Game theory extended example

information set game theory

Player 1 would like to fool player 2 into thinking they have played U when they have actually played D so that player 2 will play D' and player 1 will receive 3.

This general definition was introduced by Harold W. In the second game it is less clear: player 2 cannot observe player 1's move.

Each firm can decide to stop colluding and start a price war, in order to increase their market share, even force the other to quit the market.

Game theory extended example

If type 1 plays U and type 2 plays D, player 2 will play D' whatever action they observe, but then type 1 prefers D. Strategic form Extensive form In game theorythe extensive form is away of describing a game using a game tree. However, if they play D'type 2 would prefer to play U.

One player does not always observe the choice of another for example, moves may be simultaneous or a move may be hidden.

extensive form game theory

The tree shows clearly that player 1 moves first and player 2 observes this move. Examples of such games include tic-tac-toechessand infinite chess. At any rational player's node, the player must choose one of the equivalence classes for the edges, which determines precisely one outgoing edge except in general the player doesn't know which one is being followed.

If both players are rational and both know that both players are rational and everything that is known by any player is known to be known by every player i. There is one separating perfect Bayesian equilibrium ; i.

A good example of a sequential game described with the extensive form is when considering collusion agreementsas depicted in the second game tree.

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Game theory I: Extensive form