Final answer:
Backward induction is a strategy used in game theory to find the subgame-perfect Nash equilibrium (SPNE) of sequential games. It involves working backwards from the final stage of the game and considering the optimal strategies at each decision point. By eliminating dominated strategies, we can identify the SPNE.
Step-by-step explanation:
Backward induction is a strategy used in game theory to solve sequential games and find the subgame-perfect Nash equilibrium (SPNE). It involves working backwards from the final stage of the game, considering the optimal strategies at each decision point.
By iteratively eliminating dominated strategies, we can identify the SPNE of the game.
For example, let's consider a simple sequential game called the Centipede game. In this game, there are two players who take turns either continuing the game or stopping it. The payoffs increase as the game progresses. Using backward induction, we start at the final stage and determine the optimal strategy at each decision point, ultimately leading to the SPNE.
Backward induction is a powerful tool that helps us analyze complex sequential games and identify the players' optimal strategies. It allows us to consider the long-term consequences of each decision and find the subgame-perfect equilibrium.