Game Theory and Strategic Behavior1. Modeling Strategic Behavior2. Prisoner’s Dilemma3. A Game of Chicken4. A Soccer Game5. Win Midterm Points1Modeling Strategic Thinking• Up until now, we have assumed that each person or firm solved his orher economic problem not taking into account the actions of others.• However in many economic decisions, one must take into account theactions of others.• Game theory is the branch of microeconomics concerned with the anal-ysis of optimal decision making in competitive situations.• Why a game? If you are playing chess, your moves will depend onthe moves of the other player. It would be dumb to move your piecesignoring what you opponent is doing (or you expect her to do).2• We are going to look just at one-shot, simultaneous-move games.That is, two or more players (we will only study two player games)make a single decision, at the same time.• These games will be noncooperative in the sense that negotiation andenforcement of binding contracts is not possible.• We want to consider the optimal strategies for players in these games.• A strategy is a plan for the actions that a player in a game will takeunder every conceivable circumstance that the player might face.3The Prisoner’s Dilemma• The classic game ...• Two suspects in crime are arrested and placed in separate cells.• The police, who have no real evidence against either, privately give eachprisoner the chance to confess and implicate the other suspect for thecrime.• They tell each prisoner that– if neither confesses, both will be convicted on a minor charge andspend 2 years in jail.– if both confess, both will be convicted on a more serious charge andspend 5 years in jail.– if one confesses and the other doesn’t, the one who confesses will gofree while the one who does not confess will spend 10 years in jail.• We can display this came in a payoff matrix which is a table showingthe payoff for each player given her decision and the decision of theother player.4A Payoff MatrixSuspect Twoconfess don’t confessSuspect Oneconfess −5, −5 0, −10don’t confess −10, 0 −2, −25• A dominant strategy is a strategy that is better than any other a playermight choose, no matter what strategy the other player follows.• The dominant strategy for each prisoner is to confess. Why?• A dominated strategy is a strategy such that the player has anotherstrategy that gives a higher payoff no matter what the other playerdoes.• We want to eliminate the dominated strategies.• The Nash equilibrium is the outcome in which each player chooses thestrategy that yields the highest payoff given the strategies chosen bythe other player.– Each player asks himself, taking as given what the other player isdoing, do I want to change my decision?– If each player answers no, we have found a Nash equilibrium.6Comments on the Prisoner’s Dilemma• The prisoner’s dilemma there is a tension between the collective interestof all of the players and the self-interest of individual players.• Earlier in the course we argued that individual pursuit of self-interestpromotes the greatest good for all. This is Adam Smith’s celebratedinsight of the invisible hand.• But as the prisoner’s dilemma shows, there are cases in which rationalindividuals acting in their own self interest can result in outcomes thatno one favors.• This occurs particularly when relative performance rather than absoluteoutcomes matter.• See Robert Frank’s New York Times article on hockey players in thereading packet.7Other Examples of the Prisoner’s Dilemma• Sling Mud in a political race ...– If both candidates run a positive campaign and refuse to engage innegative ads, they both have a 50-50 chance of winning.– If one candidate runs a negative campaign while the other doesn’tthey odds of winning become 60-40 in favor of the negative candi-date.– If both candidates run a negative campaign, they both have a 50-50chance of winning.8Politician Twodirty campaign clean campaignPolitician Onedirty campaign 50%, 50% 60%, 40%clean campaign 40%, 60% 50%, 50%9Arms Races ...Indiabigger military smaller militaryPakistanbigger military −5, −5 0, −10smaller military −10, 0 −2, −210Collusion with a competing firm ...Company Twoset price low set price highCompany Oneset price low $2, $2 $10, $1set price high $1, $10 $5, $511The Game of Chicken• Two teenagers each get into their cars at opposite ends of the road andbegin to drive toward each other at break-neck speed.– If one car swerves before the other, the one that did not swerve (i.e.stays) proves his manhood and becomes a hero to his friends. Theone who swerved loses faces and becomes the ‘chicken’.– If both swerve, nothing happens. Neither gain status, but neitherare a chicken.– If both stay, both end up in the hospital with serious injuries.12Teenager TwoSwerve StayTeenager OneSwerve 0, 0 −10, 10Stay 10, −10 −100, −100• Is there a dominate strategy?• Is there a Nash equilibrium? Is there more than one?13Other Examples of the Game of Chicken• Often occurs in economics when two firms compete in a market thatcan profitably support only one firm.• Consider the satellite radio market– Two companies: XM and Sirius– Almost all the costs to running the firm are fixed costs. The marginalcost of an additional subscriber is close to zero.– Need LOTS of subscribers to be profitable.SiriusStay ExitXMStay −$200, −$200 $300, $0Exit $0, $300 $0, $014Pure versus Mixed Strategies• Consider a soccer game in which the game is tied and may be decidedby a single penalty kick.– If the goalie dives (to the kicker’s) right, and the kicker aims right,goal is blocked and game continues.– If the goalie dives left, and the kicker aims left, goal is blocked andgame continues.– If the goalie dives right, and the kicker aims left, goal is made andgame is over.– If the goalie dives left, and the kicker aims right, goal is made andgame is over.15KickerAim Right Aim LeftGoalieDive to Kicker’s Right 0, 0 −1, 1Dive to Kicker’s Left −1, 1 0, 016• This game does not appear to have a Nash equilibrium.– If the goalie believes the kicker will aim right, the goalie’s best strat-egy is dive right.– But if the kicker believes that the goalie believes that the kicker willaim right (and thus dive right), the kicker’s best strategy is to kickleft.– Well if the goalie believes that the kicker believes that