1 1 ba 210 lesson iii.5 strategic uncertainty when interests conflictoverviewoverview

1 1BA 210 Lesson III.5 Strategic Uncertainty when Interests ConflictBA 210 Lesson III.5 Strategic Uncertainty when Interests Conflict

OverviewOverview

OverviewOverview

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Game Theory Game Theory in Part III completes Game Theory in Part II for in Part III completes Game Theory in Part II for those games where information is strategically revealed or those games where information is strategically revealed or withheld. withheld.

In many games, a player may not know all the information that is In many games, a player may not know all the information that is pertinent for the choice that he has to make at every point in the pertinent for the choice that he has to make at every point in the game. His uncertainty may be over variables that are either game. His uncertainty may be over variables that are either internal or external to the game.internal or external to the game.

BA 210 Lesson III.5 Strategic Uncertainty when Interests ConflictBA 210 Lesson III.5 Strategic Uncertainty when Interests Conflict

OverviewOverview

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A player may be potentially uncertain A player may be potentially uncertain about what moves the about what moves the other player is making at the same time he makes his own move; other player is making at the same time he makes his own move; we call that strategic uncertainty. All the simultaneous move we call that strategic uncertainty. All the simultaneous move games in Part II were simple enough that that uncertainty was games in Part II were simple enough that that uncertainty was resolved by eliminating dominated strategies. resolved by eliminating dominated strategies.

Part III’s Lesson 5 considers games where strategic uncertainty Part III’s Lesson 5 considers games where strategic uncertainty remains because uncertainty is not resolved by eliminating remains because uncertainty is not resolved by eliminating dominated strategies, and because players’ interests conflict (as in dominated strategies, and because players’ interests conflict (as in sports) so players conceal information about their own moves. sports) so players conceal information about their own moves. Lesson 6 considers games where players easily reveal Lesson 6 considers games where players easily reveal information about their own moves because players’ interests information about their own moves because players’ interests align (as in setting a standard industry format).align (as in setting a standard industry format).

BA 210 Lesson III.5 Strategic Uncertainty when Interests ConflictBA 210 Lesson III.5 Strategic Uncertainty when Interests Conflict

OverviewOverview

4 4BA 210 Lesson III.5 Strategic Uncertainty when Interests Conflict

Lesson III.5 Strategic Uncertainty when Interests ConflictLesson III.5 Strategic Uncertainty when Interests ConflictExample 1: Example 1: Unpredictable ActionsUnpredictable ActionsExample 2: Mixing with Perfect ConflictExample 2: Mixing with Perfect ConflictExample 3: Mixing with Major ConflictExample 3: Mixing with Major ConflictExample 4: Mixing with Minor ConflictExample 4: Mixing with Minor ConflictSummarySummaryReview QuestionsReview Questions

Lesson OverviewLesson Overview


Example 1: Unpredictable ActionsExample 1: Unpredictable Actions



Comment: Comment: Bob Gustavson, professor of health science and men's Bob Gustavson, professor of health science and men's soccer coach at John Brown University in Siloam Springs, soccer coach at John Brown University in Siloam Springs, Arkansas, says “When you consider that a ball can be struck Arkansas, says “When you consider that a ball can be struck anywhere from 60-80 miles per hour, there's not a whole lot of anywhere from 60-80 miles per hour, there's not a whole lot of time for the goalkeeper to react”. Gustavson says skillful goalies time for the goalkeeper to react”. Gustavson says skillful goalies use cues from the kicker. They look at where the kicker's plant use cues from the kicker. They look at where the kicker's plant foot is pointing and the posture during the kick. Some even study foot is pointing and the posture during the kick. Some even study tapes of opponents. But most of all tapes of opponents. But most of all they take a guess — jump left they take a guess — jump left or right at the same time the kicker is committing himself to or right at the same time the kicker is committing himself to kicking left or rightkicking left or right..



