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In game theory, backward induction is a solution methodology that follows from applying sequential rationality to identify an optimal action for each information set in a given game tree. It develops the implications of rationality via individual information sets in the extensive-form representation of a game.
A generalization of backward induction is subgame perfection. Backward induction assumes that all future play will be rational. In subgame perfect equilibria, play in every subgame is rational (specifically a Nash equilibrium). Backward induction can only be used in terminating (finite) games of definite length and cannot be applied to games ...
One game in which the backward induction solution is well known is tic-tac-toe. Reinhard Selten proved that any game which can be broken into "sub-games" containing a sub-set of all the available choices in the main game will have a subgame perfect Nash Equilibrium strategy (possibly as a mixed strategy giving non-deterministic sub-game decisions).
Various methods exist to solve game trees. If a complete game tree can be generated, a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minmax algorithms such as MCTS can be used in cases where a complete game tree is not feasible.
Strictly speaking, chess is an infinite game therefore backward induction does not provide the minmax theorem in this game. [6] Backward induction is a process of reasoning backward in time. It is used to analyse and solve extensive form games of perfect information. This method analyses the game starting at the end, and then works backwards to ...
In game theory, the centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either to take a slightly larger share of an increasing pot, or to pass the pot to the other player. The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes ...
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To solve any extensive form game, backward induction must be used. It involves working backward up the game tree to determine what a rational player would do at the last vertex of the tree, what the player with the previous move would do given that the player with the last move is rational, and so on until the first vertex of the tree is ...