An Example of Backward Induction in Game Theory
Consider the ultimatum game, where one player proposes to split a dollar with another. The first player (the proposer) suggests a division of the dollar between the two players. The second player is then given the option to either accept the split or reject it. If the second player accepts, both get the amount suggested by the proposer. If rejected, neither receives anything.
Consider the actions of the second player given any arbitrary proposal by the first player (that gives the second player more than zero). Since the only choice the second player has at each of these points in the game is to choose between something and nothing, one can expect that the second will accept. Given that the second will accept all proposals offered by the first (that give the second anything at all), the first ought to propose giving the second as little as possible. This is the unique subgame perfect equilibrium of the Ultimatum Game. (However, the Ultimatum Game does have several other Nash equilibria which are not subgame perfect.)
See also centipede game.
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