Prisoner's Dilemma

The rules of the game are common knowledge:

-Each player knows the set of players, strategies and payoffs from all possible combinations of strategies: call this information "X." -Each player knows that all players know X, that all players know that all players know X, that all players know.., ad infinitum.

Two players, prisoners 1, 2

-Each prisoner has two possible actions -Prisoner 1: Don't Confess, Confess -Prisoner 2: Don't Confess, Confess -Players choose actions simultaneously without knowing the action chosen by the other -Payoff consequences quantified in prison years -If neither confesses, each gets 1 year -If both confess, each gets 5 years -If 1 confesses, he goes free and other gets 15 years -Fewer years=greater satisfaction=>higher payoff -Prisoner 1 payoff first, followed by prisoner 2 payoff

Payoffs

-Payoffs are known and fixed. People treat expected payoffs the same as certain payoffs (they are risk neutral). -Example: a risk neutral person is indifferent between $25 for certain or a 25% chance of earning $100 and a 75% chance of earning 0. -We can relax this assumption to capture risk averse behavior. -rely on the perceptions of leaders and how they prioritize their payoffs

Equilibrium

-The interaction of all (rational) players' strategies results in this outcome -each player is playing the strategy that is a "best response" to the strategies of the other players -No one has an incentive to change his strategy given the strategy choices of the others. -Equilibrium is not: The best possible outcome. -Equilibrium in the one-shot prisoners' dilemma is for both players to confess. -A situation where players always choose the same action. Sometimes equilibrium will involve changing action choices (known as a mixed strategy equilibrium).

Prisoner's Dilemma Scenario: A & B

-actors: two actors, A and B -have to come up with options of what to do -ex. both caught by the police but don't have enough to charge them -will charge them with one of two things -have options to either confess or not confess -If actor B confesses, and actor A doesn't, B gets 0 A gets 10 -if A confesses, but B doesn't, A gets 0 and B gets 10 -if both confess, each get 5 and 5 cause its split (the equivalent of going to war) -if both don't confess, each get 1 and 1 year -put into 2 different cells, so don't know what the other person is saying -gives us a framework to apply to states -have to take into account incomplete information about the aggressor -if you want cooperation, have to pay attention to the issues -wars usually if issues are indivisible (usually something that politicians create)

Game Theory

-looks at interaction between actors based on them being rational -substitute actors for states -can apply prisoner's dilemma to game theory

Strategy

-must be a "comprehensive plan of action", a decision rule or set of instructions about which actions a player should take following all possible histories of play. -It is the equivalent of a memo, left behind on vacation, that specifies the actions you want taken in every situation which could arise during your absence. -will depend on whether the game is one-shot or repeated. -Ex of one-shot strategies Prisoners' Dilemma: Don't Confess, Confess

non zero-sum

-players interests are not always in direct conflict, so that there are opportunities for both to gain. -For example, when both players choose Don't Confess in the Prisoners' Dilemma

zero-sum game

players' interests are in direct conflict, e.g. in football, one team wins and the other loses; payoffs sum to zero.

All players behave...

rationally -They understand and seek to maximize their own payoffs. -They are flawless in calculating which actions will maximize their payoffs.