Explain the concept of backward induction in game theory.

Explain the concept of backward induction in game theory.

Backward induction is a strategic decision-making process used in game theory to determine the optimal strategy for each player in a sequential game. It involves working backwards from the final stage of the game to the initial stage, considering the possible actions and payoffs at each stage.

In backward induction, the first step is to analyze the final stage of the game, where players make their last moves. By considering the possible outcomes and payoffs at this stage, players can determine the best strategy to maximize their own utility.

Next, players move to the second-to-last stage and consider the optimal strategy for that stage, taking into account the strategy determined in the final stage. This process continues until reaching the initial stage of the game.

By working backwards, players can anticipate the actions and reactions of other players, allowing them to make rational decisions based on the expected behavior of others. Backward induction helps identify the subgame perfect Nash equilibrium, which represents the optimal strategy for each player at every stage of the game.