is the subsidy’s effect on p and q? What happens if both governments subsidize their firms? Is a subsidy war good for both firms?

Solution Approach

We need to focus on two markets. An oligopolistic market has few sellers and barriers to entry, firms have market power and may or may not collude to form cartels. A monopolistic competitive market has firms with market power, but there is free entry in the long run.

Empirical Methods

Within a cartel, oligopoly firms collude to raise price and profits.

Oligopoly firms can independently set quantities (Cournot Model) or prices (Bertrand Model).

In monopolistic competitive markets, firms charge prices above marginal cost but make no economic profit in the long run.

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Learning Objectives (1 of 2)

11.1 Cartels

Describe how firms in a cartel raise their profits by coordinating their actions

11.2 Cournot Oligopoly

Model how firms independently choose their output levels to determine the Nash-Cournot equilibrium

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Learning Objectives (2 of 2)

11.3 Bertrand Oligopoly

Show how firms independently choose their prices to determine the Nash-Bertrand equilibrium

11.4 Monopolistic Competition

Explain how two conditions determine the monopolistic competition equilibrium

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11.1 Cartels (1 of 5)

Why Cartels Succeed or Fail

Oligopolistic firms have an incentive to form cartels in which they collude in setting prices or quantities so as to increase their profits.

The Organization of Petroleum Exporting Countries (O P E C) is a well-known example of an international cartel.

Typically, each member of a cartel agrees to reduce its output from the level it would produce if it acted independently. As a result, the market price rises and the firms earn higher profits.

If the firms reduce market output to the monopoly level, they achieve the highest possible collective profit.

However, each member has an incentive to cheat.

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11.1 Cartels (2 of 5)

Why Cartels Form

A cartel forms if members of the cartel believe that they can raise their profits by coordinating their actions.

A cartel takes into account how changes in any one firm’s output affect the profits of all members of the cartel.

Therefore, the aggregate profit of a cartel can exceed the combined profits of the same firms acting independently.

Competitive market versus cartel:

In Figure 11.1, there are n competitive firms and no further entry is possible.

In panel b, at the point of competitive equilibrium, the market output is Q c = n q c

and price is p c. In panel a, each firm takes p c and produces

If the n firms form a cartel and act like a monopoly, the market output reduces to Q m but the price goes up to p m in panel b. The cartel profit increases and individual profits go up if firms charge p m and reduce output to q m in panel a.

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Figure 11.1 Comparing Competition with a Cartel

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11.1 Cartels (3 of 5)

Why Cartels Fail

External reasons:

Cartels are generally illegal in developed countries. High fines and jail terms may prevent collusion.

Some cartels fail because they do not control enough of the market to significantly raise the price.

Internal reasons:

Cartel members have incentives to cheat if a member thinks its firm is just one of many firms so its extra output hardly affects the market price and the other firms in the cartel can’t tell who is producing more.

In panel a of Figure 11.1, each firm agreed to q m. However, a price taker firm maximizes profit selling q*, where p m= M C. It makes extra money by producing more than q m, as long as M R > M C.

As more and more firms cheat, p m falls. Eventually, the cartel collapses.

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11.1 Cartels (4 of 5)

Maintaining Cartels

To keep firms from violating a cartel agreement, the cartel must detect cheating and punish violators.

Detection and Enforcement

Cartels use different techniques to detect cheating.

Some cartels may give members the right to inspect each other’s accounts or divide the market by region or by customers.

Cartels may turn to industry organizations to collect data on a firm’s market share.

Cartels use various methods to enforce their agreements.

Most-favored-customer clause: The seller would not offer a lower price to any other current or future buyer without offering the same price decrease to the firms that signed these contracts.

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11.1 Cartels (5 of 5)

Common Confusion:

Requiring government agencies to report which company had the lowest bid for a government contract and the level of the bid is good for the public.

Although society benefits in many ways from government transparency, disclosing this type of information can help a cartel enforce its agreement.

Government Support and Barriers to Entry

Sometimes governments help create and enforce cartels, exempting them from antitrust and competition laws.

With high barriers to entry, cartel members are few. The fewer the firms in a market, the easier to find cheaters and to impose penalties.

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11.2 Cournot Oligopoly (1 of 8)

The Cournot Model

Four assumptions: Few firms and no entry, identical costs and identical products, firms set their quantities independently and simultaneously.

Strategic choices: Firms set quantities. So, the price adjusts as needed until the market clears. Profits are interdependent.

Firms use their residual demand curves: Market demand that is not met

by other sellers at any given price,

Figure 11.2, panel b, shows

the residual demand curve for American if

A firm maximizes profit with best responses that come from

In Figure 11.2, panel b, if American believes q U=64, then its best response is q A=64.

