KRUGMAN'S MICROECONOMICS for AP* Game Theory Margaret Ray and David Anderson Micro: Econ: Module

What you will learn in this Module : How oligopoly can be analyzed using game theory. The concept of the prisoners’ dilemma. How repeated interactions among oligopolists can result in collusion in the absence of any formal agreement. John Nash

Game Theory Game Theory: study of how interdependent decision makers make choices.

Non-Cooperative Games Each player competes to maximize individual payoffs and ignores the effects of his/her action on the payoffs received by the rival.

Terms to Know Payoff matrix Dominant strategy Nash equilibrium

Prisoner’s Dilemma Each player has an incentive to choose an action that benefits his/herself at the other player’s expense. Both players are then worse off than if they had acted cooperatively. The payoff matrix below summarizes the strategies and outcomes. The payoffs are measured as years in prison, so smaller numbers are preferred. Crook 2 ConfessSilent Crook 1 Confess #1: 5 years #2: 5 years #1: 1 year #2: 20 years Silent #1: 20 years #2: 1 year #1: 2 years #2: 2 years

Prisoner’s Dilemma Confession is the dominant strategy when the game is played simultaneously and they cannot talk (collude). No matter what Crook #2 does, it’s always better for Crook #1 to confess. The same is true of Crook #2’s thinking. This is the Nash equilibrium.Confession is the dominant strategy when the game is played simultaneously and they cannot talk (collude). No matter what Crook #2 does, it’s always better for Crook #1 to confess. The same is true of Crook #2’s thinking. This is the Nash equilibrium. Characteristic of the prisoner’s dilemma is that players pursue their dominant strategy and the game comes to Nash equilibrium. However, the outcome is an undesirable one and could have been avoided through some kind of cooperative agreement (collusion).Characteristic of the prisoner’s dilemma is that players pursue their dominant strategy and the game comes to Nash equilibrium. However, the outcome is an undesirable one and could have been avoided through some kind of cooperative agreement (collusion). The payoff matrix below summarizes the strategies and outcomes. The payoffs are measured as years in prison, so smaller numbers are preferred. Crook 2 ConfessSilent Crook 1 Confess #1: 5 years #2: 5 years #1: 1 year #2: 20 years Silent #1: 20 years #2: 1 year #1: 2 years #2: 2 years

Repeated Interaction and Tacit Collusion Repeated interaction can lead to strategic behavior Tit for tat strategy Tacit Collusion

Figure 65.2 The Prisoners’ Dilemma Ray and Anderson: Krugman’s Economics for AP, First Edition Copyright © 2011 by Worth Publishers

Figure 65.3 How Repeated Interaction Can Support Collusion Ray and Anderson: Krugman’s Economics for AP, First Edition Copyright © 2011 by Worth Publishers

Golden Balls Game – Split or Steal? On the British game show Golden Balls, the final round is set up like a less penitentiary "prisoner's dilemma": Contestants must choose between spliting the jackpot or stealing it for themselves.On the British game show Golden Balls, the final round is set up like a less penitentiary "prisoner's dilemma": Contestants must choose between spliting the jackpot or stealing it for themselves.prisoner's dilemmaor stealing it for themselvesprisoner's dilemmaor stealing it for themselves The catch is, if they both choose to steal, they both walk away with nothing.The catch is, if they both choose to steal, they both walk away with nothing. Players are given 30 seconds to discuss their intentions before making a final decision. Naturally, in most cases, the objective is to convince the other contestant that you are keen to split, and then turn around and pick Steal. It's quite a horrible sight to behold.Players are given 30 seconds to discuss their intentions before making a final decision. Naturally, in most cases, the objective is to convince the other contestant that you are keen to split, and then turn around and pick Steal. It's quite a horrible sight to behold.a horrible sight to beholda horrible sight to behold First four videos

Split or Steal – Game Theory This is similar to the prisoner's dilemma, a well-studied problem in game theory. A key difference is that, in the standard Prisoner's Dilemma payoffs, if the one player defects (or steals), the other player is better off defecting than cooperating (splitting), but in Golden Balls, if the one player steals, the other player gets the same amount (nothing) either way.This is similar to the prisoner's dilemma, a well-studied problem in game theory. A key difference is that, in the standard Prisoner's Dilemma payoffs, if the one player defects (or steals), the other player is better off defecting than cooperating (splitting), but in Golden Balls, if the one player steals, the other player gets the same amount (nothing) either way. prisoner's dilemmagame theoryprisoner's dilemmagame theory ResultSplitSteal Split50%50%100%0% Steal0%100%0%0%

Split or Steal – Game Theory There are three Nash equilibria in the game, which are outcomes at which a player cannot do better on his or her own by changing his or her strategy. The outcome SteveThere are three Nash equilibria in the game, which are outcomes at which a player cannot do better on his or her own by changing his or her strategy. The outcome Steve was hoping for by choosing “split” (50/50) was not a Nash equilibrium because Sarah knows she can do better if she chooses steal when Steve chooses split. Steve doomedwas hoping for by choosing “split” (50/50) was not a Nash equilibrium because Sarah knows she can do better if she chooses steal when Steve chooses split. Steve doomed himself by choosing split because he should know that Sarah’s dominant strategy is to choose steal. However, Sarah would also have doomed herself by choosing split because she should assume that Steve would also chose steal since steal is a dominant strategy for him too.himself by choosing split because he should know that Sarah’s dominant strategy is to choose steal. However, Sarah would also have doomed herself by choosing split because she should assume that Steve would also chose steal since steal is a dominant strategy for him too. Player One SplitSteal Player Two Spli t 50/500/100 Steal 100/00/0 Nash Equilibria

