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 reasoning backwards from the end of the game to the beginning, considering the possible actions and outcomes at each stage.

In a sequential game, players take turns making decisions, and the outcome of each player's decision depends on the decisions made by the previous players. Backward induction starts by analyzing the final stage of the game and working backwards to the initial stage.

The process begins by considering the last stage of the game and identifying the possible actions and payoffs for each player at that stage. Then, moving one step back, the decision-maker considers the possible actions and payoffs at the previous stage, taking into account the optimal strategies of the players at the final stage. This process continues until reaching the initial stage of the game.

At each stage, the decision-maker assumes that the other players will act rationally and choose their optimal strategies. By reasoning backwards, the decision-maker can determine the optimal strategy for each player at each stage, considering the potential actions and payoffs of all players involved.

Backward induction is based on the assumption of perfect rationality and complete information, meaning that players have a complete understanding of the game and its rules, as well as the ability to accurately predict the actions and payoffs of other players. It is a powerful tool in game theory that helps to identify the subgame perfect Nash equilibrium, which represents the optimal strategy for each player at every stage of the game.