21 - Backward induction

Summary

In Chapter 19, we demonstrated how to find perfect equilibrium by backward induction in games with a finite number of nodes, in which a unique player plays at each node. We saw how this solution concept excludes Nash equilibria that rely on non-credible threats. In Chapter 20, we saw how strategic behavior that embodies commitment can be reflected in subgame perfect equilibria found by backward induction.

At the same time, even when backward induction leads us to find a unique subgame perfect equilibrium, there are instances in which this equilibrium is not consistent with players’ actual real-life behavior, nor with our intuition concerning “reasonable” or “foreseeable” behavior of players in the strategic situation at hand. In this chapter, we will present two key examples illustrating the limitations of this solution concept: the “ultimatum game” and the “centipede game.” We will analyze the reasons for the limitations that these games illustrate.

The ultimatum game

This is a very simply structured two-player game. Player 1 gets an amount X of money. She must offer part of it, Y, to player 2. If player 2 accepts the offer, the transaction takes place: player 1 gets the payoff X – Y and player 2 gets the payoff Y. If, however, player 2 refuses the offer, both players get the payoff 0.