Microeconomics: unit 1 STATIC GAMES
STATIC GAMES
Definition: The study of behavior in situations of interdependence is known as game* theory
Game theory;
-Cooperative games: groups of players may enforce cooperative behavior, the game
is a competition between coalitions of players
-Non-cooperative games: Decisions are made independently;
-Static games: no additional information
-Dynamic games: additional information appears
Parts of a game;
-Players: Who is involved?
-N: set of players
-n: number of players
-i: a particular player
-Strategies: which are the possible actions ?
-Si: Player i set of strategies
-si: Player i particular strategy
-(s1, s2, s3,...,sn) particular strategy prg
-Payoff: which are the preferences over the possible outcomes?
-Ui: player i payoff function
-Ui: S1xS2xS3x….xSn -> R
The normal form representation specifies the players’ strategies and possible payoffs:
G= {S1, S2,...., Sn; u1, u2,....,un}
Rationality: Each individual aims to maximise its welfare (the individual’s payoff can be
altruistic)
Common knowledge: the fact that the individuals’ are rational si public knowledge
Solution: It’s a formal rule to predict the strategies that will be adopted by the players
involved in the game.
- Aim of the game: to predict how the game will be played
Strictly dominated strategy: When there’s some other strategy available to the player that
always has a higher payoff regardless of the strategies that the other players choose.
Rationalizable strategies: It’s the set of strategies profiles that survives the iterated
elimination of strictly dominated strategies.
Nash equilibrium:
- Each player’s strategy must be the best response to the other player’s strategies
- No player wants to deviate from their strategy
*Game: Formal representation of a situation in which a number of individuals interact in a
setting of strategic interdependence