Question: Question: Consider a penalty kick in soccer. The goalie either Consider a penalty kick in soccer. The goalie either jumps left or right after the kicker has committed himself to jumps left or right after the kicker has committed himself to kicking left or right. The kicker’s payoffs are the probability of kicking left or right. The kicker’s payoffs are the probability of him scoring, and the goalie’s payoffs are the probability of the him scoring, and the goalie’s payoffs are the probability of the kicker not scoring. Those actions and payoffs define a normal kicker not scoring. Those actions and payoffs define a normal form form for this for this Penalty Kick GamePenalty Kick Game. Try to predict strategies or . Try to predict strategies or recommend strategies.recommend strategies.

Left RightLeft .1,.9 .8,.2Right .4,.6 .3,.7

Goalie

Kicker




Goalie

Kicker

Answer: Answer: To predict actions or To predict actions or recommend actions, sincerecommend actions, sincethe game has simultaneousthe game has simultaneousmoves, first look for dominate moves, first look for dominate or dominated actions. There are none.or dominated actions. There are none.

Then look for a Then look for a Nash equilibrium. There is none. If the Kicker Nash equilibrium. There is none. If the Kicker were known to kick Left, the Goalie guards Left. But if the were known to kick Left, the Goalie guards Left. But if the Goalie were known to guard Left, the Kicker kicks Right. But if Goalie were known to guard Left, the Kicker kicks Right. But if the Kicker were known to kick Right, the Goalie guards Right. the Kicker were known to kick Right, the Goalie guards Right. But if the Goalie were known to guard Right, the Kicker kicks But if the Goalie were known to guard Right, the Kicker kicks Left. Left. So thereSo there is no Nash equilibrium. is no Nash equilibrium.



Finally, look to see if any Finally, look to see if any action can be eliminated becauseaction can be eliminated becauseit is not rationalizable (that is, itit is not rationalizable (that is, itis not a best response to someis not a best response to someaction by the other player. action by the other player.

But all actions are rationalizable. But all actions are rationalizable.

On the one hand, it is rational to On the one hand, it is rational to kick left kick left if the Kicker believes if the Kicker believes the Goalie jumps right. On the other hand, it is rational for the the Goalie jumps right. On the other hand, it is rational for the Kicker to Kicker to kick right kick right if he believes the Goalie jumps left.if he believes the Goalie jumps left.

Likewise, it is rational for the Goalie to Likewise, it is rational for the Goalie to jump left jump left if the Goalie if the Goalie believes the Kicker believes the Kicker kicks leftkicks left, and it is rational for the Goalie to , and it is rational for the Goalie to jump right jump right if the Goalie believes the Kicker if the Goalie believes the Kicker kicks rightkicks right..


Goalie

Kicker



Since there are no dominanceSince there are no dominancesolutions and there are nosolutions and there are noNash equilibria for this gameNash equilibria for this gameof simultaneous moves, of simultaneous moves, actions are unpredictable, and game theory has no actions are unpredictable, and game theory has no recommendation; either action is acceptable.recommendation; either action is acceptable.


Goalie

Kicker



Example 2: Mixing with Perfect ConflictExample 2: Mixing with Perfect Conflict

Example 2: Mixing with Perfect Example 2: Mixing with Perfect ConflictConflict


Comment: Example 1’s Comment: Example 1’s choices for the goalie were choices for the goalie were jump left or jump left or jump rightjump right. Call those actions because, in Example 2, . Call those actions because, in Example 2, strategiesstrategies are going to be more complicated; they will be probabilities for are going to be more complicated; they will be probabilities for taking specific actions --- say, jump left with probability 0.24 and taking specific actions --- say, jump left with probability 0.24 and jump right with probability 0.76jump right with probability 0.76



Question: Question: Consider the normal form below for the Consider the normal form below for the Penalty Kick Penalty Kick GameGame in soccer. P in soccer. Predict strategies or recommend strategies if redict strategies or recommend strategies if this game is repeated throughout the careers of the kicker and the this game is repeated throughout the careers of the kicker and the goalie.goalie.


