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Efficiency and Competition in the Long Run: The Survival of the Unfit

By Gábor Virág

Abstract

A dynamic incomplete information game is analyzed where each period the current incumbent competes against a randomly assigned entrant by expanding effort to stay in the competition. The stage game is modelled as an all pay auction with private valuations for the prize. We focus on equilibria where the market’s belief about the current incumbent’s type is stationary and the players follow stationary strategies when choosing their effort levels. The main result is that even if the competition is very fierce (i.e. the entrants arrive very frequently), dynamic efficiency is not obtained. The reason is that the entrant plays more aggressively than the incumbent, which makes it possible that an entrant with a lower type wins against an incumbent with a higher type. This result also holds if the competition takes the form of a first price auction or any other form where the entrant is more aggressive than the incumbent. In an example we show that if the incumbent is challenged more often, then the equilibrium type of the incumbent is higher on average. When the value of the prize is the same for all players (the common value case) the equilibrium rent of the bidders is fully dissipated as the incumbent is challenged infinitely often. Therefore, full rent dissipation is possible when the future becomes important, a contribution to the public choice literature. The main technical contribution lies in a new method of showing the existence of stationary equilibrium in incomplete information games

Year: 2007
OAI identifier: oai:CiteSeerX.psu:10.1.1.177.989
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