Game Theory Questions Medium
Backward induction is a concept in game theory that involves reasoning backward from the end of a game to determine the optimal strategy for each player at each stage of the game. It is commonly used in sequential games, where players take turns making decisions, and the outcome of each decision affects the subsequent decisions and payoffs.
The process of backward induction starts by considering the final stage of the game and determining the optimal strategy for the player who moves last. This is done by evaluating the payoffs associated with each possible action and selecting the action that maximizes the player's payoff.
Once the optimal strategy for the last player is determined, the analysis moves to the previous stage of the game, considering the second-to-last player's optimal strategy. This player takes into account the actions and payoffs of the last player and selects the action that maximizes their own payoff. This process continues backward through each stage of the game until reaching the first player.
By reasoning backward in this way, backward induction allows players to anticipate the actions and responses of other players, leading to the identification of subgame-perfect Nash equilibria. These equilibria represent strategies that are optimal for each player at every stage of the game, given the actions and payoffs of the other players. Backward induction is a powerful tool in game theory for analyzing and predicting the outcomes of sequential games.