Nash-Cournot equilibrium: A set of quantities chosen by firms such that, holding the quantities of all other firms constant, no firm can obtain a higher profit by choosing a different quantity.

The quantity of equilibrium must be on the best-response curve for all firms.

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11

Figure 11.2 American Airlines’ Profit-Maximizing Output

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11.2 Cournot Oligopoly (2 of 8)

Airlines

American and United Airlines compete for customers on flights between Chicago and Los Angeles (duopoly). Q = q A + q U

A Graphical Approach

The strategies for American and United depend on their residual demand curves and marginal costs.

Residual Demands: If American thinks United flies q U passengers, American’s

residual demand is

(Figure 11.2, panel b). Alternatively, United’s

residual demand is

Best Responses: To maximize profit, American sets

and finds its best-response

curve for all possible q U. Figure 11.3 shows that if q U = 64, American’s best response is q A = 64, shuts down if q U = 192, and so on. It also shows United’s best-response curve.

Nash-Cournot Equilibrium: There is only one pair of outputs where both firms are on their best-response curves, q A = q U = 64. At this intersection, both firms maximize profits, are on their best-response curves, and don’t want to change their outputs.

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Figure 11.3 Best-Response Curves for American and United Airlines

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11.2 Cournot Oligopoly (3 of 8)

An Algebraic Approach

Residual Demand, M R and M C

The market demand function is Q = 339 − p. The residual demand function for American is q A = (339 − p) − q U or p = 339 − q A − q U.

American’s marginal revenue function is

Both airlines have M C = A C = $147 per passenger per flight.

M R = M C and Best Responses

American’s best-response: q A = 96 − 0.5 q U

Similarly, United’s best response: q U = 96 − 0.5 q A

Nash-Cournot Equilibrium

Solving the two best responses by substitution, q A = 96 − 0.5 (96 − 0.5 q A)

The Nash-Cournot equilibrium values: q A = q U = 64, Q = q A + q U = 128, p=$211

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11.2 Cournot Oligopoly (4 of 8)

Airlines Cournot Model Using Calculus

Inverse residual Demand, M R and M C

The market demand function is Q = 339 − p.

The residual demand function for American is q A = (339 − p) − q U.

Inverse residual demand is p = 339 − q A − q U.

American’s revenue function:

American’s marginal revenue function:

United’s revenue function:

United’s marginal revenue function:

Best Responses and Nash-Cournot Equilibrium

Same steps and calculations as presented in the algebraic approach

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11.2 Cournot Oligopoly (5 of 8)

The Number of Firms

If two Cournot firms set output independently, the price to consumers is lower than the monopoly price. If there are more than two, the price is even lower.

Table 11.1 illustrates how each firm’s output, q, the market quantity, Q, and the price vary with the number of firms in our airlines example.

If n = 1, Q = 69, p = $243, a monopoly outcome.

If n = 2, Q = 128, p = $211, a duopoly outcome as we found earlier.

If n is very large, Q = 192 and p = $147 = M C.

With 100 firms, the price is only 1.3% above the competitive price and output is only 1.1% below the competitive quantity.

The Nash-Cournot equilibrium approaches the competitive outcome.

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Table 11.1 Nash Cournot Equilibrium Varies with the Number of Firms

Number of Firms, nFirm Output, qMarket Output, QPrice, pFirm Profit, π ($ thousands)
1 (monopoly)96962439,216
2 (duopoly)641282114,096
3481441952,304
4381541851,475
5321601791,024
1018175164305
50418815114
100 (nearly competitive)21901494

Note: The numbers in this table are rounded.

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11.2 Cournot Oligopoly (6 of 8)

Nonidentical Firms

Oligopoly firms can have different costs and differentiate their products.

Unequal Costs

In the Cournot model, a firm’s best-response function comes from M R = M C. If M C rises or falls, then the firm’s best-response function shifts.

Consider the airline example, products are identical, so American and United charge the same price. United’s M C drops from $147 to $99, so in Figure 11.4, panel a, the new q U = 88 rather than 64.

United’s best-response function shifts to the right in panel b of Figure 11.4. United wants to produce more than before for any given level of American’s output.

There is no change for American’s best-response function.

In panel b of Figure 11.4, the Nash-Cournot equilibrium shifts from e1 to e2, at which United sells 96 and American sells 48.

United’s profit increases from $4.1 million to $9.2 million, while American’s profit falls to $2.3 million. Consumers also win because p falls from $211 to $195.

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Figure 11.4 Effect of a Drop in One Firm’s Marginal Cost on a Nash-Cournot Equilibrium

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11.2 Cournot Oligopoly (7 of 8)

Differentiated Products

By differentiating its product from those of a rival, an oligopolistic firm can shift its demand curve to the right and make it less elastic.