Split or Steal – Game Theory !Golden balls. the weirdest split or steal ever! Nick Ibraham

Split or Steal – Game Theory In this episode, Nick immediately takes control of the negotiations by insisting that he is going tosteal, which is a very unorthodox approach to this game, in which the traditional strategy is to try and convince your opponent that you are going to split. By establishing a credible threat to steal, Nick puts all the pressure on Ibraham to decide only one of two things:In this episode, Nick immediately takes control of the negotiations by insisting that he is going tosteal, which is a very unorthodox approach to this game, in which the traditional strategy is to try and convince your opponent that you are going to split. By establishing a credible threat to steal, Nick puts all the pressure on Ibraham to decide only one of two things: Does Ibraham trust that Nick will split the money with him after he has stolen the full jackpot?Does Ibraham trust that Nick will split the money with him after he has stolen the full jackpot?

Split or Steal – Game Theory Would Ibraham rather both of them go home without any money at all than Nick win the jackpot and possibly not split it with him later on?Would Ibraham rather both of them go home without any money at all than Nick win the jackpot and possibly not split it with him later on? Nick’s strategy is brilliant. By the end of the negotiation, Nick has convinced Ibraham 100% that he is going to steal the money. Ibraham may only have had a confidence level of 50% that Nick was honest about splitting the money with him after the show, but with a 50% confidence level, Ibrahim’s possible payoffs are:Nick’s strategy is brilliant. By the end of the negotiation, Nick has convinced Ibraham 100% that he is going to steal the money. Ibraham may only have had a confidence level of 50% that Nick was honest about splitting the money with him after the show, but with a 50% confidence level, Ibrahim’s possible payoffs are:

Split or Steal – Game Theory Choose steal and go home with nothing.Choose steal and go home with nothing. Choose split and have a 50/50 chance of going home with half the jackpot (based on his level of confidence in Nick’s promise to split the money after the show).Choose split and have a 50/50 chance of going home with half the jackpot (based on his level of confidence in Nick’s promise to split the money after the show).

Split or Steal – Game Theory In other words, with a jackpot of 14,000 pounds, the payoffs for Ibrahim became:In other words, with a jackpot of 14,000 pounds, the payoffs for Ibrahim became: If he splits: 0 pounds or 0.5(14,000) = 7,000 poundsIf he splits: 0 pounds or 0.5(14,000) = 7,000 pounds If he steals: 0 pounds or 0 pounds (assuming his confidence level in Nick’s intention to steal is 100%).If he steals: 0 pounds or 0 pounds (assuming his confidence level in Nick’s intention to steal is 100%).

Split or Steal – Game Theory Clearly Ibraham now has a dominant strategy: to split. In the typical version of this game, a player’s dominant strategy is always to steal (as explained below), since the possible payoffs are:Clearly Ibraham now has a dominant strategy: to split. In the typical version of this game, a player’s dominant strategy is always to steal (as explained below), since the possible payoffs are: If you split: 0 pounds or half the jackpotIf you split: 0 pounds or half the jackpot If you steal: 0 pounds or the whole jackpot.If you steal: 0 pounds or the whole jackpot.

Split or Steal – Game Theory But because Nick has convinced his opponent that he will steal, and then split the winnings, Ibraham’s dominant strategy shifted to split, since the possible payoffs have changed. Ultimately, Ibraham does what is most rational given his confidence in Nick’s threat to steal, and that is to split. Ibraham then chooses split (as he should), but then to everyone’s surprise, Nick chooses split, not steal as he had threatened to do throughout the negotiation.But because Nick has convinced his opponent that he will steal, and then split the winnings, Ibraham’s dominant strategy shifted to split, since the possible payoffs have changed. Ultimately, Ibraham does what is most rational given his confidence in Nick’s threat to steal, and that is to split. Ibraham then chooses split (as he should), but then to everyone’s surprise, Nick chooses split, not steal as he had threatened to do throughout the negotiation.

Split or Steal – Game Theory This a surprising twist, since from Nick’s perspective stealing is clearly now a dominant strategy! Nick had convinced Ibraham to split, which means Nick faced a greater payoff by stealing. But by splitting, Nick shows that he had intended to split all along, but first needed to convince Ibraham otherwise to establish splitting as Ibraham’s dominant strategyThis a surprising twist, since from Nick’s perspective stealing is clearly now a dominant strategy! Nick had convinced Ibraham to split, which means Nick faced a greater payoff by stealing. But by splitting, Nick shows that he had intended to split all along, but first needed to convince Ibraham otherwise to establish splitting as Ibraham’s dominant strategy.