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Multi-stage Game
In game theory, a multi-stage game is a sequence of several simultaneous games played one after the other. This is a generalization of a repeated game: a repeated game is a special case of a multi-stage game, in which the stage games are identical. Multi-Stage Game with Different Information Sets As an example, consider a two-stage game in which the stage game in ''Figure 1'' is played in each of two periods: The payoff to each player is the simple sum of the payoffs of both games. Players cannot observe the action of the other player within a round; however, at the beginning of Round 2, Player 2 finds out about Player 1's action in Round 1, while Player 1 does not find out about Player 2's action in Round 1. For Player 1, there are 2^3=8 strategies. For Player 2, there are 2^5=32 strategies. The extensive form of this multi-stage game is shown in ''Figure 2'': In this game, the only Nash Equilibrium in each stage is (B, b). (BB, bb) will be the Nash Equilibrium for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