The less elastic the demand curve, the more the firm can charge because consumers are willing to pay more for a product that “seems” superior.

Although differentiation leads to higher prices, which harm consumers, differentiation is desirable in its own right.

Consumers value having a choice, and some may greatly prefer a new brand to existing ones.

If consumers think products differ, the Cournot quantities and prices may differ across firms.

Each firm faces a different inverse demand function and hence charges a different price.

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11.2 Cournot Oligopoly (8 of 8)

Mergers

Two or more firms combine their assets and operations into one firm with the objective to increase profits.

Firms typically merge to reduce costs or to increase market power.

A merger may provide cost advantages by allowing the new firm to realize increased economies of scale (Chapter 6).

A merger may produce economies of scope (Chapter 6).

A vertical merge between a firm and a supplier may lower cost by allowing for a more efficient supply chain.

Horizontal mergers may increase market power and reduce competition.

If such mergers increase market power, raising prices harms consumers and reduces total welfare.

Most countries have antitrust or competition laws that subject mergers and acquisitions to legal scrutiny (Chapter 16).

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11.3 Bertrand Oligopoly (1 of 6)

The Bertrand Model

Model rationality

Bertrand oligopoly firms set prices and then consumers decide how many units to buy.

Logic of best responses

In a duopoly setting, Firm 1’s best-response curve comes from answering “What is Firm 1’s best response—what price should it set—if Firm 2 sets a price of p2 = x?” for all possible values of x.

Similarly, Firm 2’s best-response curve: “What is Firm 2’s best response (p2) if Firm 1 sets a price of p1 = y?” for all possible values of y.

Nash-Bertrand equilibrium

The Nash-Bertrand equilibrium is a set of prices such that no firm can obtain a higher profit by choosing a different price if the other firms continue to charge these prices.

The Nash-Bertrand equilibrium differs from the Nash-Cournot equilibrium; it depends on whether firms produce identical or differentiated products.

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11.3 Bertrand Oligopoly (2 of 6)

Identical Products

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11.3 Bertrand Oligopoly (3 of 6)

Identical Products

Let us focus in a price-setting oligopoly where firms have identical costs and produce identical products.

Best-Response Curves and Nash-Bertrand Equilibrium

Two firms with identical costs and identical products, M C = A C = $5.

In Figure 11.5, Firm 1’s best-response curve starts at $5 and then lies slightly above the 45° line. That is, Firm 1 undercuts its rival’s price as long as its price remains above $5.

Firm 2’s best-response curve also starts at $5 and undercuts its rival’s price if p2 > 5.

Nash-Bertrand Equilibrium at intersection point e, p2 = p1 = $5 = M C.

The Nash-Bertrand equilibrium when firms produce identical products is the same equilibrium as perfect competition equilibrium.

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Figure 11.5 Nash-Bertrand Equilibrium with Identical Products

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11.3 Bertrand Oligopoly (4 of 6)

Bertrand versus Cournot with Identical Products

The Nash-Bertrand equilibrium differs substantially from the Nash-Cournot equilibrium. Zero profits (p = M C) versus positive profits (p > M C).

The Cournot model seems more realistic than the Bertrand model in two ways:

Bertrand’s “Competitive” Equilibrium is Implausible.

In a market with few firms, why would the firms compete so vigorously that they would make no profit?

Oligopolies typically charge a higher price than competitive firms. So, the Nash-Cournot equilibrium is more plausible.

Bertrand’s Equilibrium Price is insensitive to demand conditions and the number of firms. It depends only on costs.

The Nash-Cournot equilibrium price is sensitive to demand conditions and the number of firms as well as on cost. So, it is better to study homogeneous goods markets.

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11.3 Bertrand Oligopoly (5 of 6)

Differentiated Products

Two firms, identical costs M C = A C = $5 and differentiated products

Best-Response Curves and Nash-Bertrand Equilibrium

In Figure 11.6, neither firm’s best-response curve lies along a 45° line through the origin because Coke and Pepsi are similar but some consumers prefer one to the other independently of the price. So neither firm has to exactly match a price cut by its rival.

Nash-Bertrand Equilibrium at intersection point e, p2 = p1 = $13 > M C. Each firm sets its best-response price given the price the other firm is charging. Neither firm wants to change its price.

This equilibrium is plausible: Firms set p > M C, and prices are sensitive to demand conditions and number of firms.

Bertrand firms may earn positive profits in equilibrium if they differentiate their products.

Product differentiation is costly. But, if the alternative is zero profit in a Bertrand homogenous-good equilibrium, it is worth the cost.

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Figure 11.6 Nash-Bertrand Equilibrium with Differentiated Products

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11.3 Bertrand Oligopoly (6 of 6)

Managerial Implication: Differentiating a Product Through Marketing

A manager can often increase a firm’s profit by differentiating its product so that it can charge a higher price.