Goalie

Kicker



Answer: Answer: If the game were notIf the game were notrepeated, repeated, then since there are no then since there are no dominance solutions and there dominance solutions and there are no Nash equilibria (in pureare no Nash equilibria (in purestrategies) for this game of simultaneous moves, strategies) for this game of simultaneous moves, actions are actions are unpredictable, and game theory has no recommendation; either unpredictable, and game theory has no recommendation; either action is acceptable. For example, the Kicker could kick Left and action is acceptable. For example, the Kicker could kick Left and the Goalie could jump Left.the Goalie could jump Left.


Goalie

Kicker



But since the game is repeated, But since the game is repeated, actions need to become actions need to become unpredictable because unpredictable because predictable actions can be predictable actions can be exploited. exploited.

For example, see how predicting actions helps the Goalie. If the For example, see how predicting actions helps the Goalie. If the Kicker chooses Left predictably, the Goalie can choose Left and Kicker chooses Left predictably, the Goalie can choose Left and keep the Kicker at payoff .1 and the Goalie at .9; and if the keep the Kicker at payoff .1 and the Goalie at .9; and if the Kicker chooses Right predictably, the Goalie can choose Right Kicker chooses Right predictably, the Goalie can choose Right and keep the Kicker at payoff .3 and the Goalie at .7. and keep the Kicker at payoff .3 and the Goalie at .7.


Goalie

Kicker


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Goalie

Kicker

BA 210 Lesson III.5 Strategic Uncertainty when Interests Conflict

The Nash equilibrium strategy for the Kicker The Nash equilibrium strategy for the Kicker is the mixed is the mixed strategy for which the Goalie would not benefit if he could strategy for which the Goalie would not benefit if he could predict the Kicker’s mixed strategy. Suppose the Goalie predicts predict the Kicker’s mixed strategy. Suppose the Goalie predicts p and (1-p) are the probabilities the Kicker chooses Left or Right. p and (1-p) are the probabilities the Kicker chooses Left or Right. The Goalie expects .9p + .6(1-p) from playing Left, and .2p The Goalie expects .9p + .6(1-p) from playing Left, and .2p + .7(1-p) from Right. The Goalie does not benefit if those payoffs + .7(1-p) from Right. The Goalie does not benefit if those payoffs equal, .9p + .6(1-p) = .2p + .7(1-p), or .6 + .3p = .7 - .5p, or equal, .9p + .6(1-p) = .2p + .7(1-p), or .6 + .3p = .7 - .5p, or p = 1/8 = 0.125 p = 1/8 = 0.125


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Goalie

Kicker


The Nash equilibrium strategy for the Goalie The Nash equilibrium strategy for the Goalie is the mixed is the mixed strategy for which the Kicker would not benefit if he could strategy for which the Kicker would not benefit if he could predict the Goalie’s mixed strategy. Suppose the Kicker predicts predict the Goalie’s mixed strategy. Suppose the Kicker predicts q and (1-q) are the probabilities the Goalie chooses Left or Right. q and (1-q) are the probabilities the Goalie chooses Left or Right. The Kicker expects .1q + .8(1-q) from playing Left, and .4q The Kicker expects .1q + .8(1-q) from playing Left, and .4q + .3(1-q) from Right. The Kicker does not benefit if those payoffs + .3(1-q) from Right. The Kicker does not benefit if those payoffs equal, .1q + .8(1-q) = .4q + .3(1-q), or .8 - .7q = .3 + .1q, orequal, .1q + .8(1-q) = .4q + .3(1-q), or .8 - .7q = .3 + .1q, orq = 5/8 = 0.625 q = 5/8 = 0.625



Comment: Randomizing actions Comment: Randomizing actions adds strategies (called mixed adds strategies (called mixed strategies) that solve some games that have no dominance strategies) that solve some games that have no dominance solution or Nash Equilibrium (in pure strategies, where all solution or Nash Equilibrium (in pure strategies, where all probability is on one particular action). For example, probability is on one particular action). For example, in the in the Penalty Kick Game, there was Penalty Kick Game, there was no Nash equilibrium with pure no Nash equilibrium with pure strategiesstrategies, and there were , and there were multiple rationalizable pure strategies.multiple rationalizable pure strategies. It turns out that most games have at least one Nash equilibrium in It turns out that most games have at least one Nash equilibrium in mixed strategies. mixed strategies.

