Evolutionary Stability in First Price Auctions

This paper studies the evolutionary stability of the unique Nash equilibrium of a first price sealed bid auction. It is shown that the Nash equilibrium is not asymptotically stable under payoff monotonic dynamics for arbitrary initial populations. In contrast, for some classes of bid functions, when the initial population includes a continuum of strategies around the equilibrium, the replicator dynamic does converge to the Nash equilibrium. Simulations are presented for the replicator and Brown–von Neumann–Nash (BNN) dynamics. They suggest that the convergence for the replicator dynamic is slow compared to that for the BNN dynamic.