What is a Game There are many types of games board games card games video games field games e g football etc We W focus f on games where h There are 2 or more players There is some choice of action where strategy gy matters The game has one or more outcomes e g someone wins someone loses The Th outcome t depends d d on the th strategies t t i chosen h by b all ll players l there is strategic interaction What does this rule out Games of pure chance e g bingo slot machines Strategies don t matter Games without strategic interaction between players players e g eg Solitaire Why Do Economists Study Games Games are a convenient way in which to model strategic interactions among economic agents y economic issues involve strategic g Many interaction Behavior in imperfectly competitive markets e g Coca Cola DQG Pepsi Behavior in auctions e g g when to bid in dynamic internet auctions Behavior in economic negotiations g e g g trade Game theory is not limited to Economics Three Elements of a Game 1 The players 1 how many players are there does d nature chance t h play l a role l 2 A complete description of the strategies of each h player l 3 A description of the consequences payoffs ff for f eachh player l for f every possible profile of strategy choices of all players players Illustration The Prisoner s Dil Dilemma Game G Two players prisoners 1 2 Each is questioned by detectives separately and without communication Each has two strategies Prisoner 1 Don t Confess Confess Prisoner 2 Don t Confess Confess Payoff consequences quantified in prison years negative numbers fewer years less negative payoffs greater satisfaction In strategic normal i l form f game ddepiction i i Prisoner i 1 payoff first followed by professor 2 payoff Prisoners Dilemma Game Prisoners in Normal or Strategic Form Pi Prisoner 2 2 s Strategies St t i Don t Prisoner 1 s Confess Strategies g Confess Don t Confess Confess 1 1 15 0 0 15 0 15 5 5 55 Dilbert Illustration http www gametheory net media Dilbert wmv Prisoners Dilemma Game in Extensive Extensive Form Prisoner 1 Don t Confess Confess Prisoner 2 Don t Confess 1 1 This line represents D FRQVWULQDW RQ WKHinformation that Prisoner 2 has available While Prisoner 2 moves second she does not know what Prisoner 1 has chosen Prisoner 2 Confess 15 0 Don t Confess 0 15 Payoffs are Prisoner 1 payoff Prisoner 2 payoff Confess 5 5 Prisoners Dilemma is an example Prisoners of a Non Zero Sum Game A zero sum game is one in which the players interests are in direct conflict e g in football one team wins and the other loses If a win 1 and a loss 1 the sum is zero More M generally ll the h sum at stake k can be b a constant A game is non zero non constant sum if players interests are not always in direct conflict conflict so that there are opportunities for both to gain For example example when both players choose Don Don tt Confess in Prisoners Dilemma The Prisoners Dilemma is applicable to many other situations situations Nuclear arms races Settle a divorce amicably or hire a lawyer Immediately merge left when signs indicate the right lane ahead is closed or continue driving in right lane up to the merge point Full price menu or value price menu Can you think of other applications Labels or Framing Non Binding Pregame Communication i i or Cheap h Talk should does it matter in the PD http www youtube com watch v p3Uos2fzIJ0 Split Steal Split 50 075 50 075 0 100 150 Steal 100 150 0 0 0 Simultaneous v Sequential Move Games Games where players choose actions simultaneously are simultaneous move games Examples Prisoners Dilemma Sealed Bid Auctions Must anticipate what your opponent will do right now recognizing that your opponent is doing the same Games where players choose actions in a particular sequence are sequential i l move games Examples Chess Bargaining Negotiations Must look ahead in order to know what action to choose now now Many sequential move games have deadlines time limits on moves Many strategic situations involve both sequential and simultaneous moves The Investment Game is a Sequential Move Game S d Sender Don t Send If sender d sends d invests 4 the amount at stake is tripled p 12 Send 4 0 Receiver Keep 0 12 Return 6 6 The investment game is depicted in extensive form One Shot versus Repeated p Games One shot play of the game occurs once Players likely to not know much about one another another Example tipping on your vacation Repeated play of the game is repeated with the same players Indefinitelyy versus finitely y repeated p ggames Reputational concerns matter opportunities for cooperative behavior may arise Advise If you plan to pursue an aggressive strategy ask yourself whether you are in a one shot or in a repeated game game If a repeated game game think thi k again i Strategies g A strategy must be a comprehensive plan of action a decision rule or set of instructions about which actions a player should take It is the equivalent of a memo left behind when you go on vacation that specifies the actions you want taken in every situation which could conceivably arise during your absence absence Strategies will depend on whether the game is one shot or repeated Examples of one one shot shot strategies Prisoners Dilemma Don t Confess Confess Investment Game Sender Don t Send Send Receiver Keep Return How do strategies change when the game is repeated Repeated p Game Strategies g In repeated games the sequential nature of the relationship allows for the adoption p of strategies g that are contingent g on the actions chosen in previous plays of the game Most contingent strategies are of the type known as trigger strategies Example trigger strategies In prisoners dilemma Initially play Don t confess If your opponent plays Confess then play Confess in the next round If your opponent plays Don t confess then play Don t confess in the next round This is known as the tit for tat strategy In the investment game if you are the sender Initially play Send Play Send as long as the receiver plays Return Return If the receiver plays Keep never play Send again This is known as the grim trigger strategy Information Players have perfect information if they know exactly what has happened every time a decision needs to be made e g in Chess Otherwise Otherwise the game is one of imperfect information E Example l In I the th repeated t d investment i t t game the th sender and receiver might be differentially informed about the investment outcome outcome For example the receiver may