 As in the fixed-length PD, a backward induction argument easily establishes that a rational player should take two bills on his first move, giving her a payoff of two or three dollars, depending on whether she moves first or second, and leaving the remainder of the \(n\) dollars undistributed. In more technical terms, the only nash equilibria of the game are those where the first player takes two dollars on the first move and the only subgame perfect equilibrium is the one in which both players take two dollars on any turn they should get. Again, common sense and experimental evidence suggest that real players rarely act in this way and this leads to questions about exactly what assumptions this kind of argument requires and whether they are realistic. (In addition to the sample mentioned in the section on finitely iterated PDs, see, for example, Aumann 1998, Selten 1978, and Rabinowicz.) The centipede also raises some of the same questions about cooperation and socially desirable altruism as does the PD and it is a favorite tool in empirical investigations of game playing.