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Perfect information A game of imperfect information the dotted line represents ignorance on the part of player 2, formally called an information set An important subset of sequential games consists of games of perfect information. A game is one of perfect information if all players know the moves previously made by all other players.
Most games studied in game theory are imperfect-information games. Games of incomplete information can be reduced, however, to games of imperfect information by introducing " moves by nature ".
Examples include chess and go. Games that involve imperfect information may also have a strong combinatorial character, for instance backgammon. There is no unified theory addressing combinatorial elements in games. There are, however, mathematical tools that can solve particular problems and answer general questions.
These methods address games with higher combinatorial complexity than those usually considered in traditional or "economic" game theory.
A related field of study, drawing from computational complexity theoryis game complexitywhich is concerned with estimating the computational difficulty of finding optimal strategies. The practical solutions involve computational heuristics, like alpha-beta pruning or use of artificial neural networks trained by reinforcement learningwhich make games more tractable in computing practice.
Determinacy Games, as studied by economists and real-world game players, are generally finished in finitely many moves. Pure mathematicians are not so constrained, and set theorists in particular study games that last for infinitely many moves, with the winner or other payoff not known until after all those moves are completed.
The focus of attention is usually not so much on the best way to play such a game, but whether one player has a winning strategy. The existence of such strategies, for cleverly designed games, has important consequences in descriptive set theory.
Discrete and continuous games[ edit ] Much of game theory is concerned with finite, discrete games, that have a finite number of players, moves, events, outcomes, etc. Many concepts can be extended, however. Continuous games allow players to choose a strategy from a continuous strategy set.
For instance, Cournot competition is typically modeled with players' strategies being any non-negative quantities, including fractional quantities. Differential games[ edit ] Differential games such as the continuous pursuit and evasion game are continuous games where the evolution of the players' state variables is governed by differential equations.
The problem of finding an optimal strategy in a differential game is closely related to the optimal control theory.
In particular, there are two types of strategies: A particular case of differential games are the games with a random time horizon.
Therefore, the players maximize the mathematical expectation of the cost function. It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval. Evolutionary game theory[ edit ] Evolutionary game theory studies players who adjust their strategies over time according to rules that are not necessarily rational or farsighted.
Such rules may feature imitation, optimization or survival of the fittest. In biology, such models can represent biological evolutionin which offspring adopt their parents' strategies and parents who play more successful strategies i. In the social sciences, such models typically represent strategic adjustment by players who play a game many times within their lifetime and, consciously or unconsciously, occasionally adjust their strategies.Free online horse game where people of all ages can learn the responsibility that comes along with taking care of horses, and have fun at the same time.
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