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**Chapter 10 Game Theory and Strategic Behavior**

Managerial Economics in a Global Economy, 5th Edition by Dominick Salvatore Chapter 10 Game Theory and Strategic Behavior

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Strategic Behavior Decisions that take into account the predicted reactions of rival firms Interdependence of outcomes Game Theory Players Strategies Payoff matrix

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**Strategic Behavior Types of Games Zero-sum games Nonzero-sum games**

Nash Equilibrium Each player chooses a strategy that is optimal given the strategy of the other player A strategy is dominant if it is optimal regardless of what the other player does

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Advertising Example 1

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Advertising Example 1 What is the optimal strategy for Firm A if Firm B chooses to advertise?

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Advertising Example 1 What is the optimal strategy for Firm A if Firm B chooses to advertise? If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

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Advertising Example 1 What is the optimal strategy for Firm A if Firm B chooses not to advertise?

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Advertising Example 1 What is the optimal strategy for Firm A if Firm B chooses not to advertise? If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 3. Again, the optimal strategy is to advertise.

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Advertising Example 1 Regardless of what Firm B decides to do, the optimal strategy for Firm A is to advertise. The dominant strategy for Firm A is to advertise.

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Advertising Example 1 What is the optimal strategy for Firm B if Firm A chooses to advertise?

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Advertising Example 1 What is the optimal strategy for Firm B if Firm A chooses to advertise? If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

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Advertising Example 1 What is the optimal strategy for Firm B if Firm A chooses not to advertise?

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Advertising Example 1 What is the optimal strategy for Firm B if Firm A chooses not to advertise? If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

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Advertising Example 1 Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

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Advertising Example 1 The dominant strategy for Firm A is to advertise and the dominant strategy for Firm B is to advertise. The Nash equilibrium is for both firms to advertise.

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Advertising Example 2

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Advertising Example 2 What is the optimal strategy for Firm A if Firm B chooses to advertise?

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Advertising Example 2 What is the optimal strategy for Firm A if Firm B chooses to advertise? If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

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Advertising Example 2 What is the optimal strategy for Firm A if Firm B chooses not to advertise?

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Advertising Example 2 What is the optimal strategy for Firm A if Firm B chooses not to advertise? If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 6. In this case, the optimal strategy is not to advertise.

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Advertising Example 2 The optimal strategy for Firm A depends on which strategy is chosen by Firms B. Firm A does not have a dominant strategy.

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Advertising Example 2 What is the optimal strategy for Firm B if Firm A chooses to advertise?

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Advertising Example 2 What is the optimal strategy for Firm B if Firm A chooses to advertise? If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

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Advertising Example 2 What is the optimal strategy for Firm B if Firm A chooses not to advertise?

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Advertising Example 2 What is the optimal strategy for Firm B if Firm A chooses not to advertise? If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

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Advertising Example 2 Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

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Advertising Example 2 The dominant strategy for Firm B is to advertise. If Firm B chooses to advertise, then the optimal strategy for Firm A is to advertise. The Nash equilibrium is for both firms to advertise.

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**A Normal Form Game Player 2 12,11 11,12 14,13 Player 1 11,10 10,11**

12,12 10,15 10,13 13,14

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**Putting Yourself in your Rival’s Shoes**

What should player 2 do? 2 has no dominant strategy! But 2 should reason that 1 will play “a”. Therefore 2 should choose “C”. Player 2 12,11 11,12 14,13 Player 1 11,10 10,11 12,12 10,15 10,13 13,14

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**The Outcome This outcome is called a Nash equilibrium:**

Player 2 12,11 11,12 14,13 11,10 10,11 12,12 10,15 10,13 13,14 Player 1 This outcome is called a Nash equilibrium: “a” is player 1’s best response to “C”. “C” is player 2’s best response to “a”.

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**The Market-Share Game in Normal Form**

Manager 2 Manager 1

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**No Equilibrium - Child’s play**

Player 2 Player 1

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**Multiple Equilibria - Battle of the Sexes**

Him Her

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Prisoners’ Dilemma Two suspects are arrested for armed robbery. They are immediately separated. If convicted, they will get a term of 10 years in prison. However, the evidence is not sufficient to convict them of more than the crime of possessing stolen goods, which carries a sentence of only 1 year. The suspects are told the following: If you confess and your accomplice does not, you will go free. If you do not confess and your accomplice does, you will get 10 years in prison. If you both confess, you will both get 5 years in prison.

