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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] |
Simultaneous Game
In game theory, a simultaneous game or static game is a game where each player chooses their action without knowledge of the actions chosen by other players. Simultaneous games contrast with sequential games, which are played by the players taking turns (moves alternate between players). In other words, both players normally act at the same time in a simultaneous game. Even if the players do not act at the same time, both players are uninformed of each other's move while making their decisions. Normal form game, Normal form representations are usually used for simultaneous games. Given a continuous game, players will have different Information set (game theory), information sets if the game is simultaneous than if it is sequential because they have less information to act on at each step in the game. For example, in a two player continuous game that is sequential, the second player can act in response to the action taken by the first player. However, this is not possible in a simu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repeated Game
In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of their current action on the future actions of other players; this impact is sometimes called their reputation. Single stage game or single shot game are names for non-repeated games. Example Consider two gas stations that are adjacent to one another. They compete by publicly posting pricing, and have the same and constant marginal cost ''c'' (the wholesale price of gasoline). Assume that when they both charge , their joint profit is maximized, resulting in a high profit for everyone. Despite the fact that this is the best outcome for them, they are motivated to deviate. By modestly lowering the price, either can steal all of their competitors' customers, nearly doub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
