The Evolutionary Foundations of Backward and Forward Induction
We examine the evolutionary foundations of common equilibrium refinement ideas for extensive form games, such as backward and forward induction, by examining the limiting outcome of an evolutionary process driven by stochastic learning and (rare) mutations. We show that the limiting outcome in a class of extensive form games with perfect information always includes the subgame perfect equilibrium outcome, but also contains other outcomes if the subgame perfect outcome fails a (strong) local stability property. The evolutionary system imposes a forward induction requirement that strengthens van Damme's; it selects announcement proof equilibria in a class of cheap talk games; and it yields refinement results in some signaling games. The evolutionary model thus yields results that would often be interpreted as satisfying forward induction, but does not always impose sufficient discipline on actions and conjectures at unreached subgames to yield results consistent with backward induction.
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