It is easier and less expensive to differentiate a product using marketing rather than by physically differentiating the product. For instance, Coca-Cola and Pepsico differentiate their uncarbonated, unflavor water with marketing.

Both, Pepsico’s top-selling bottled water, Aquafina, and Coke’s Dasani have logos from which consumers may infer the water comes from natural springs. However, both are basically bottled public water.

In a recent blind taste test reported in Slate, no one could distinguish between Aquafina and Dasani, and both are equally clean and safe. However, many consumers, responding to perceived differences created by marketing, strongly prefer one or the other of these brands and pay a premium for these products.

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11.4 Monopolistic Competition (1 of 4)

The monopolistic competition market structure has the price-setting characteristics of monopoly or oligopoly and the free entry of perfect competition.

These firms face downward sloping demand curves and have oligopoly market power.

But, they earn zero profit due to free entry.

First Reason for Downward-Sloping Demand

Market demand may be limited so there is room for only few firms. The residual demand curve facing a single firm is downward sloping.

For example in a small town, the market may be large enough to support only a few plumbing firms, each provides a similar service.

Second Reason for Downward-Sloping Demand

Firms differentiate their products. So each firm can retain those customers who particularly like that firm’s product even if its price is higher than those of rivals.

For example, gourmet food trucks serve differentiated food in monopolistically competitive markets.

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11.4 Monopolistic Competition (2 of 4)

Managerial Implication: Managing in the Monopolistically Competitive Food Truck Market

Young entrepreneurs should consider monopolistically competitive markets, as entry costs are often low and a cleverly differentiated product can often succeed.

One of the hottest food phenomena in the United States is gourmet food trucks.

The cost of entry is very low, from $50k to lease the equipment and pay ancillary expenses, to $250k or more for a deluxe truck.

Potential entrants can go to mobilefoodnews.com to learn about local laws, where to buy equipment and obtain insurance.

Managers could use internet sites and social media to attract customers to their locations. Fans can find the location of trucks in cities around the country at Mobimunch.com.

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11.4 Monopolistic Competition (3 of 4)

Equilibrium

Firms have identical cost functions and produce identical products.

In Figure 11.7, a monopolistically competitive firm, facing the firm-specific demand curve D, sets its output where M R = M C.

At that quantity, the firm’s average cost curve, A C, is tangent to its demand curve, p = A C.

At the equilibrium, the monopolistically competitive firm makes zero profit. The entry and exit responses of firms ensure this.

In most cities, fast-food restaurants are an example of a monopolistically competitive industry.

These restaurants differentiate their food, so each may face a downward-sloping demand curve. However, restaurants can easily enter and exit the market, so the marginal firm earns zero economic profit.

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Figure 11.7 Monopolistic Competition

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11.4 Monopolistic Competition (4 of 4)

Profitable Monopolistically Competitive Firms

Identical Costs and Products, Zero Profit

If all firms in a monopolistically competitive market produce identical products and have identical costs, each firm earns zero economic profit in the long run.

Thus, all firms in the industry are on the margin of exiting the market because even a slight decline in profitability would generate losses.

Differentiated Costs and Products, Positive Profit

If those firms have different cost functions or produce differentiated products: most likely firms differ from each other in their profitability.

If so, low-cost firms or firms with superior products may earn positive economic profits in the long run.

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Managerial Solution

Gaining an Edge from Government Aircraft Subsidies

If only one firm receives a subsidy, how can it gain competitive advantage? What is the subsidy’s effect on p and q? What happens if both governments subsidize their firms? Is a subsidy war good for both firms?

Solution

Assume Airbus and Boeing compete in a Cournot model, produce identical products with identical costs and face a linear demand curve.

A government per-unit subsidy to one firm would make its M C lower than its rival’s and its best-response curve shifts out.

If only Airbus is subsidized, Airbus should produce more given any expected q from Boeing. Airbus’ q and π rise while Boeing’s q and π fall.

If both governments give identical subsidies, both firms produce more, total Q increases, p falls (both move to competitive equilibrium) and both π fall. Each government is subsidizing final consumers in other countries without giving its own firm a competitive advantage. A subsidy war is not in these countries’ best interests.

These firms should not stop lobbying for subsidies to avoid being at a competitive disadvantage if its rival received a subsidy and it did not.

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Copyright

This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved

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MRMC

=

3392.

r

AU

MRqq

=–

, so 3392147

r

AU

MRMCqq

=–=

2

()

339 339

AAAUAAAUA

Rpqqqqqqqq

==–=–

/3392

r

AAAU

MRdRdqqq

==–

2

339

UUUUA

Rqqqq

=–

/3392

r

UUUA

MRdRdqqq

==–

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Perloff_mes3_PPT_1

2.pptx