Figure 3.

An additional reward in biological auctions results in a qualitatively different equilibrium. The mixed strategy equilibrium changes with the number of participants, n, in an auction. (a) Mixed equilibrium functions have a negative exponential shape in biological all-pay auctions with one reward. (b) By contrast, in biological all-pay auctions with two rewards, the mixed equilibrium functions can also be increasing or U-shaped functions. The U-shaped mixed equilibria suggest some specialization among the individuals.