In fact, the Penalty Kick Game has a unique Nash equilibrium in In fact, the Penalty Kick Game has a unique Nash equilibrium in mixed strategies. While any of the rationalizable strategies mixed strategies. While any of the rationalizable strategies would be reasonable if the game were played once, if instead the would be reasonable if the game were played once, if instead the game were repeated, then strategies in the unique Nash game were repeated, then strategies in the unique Nash equilibrium are the only way to play that guarantees the other equilibrium are the only way to play that guarantees the other player cannot gain even if they used your history to correctly player cannot gain even if they used your history to correctly predict your strategy. predict your strategy.



Example 3: Mixing with Major ConflictExample 3: Mixing with Major Conflict

Example 3: Mixing with Major Example 3: Mixing with Major ConflictConflict


Comment: Comment: Employers are in conflict with (selfish, amoral) Employers are in conflict with (selfish, amoral) workers, who want to steal or shirk (not work, or steal time). workers, who want to steal or shirk (not work, or steal time). However, the However, the Work-Shirk Game Work-Shirk Game is not one of total conflict (it is is not one of total conflict (it is not like the Penalty Kick Game) because monitoring workers not like the Penalty Kick Game) because monitoring workers costs the employer but does not help the worker. costs the employer but does not help the worker.

Because of the conflict, the other player exploiting your Because of the conflict, the other player exploiting your systematic choice of strategy is to your disadvantage, and so systematic choice of strategy is to your disadvantage, and so there is reason to follow mixed strategies in such games. there is reason to follow mixed strategies in such games.



Question: Question: Consider the Consider the Work-Shirk GameWork-Shirk Game for an employee and for an employee and an employer. Suppose if the employee chooses to work, he an employer. Suppose if the employee chooses to work, he looses $100 of happiness from the effort of working, but he looses $100 of happiness from the effort of working, but he yields $400 to his employer. Suppose the employer can monitor yields $400 to his employer. Suppose the employer can monitor the employee at a cost of $80. Finally, if the employee chooses the employee at a cost of $80. Finally, if the employee chooses to not work and the employer chooses to monitor, then the to not work and the employer chooses to monitor, then the employee is not paid, but in every other case (“work” or “not employee is not paid, but in every other case (“work” or “not monitor”), then the employee is paid $150monitor”), then the employee is paid $150..

PPredict strategies or recommend strategies if this game is redict strategies or recommend strategies if this game is repeated daily.repeated daily.



Answer: Answer: First, complete the normal form below for the First, complete the normal form below for the Work-Work-Shirk GameShirk Game. For example, if the employee chooses to work and . For example, if the employee chooses to work and the employer chooses to monitor, then the employee looses $100 the employer chooses to monitor, then the employee looses $100 of happiness from the effort of working but is paid $150, and the of happiness from the effort of working but is paid $150, and the employer gain $400 from his employer but pays $80 for employer gain $400 from his employer but pays $80 for monitoring and pays $150 to his employee.monitoring and pays $150 to his employee.


Monitor TrustWork 50,170 50,250Shirk 0,-80 150,-150

Employer

Employee


To predict actions or To predict actions or recommend actions, sincerecommend actions, sincethe game has simultaneousthe game has simultaneousmoves, first look for dominate moves, first look for dominate or dominated actions. There are none.or dominated actions. There are none.

