Explain the concept of backward induction in sequential move games.

Explain the concept of backward induction in sequential move games.

Backward induction is a strategic decision-making process used in sequential move games within the field of game theory. It involves reasoning backwards from the final stage of a game to determine the optimal strategy for each player at each preceding stage.

In sequential move games, players take turns making decisions, and the outcome of each player's decision depends on the decisions made by previous players. Backward induction starts by considering the final stage of the game and determining the best strategy for the player who moves last. Then, working backwards, it considers the second-to-last stage and determines the best strategy for the player who moves second-to-last, taking into account the optimal strategy of the player who moves last. This process continues until reaching the first stage of the game.

By reasoning backwards, backward induction allows players to anticipate the actions and reactions of other players, leading to the identification of subgame perfect equilibria. It helps in determining the optimal strategies for each player by considering the potential outcomes and payoffs at each stage of the game.