Paul Rhode and Mark Stegeman

"Non-Nash equilibria of Darwinian dynamics with applications to duopoly "

JEL codes: C73; D43; L21
Keywords:  Duopoly; evolution, revenue maximization; imitation; relative payoffs

Abstract: Consider a symmetric, differentiated duopoly. If strategy choices, in the repeated game, follow a stochastic Darwinian process, then they cluster around a strategy profile that is typically not a one-shot Nash equilibrium. This profile is invariant under a broad class of transformations of strategy space (e.g., Bertrand vs. Cournot); this implies that mixing imitative and rational decision-makers can produce purely imitative outcomes. The evolution of objectives consistently distorts behavior toward revenue maximization and the distortion increases in "good times" of high demand and low costs. We generalize the results beyond duopoly to symmetric, two-player games.