ECO3041 - Ch 7 Game Theory

ECO3041 - Ch 7 Game Theory - Economics Department FIU Game...

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Economics Department FIU Game Theory Notes Prof Dacal
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Game theory From Wikipedia [with modifications] Game theory is a branch of applied mathematics that is used in the social sciences , most notably in economics . Game theory attempts to mathematically capture behavior in strategic situations, or games , in which an individual's success in making choices depends on the choices of others. While initially developed to analyze competitions in which one individual does better at another's expense ( zero sum games ). Traditional applications of game theory attempt to find equilibrium in these games. In equilibrium, each player of the game has adopted a strategy that they are unlikely to change (most famous the Nash equilibrium ). Representation of games A game consists of a set of players , a set of moves (or strategies ) available to those players, and a specification of payoffs for each combination of strategies. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define non-cooperative games. Extensive form An extensive form game The extensive form can be used to formalize games with some important order. Games here are often presented as trees (as pictured above). Here each node represents a point of choice for a player. The player is specified by a number listed by the node. The lines out of the node represent a possible action for that player. The payoffs are specified at the bottom of the tree. In the game pictured here, there are two players. Player 1 moves first and chooses either F or U . Player 2 sees Player 1' s move and then chooses A or R . Suppose that Player 1 chooses U and then Player 2 chooses A , then Player 1 gets 8 and Player 2 gets 2. The extensive form can also capture simultaneous-move games and games with imperfect information or asymmetric information. To represent it, either a dotted line connects different vertices to represent them as being part of the same information set (i.e., the players do not know at which point they are), or a closed line is drawn around them. 2
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ECO3041 - Ch 7 Game Theory - Economics Department FIU Game...

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