Then look for a Then look for a Nash equilibrium in pure strategies. There is Nash equilibrium in pure strategies. There is none. If the Employee were known to Work, the Employer none. If the Employee were known to Work, the Employer Trusts. But if the Employer were known to Trust, the Employee Trusts. But if the Employer were known to Trust, the Employee Shirks. But if the Employee were known to Shirk, the Employer Shirks. But if the Employee were known to Shirk, the Employer Monitors. But if the Employer were known to Monitor, the Monitors. But if the Employer were known to Monitor, the Employee Works. Employee Works. So thereSo there is no Nash equilibrium. is no Nash equilibrium.



Employer

Employee


Since the game is repeated, Since the game is repeated, actions need to become actions need to become unpredictable because unpredictable because predictable actions can be predictable actions can be exploited. exploited.

The Nash equilibrium strategy for the Employee The Nash equilibrium strategy for the Employee is the mixed is the mixed strategy for which the Employer would not benefit if he could strategy for which the Employer would not benefit if he could predict the Employee’s mixed strategy. Suppose the Employer predict the Employee’s mixed strategy. Suppose the Employer predicts p and (1-p) are the probabilities the Employee chooses predicts p and (1-p) are the probabilities the Employee chooses Work or Shirk. The Employer expects 170p - 80(1-p) from Work or Shirk. The Employer expects 170p - 80(1-p) from playing Monitor, and 250p - 150(1-p) from Trust. The Employer playing Monitor, and 250p - 150(1-p) from Trust. The Employer does not benefit if those payoffs equal, does not benefit if those payoffs equal, 170p - 80(1-p) = 250p - 150(1-p), or -80 + 250p = -150 + 400p,170p - 80(1-p) = 250p - 150(1-p), or -80 + 250p = -150 + 400p,or p = 70/150 = 0.467or p = 70/150 = 0.467



Employer

Employee


The Nash equilibrium strategy for the Employer The Nash equilibrium strategy for the Employer is the mixed is the mixed strategy for which the Employee would not benefit if he could strategy for which the Employee would not benefit if he could predict the Employer’s mixed strategy. Suppose the Employee predict the Employer’s mixed strategy. Suppose the Employee predicts q and (1-q) are the probabilities the Employer chooses predicts q and (1-q) are the probabilities the Employer chooses Monitor or Trust. The Employee expects 50q + 50(1-q) from Monitor or Trust. The Employee expects 50q + 50(1-q) from playing Work, and 0q + 150(1-q) from Shirk. The Employee does playing Work, and 0q + 150(1-q) from Shirk. The Employee does not benefit if those payoffs equal, not benefit if those payoffs equal, 50q + 50(1-q) = 0q + 150(1-q), or 50 = 150 – 150q,50q + 50(1-q) = 0q + 150(1-q), or 50 = 150 – 150q,or q = 100/150 = 0.667or q = 100/150 = 0.667



Employer

Employee


Example 4: Mixing with Minor ConflictExample 4: Mixing with Minor Conflict

Example 4: Mixing with Minor Example 4: Mixing with Minor ConflictConflict


Comment 1: Comment 1: Blu-ray Disc is designed to supersede the standard Blu-ray Disc is designed to supersede the standard DVD format. The disc has the same physical dimensions as DVD format. The disc has the same physical dimensions as standard DVDs and CDs. The name Blu-ray Disc derives from standard DVDs and CDs. The name Blu-ray Disc derives from the blue-violet laser used to read the disc. Blu-ray Disc was the blue-violet laser used to read the disc. Blu-ray Disc was developed by the Blu-ray Disc Association, a group representing developed by the Blu-ray Disc Association, a group representing makers of consumer electronics, computer hardware, and motion makers of consumer electronics, computer hardware, and motion pictures. pictures.

During the format war over high-definition optical discs, Blu-ray During the format war over high-definition optical discs, Blu-ray competed with the HD DVD format. Toshiba, the main company competed with the HD DVD format. Toshiba, the main company supporting HD DVD, conceded in February 2008, and the format supporting HD DVD, conceded in February 2008, and the format war ended.war ended. In late 2009, Toshiba released its own Blu-ray Disc In late 2009, Toshiba released its own Blu-ray Disc player.player.