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**Payoff Matrix (negative values)**

Prisoners’ Dilemma Payoff Matrix (negative values)

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**Dominant Strategy Both Individuals Confess**

Prisoners’ Dilemma Dominant Strategy Both Individuals Confess (Nash Equilibrium)

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**Normal Form Game (Simultaneous Movers - Prisoner’s Dilemma)**

Environment - Police station after a crime wave. Police have evidence on a minor crime. Police have insufficient evidence on major crime Players - Bonnie and Clyde Rules - no escape is possible Strategies - Rat or not rat Payoffs - No one rats: both get 3 years One rats and the other stays quiet: rat gets 1 year, Silent partner gets 23 years Both rat: both get 16 years

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**The Normal Form of Prisoner’s Dilemma**

Bonnie 16,16 1, 23 Clyde 23,1 3,3

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**Resolving Bonnie & Clyde**

If Bonnie Rats and Clyde doesn’t rat, then Bonnie gets 1 year Clyde rats, then Bonnie gets 16 years If Bonnie doesn’t Rat and Clyde doesn’t rat, then Bonnie gets 3 years Clyde rats, then Bonnie gets 23 years If Clyde Rats and Bonnie doesn’t rat, then Clyde gets 1 year Bonnie rats, then Clyde gets 16 years If Clyde doesn’t Rat and Bonnie doesn’t rat, then Clyde gets 3 years Bonnie rats, then Clyde gets 23 years

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**Resolving Bonnie & Clyde**

Bonnie has a dominant strategy - Rat Clyde has a dominant strategy - Rat Nash Equilibrium - set of strategies that are “best responses” to each other Nash here is: {Rat; Rat} Payoffs here are: {16 years; 16 years} Best outcome is {Don’t Rat; Don’t Rat} with payoffs of {3 yrs; 3 years} How do we get cooperation? Suppose each promised the other not to rat?

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**Application: Price Competition**

Prisoners’ Dilemma Application: Price Competition

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**Application: Price Competition Dominant Strategy: Low Price**

Prisoners’ Dilemma Application: Price Competition Dominant Strategy: Low Price

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**Application: Nonprice Competition**

Prisoners’ Dilemma Application: Nonprice Competition

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**Application: Nonprice Competition Dominant Strategy: Advertise**

Prisoners’ Dilemma Application: Nonprice Competition Dominant Strategy: Advertise

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**Application: Cartel Cheating**

Prisoners’ Dilemma Application: Cartel Cheating

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**Application: Cartel Cheating Dominant Strategy: Cheat**

Prisoners’ Dilemma Application: Cartel Cheating Dominant Strategy: Cheat

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**Extensions of Game Theory**

Repeated Games Many consecutive moves and countermoves by each player Tit-For-Tat Strategy Do to your opponent what your opponent has just done to you

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**Extensions of Game Theory**

Tit-For-Tat Strategy Stable set of players Small number of players Easy detection of cheating Stable demand and cost conditions Game repeated a large and uncertain number of times

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**Extensions of Game Theory**

Threat Strategies Credibility Reputation Commitment Example: Entry deterrence

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**Entry Deterrence No Credible Entry Deterrence**

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**Entry Deterrence No Credible Entry Deterrence**

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**International Competition**

Boeing Versus Airbus Industrie

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**Sequential Games Sequence of moves by rivals**

Payoffs depend on entire sequence Decision trees Decision nodes Branches (alternatives) Solution by reverse induction From final decision to first decision

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**High-price, Low-price Strategy Game**

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**High-price, Low-price Strategy Game**

X X

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**High-price, Low-price Strategy Game**

X Solution: Both firms choose low price. X X

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Airbus and Boeing

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Airbus and Boeing X X

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**X X X Airbus and Boeing Solution:**

Airbus builds A380 and Boeing builds Sonic Cruiser. X X

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**Integrating Case Study**

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A Game-Theoretic Approach to Strategic Behavior. Chapter Outline ©2015 McGraw-Hill Education. All Rights Reserved. 2 The Prisoner’s Dilemma: An Introduction.

A Game-Theoretic Approach to Strategic Behavior. Chapter Outline ©2015 McGraw-Hill Education. All Rights Reserved. 2 The Prisoner’s Dilemma: An Introduction.

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