Game Theory

Assumptions of rationalizability

1) People form beliefs about others' behavior 2) people best respond to their beliefs 3) these facts are common knowledge among the players -the concept is quite weak-not additional assumptions about behavior are made

Iterative removal of dominated strategies

1) delete all of the dominated strategies for each player, because a rational player would never use one -define R1 to be the strategy profiles that remain -so on, so on -each player should play a best response, the belief rationalizes -set of strategies that remain: rationalizable strategies

Things to keep in mind

1) each equilibrium is a rationalizable strategy 2) some games have more than one Nash equilibrium 3) some games have no equilibrium

Three versions of the congruity concept

1) game is repeatedly played in society or by a group of agents 2) players meet before playing a game and reach an agreement 3) outside mediator recommends to the players that they adopt a specific strategy profile

Congruity

Can refer to consistent and regular behavior in a game that is played over and over, can refer to behavior in a one-shot game in which history has aligned the beliefs of each player with strategies of the other

Social force

behavior in a game is coordinate, or congruous

Third Strategic Tension

inefficient coordination poses a problem even if the players have the same preferences over outcomes and there is no strategic uncertainty-- specter of inefficient coordination

Rational Behavior

may consist of more than just avoiding dominated strategies -one can shrewdly estimate the other players' actions by putting themselves in the others' shoes. In other words, mind games can be the art of game playing

Second Strategic Tension

rationalizability merely requires that the players' behavior be consistent with common knowledge of rationality, doesn't require require that their beliefs be correct--- Strategic Uncertainty

Nash Equilibrium

simplest notion of congruity is that the players are best responding in a setting of "strategic uncertainty": "mutual best response"

Strategic uncertainty

sometimes hinders attainment of an efficient outcome, is a part of life, but there are devices in the world that help us coordinate our behavior and avoid inefficiency