Comment 2: Comment 2: The format war over high-definition optical discs The format war over high-definition optical discs has The Blu-ray Disc Association in some conflict with Toshiba has The Blu-ray Disc Association in some conflict with Toshiba since each group has gained expertise and lower costs in since each group has gained expertise and lower costs in producing a particular format and, so, each would gain if their producing a particular format and, so, each would gain if their format were universally adopted. However, the Format War format were universally adopted. However, the Format War game is not one of total conflict (it is not like the Penalty Kick game is not one of total conflict (it is not like the Penalty Kick Game) or even of major conflict (like the Work-Shirk Game) Game) or even of major conflict (like the Work-Shirk Game) because both players loose most if neither format is universally because both players loose most if neither format is universally adopted. adopted.

Because conflict is less important than cooperation, the other Because conflict is less important than cooperation, the other player exploiting your systematic choice of strategy is to your player exploiting your systematic choice of strategy is to your advantage because you both want a universal format. So there is advantage because you both want a universal format. So there is less reason to follow mixed strategies in such games. less reason to follow mixed strategies in such games.



Question: Question: Consider the Consider the Format GameFormat Game for The Blu-ray Disc for The Blu-ray Disc Association and Toshiba. Suppose each player either adopts the Association and Toshiba. Suppose each player either adopts the Blu-ray format or the HD format. Suppose if both adopt the Blu-ray format or the HD format. Suppose if both adopt the same format, then both gain $100 million from customers that same format, then both gain $100 million from customers that value the convenience of having a universal format. Suppose if value the convenience of having a universal format. Suppose if they both adopt the Blu-ray format, then The Blu-ray Disc they both adopt the Blu-ray format, then The Blu-ray Disc Association gains an extra $10 million since their expertise with Association gains an extra $10 million since their expertise with that format gives them lower production costs. Finally, suppose if that format gives them lower production costs. Finally, suppose if they both adopt the HD format, then Toshiba gains an extra $10 they both adopt the HD format, then Toshiba gains an extra $10 million since their expertise with that format gives them lower million since their expertise with that format gives them lower production costs. production costs.

PPredict strategies or recommend strategies if this game is redict strategies or recommend strategies if this game is repeated yearly.repeated yearly.



Answer: Answer: First, complete the normal form below for the First, complete the normal form below for the Format Format GameGame. For example, if The Blu-ray Disc Association and . For example, if The Blu-ray Disc Association and Toshiba both adopt HD, then both gain $100 million from Toshiba both adopt HD, then both gain $100 million from customers that value the convenience of having a universal customers that value the convenience of having a universal format, and Toshiba gains an extra $10 million since their format, and Toshiba gains an extra $10 million since their expertise with the HD format gives them lower production costs. expertise with the HD format gives them lower production costs.

Blu-ray HDBlu-ray 110,100 0,0HD 0,0 100,110

Toshiba

Blu-ray



To predict actions or To predict actions or recommend actions, sincerecommend actions, sincethe game has simultaneousthe game has simultaneousmoves, first look for dominate moves, first look for dominate or dominated actions. There are none.or dominated actions. There are none.

Then look for a Then look for a Nash equilibrium in pure strategies. There are Nash equilibrium in pure strategies. There are two. On the one hand, both players choose Blu-ray; on the other two. On the one hand, both players choose Blu-ray; on the other than, both players choose HD.than, both players choose HD.

There is also a Nash equilibrium in mixed strategies.There is also a Nash equilibrium in mixed strategies.



