Level-K Analysis of Experimental Centipede Games

Abstract:     
The centipede game is one of the most celebrated examples of the paradox of backward induction. Experiments of the centipede game have been conducted in various settings: two-person games with linearly increasing payoffs (McKelvey and Palfrey, 1992), two-person games with constant-sum payoffs (Fey, McKelvey and Palfrey, 1996) and three-person games (Rapoport et al. 2003). The deviations from the subgame-perfect equilibrium prediction observed in laboratories have so far been attributed to some kind of fairness concern or altruism of the subjects. This paper attempts to offer another explanation for the observed deviations by using level-k analysis, a non-equilibrium model of strategic thinking. We show that level-k analysis gives consistently good predictions for the results of experimental centipede games. The results suggest that experimental results of centipede games be explained without invoking fairness or altruism.

Keywords: centipede game, level-k analysis, bounded rationality, altruism, experiment

JEL Classifications: C72, C92, D82

Working Paper Series