Toshiba

Blu-ray


The Nash equilibrium mixed The Nash equilibrium mixed strategy for Blu-ray Association strategy for Blu-ray Association is the mixed strategy for which is the mixed strategy for which Toshiba would not benefit if Toshiba would not benefit if they could predict Blu-ray Association’s mixed strategy. Suppose they could predict Blu-ray Association’s mixed strategy. Suppose Toshiba predicts p and (1-p) are the probabilities Blu-ray Toshiba predicts p and (1-p) are the probabilities Blu-ray Association chooses Blu-ray or HD. Toshiba expects 100p + 0(1-Association chooses Blu-ray or HD. Toshiba expects 100p + 0(1-p) from playing Blu-ray, and 0p + 110(1-p) from HD. Toshiba p) from playing Blu-ray, and 0p + 110(1-p) from HD. Toshiba does not benefit if those payoffs equal, does not benefit if those payoffs equal, 100p + 0(1-p) = 0p + 110(1-p), or 100p = 110 - 110p,100p + 0(1-p) = 0p + 110(1-p), or 100p = 110 - 110p,or p = 110/210 = 0.524or p = 110/210 = 0.524

The expected payoff for Toshiba (whatever its strategy) is thusThe expected payoff for Toshiba (whatever its strategy) is thus100p + 0(1-p) = 0p + 110(1-p) = 52.4100p + 0(1-p) = 0p + 110(1-p) = 52.4



Toshiba

Blu-ray


The Nash equilibrium mixed The Nash equilibrium mixed strategy for Toshiba strategy for Toshiba is the mixed is the mixed strategy for which Blu-ray strategy for which Blu-ray Association would not benefit if Association would not benefit if they could predict Toshiba’s mixed strategy. Suppose Blu-ray they could predict Toshiba’s mixed strategy. Suppose Blu-ray Association predicts q and (1-q) are the probabilities Toshiba Association predicts q and (1-q) are the probabilities Toshiba chooses Blu-ray or HD. Blu-ray Association expects 110q + 0(1-chooses Blu-ray or HD. Blu-ray Association expects 110q + 0(1-q) from playing Blu-ray, and 0q + 100(1-q) from HD. Blu-ray q) from playing Blu-ray, and 0q + 100(1-q) from HD. Blu-ray Association does not benefit if those payoffs equal, Association does not benefit if those payoffs equal, 110q + 0(1-q) = 0q + 100(1-q), or 110q = 100 – 100q,110q + 0(1-q) = 0q + 100(1-q), or 110q = 100 – 100q,or q = 100/210 = 0.476or q = 100/210 = 0.476

The expected payoff for The expected payoff for Blu-ray AssociationBlu-ray Association (whatever its (whatever its strategy) is thus strategy) is thus 110q + 0(1-q) = 0q + 100(1-q) = 52.4110q + 0(1-q) = 0q + 100(1-q) = 52.4



Toshiba

Blu-ray


Comment: Comment: The The expected payoffexpected payoffof of 52.4 f52.4 for each player in the or each player in the mixed strategy Nash equilibriummixed strategy Nash equilibriumis less than if both players hadis less than if both players hadagreed to one format or the other. That is a general lesson in agreed to one format or the other. That is a general lesson in games with only minor conflict of interest. The players are better games with only minor conflict of interest. The players are better off resolving the strategic uncertainty. The remaining lessons off resolving the strategic uncertainty. The remaining lessons take up the problem of revealing information.take up the problem of revealing information.



Toshiba

Blu-ray

35 35BA 210 Lesson III.5 Strategic Uncertainty when Interests ConflictBA 210 Lesson III.5 Strategic Uncertainty when Interests Conflict

SummarySummary

SummarySummary

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Review QuestionsReview Questions


Review QuestionsReview Questions You should try to answer some of the following questions You should try to answer some of the following questions before the next class. before the next class. You will not turn in your answers, but students may request You will not turn in your answers, but students may request to discuss their answers to begin the next class. to discuss their answers to begin the next class. Your upcoming cumulative Final Exam will contain some Your upcoming cumulative Final Exam will contain some similar questions, so you should eventually consider every similar questions, so you should eventually consider every review question before taking your exams.review question before taking your exams.

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End of Lesson III.5End of Lesson III.5


BA 210 Introduction to BA 210 Introduction to MicroeconomicsMicroeconomics

1 1 ba 210 lesson iii.5 strategic uncertainty when interests conflictoverviewoverview

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