title: Biological auctions with multiple rewards.
abstract: The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.
authors.affiliation: IST Austria (Institute of Science and Technology Austria), Am Campus 1, Klosterneuburg 3400, Austria jreiter@ist.ac.at.
authors.forename: Johannes G
authors.identifier: http://orcid.org/0000-0002-0170-7353
authors.initials: JG
authors.lastname: Reiter
authors.affiliation: IST Austria (Institute of Science and Technology Austria), Am Campus 1, Klosterneuburg 3400, Austria.
authors.forename: Ayush
authors.initials: A
authors.lastname: Kanodia
authors.affiliation: IST Austria (Institute of Science and Technology Austria), Am Campus 1, Klosterneuburg 3400, Austria.
authors.forename: Raghav
authors.initials: R
authors.lastname: Gupta
authors.affiliation: Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, 1 Brattle Square, Cambridge, MA 02138, USA.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
authors.affiliation: IST Austria (Institute of Science and Technology Austria), Am Campus 1, Klosterneuburg 3400, Austria.
authors.forename: Krishnendu
authors.initials: K
authors.lastname: Chatterjee
mesh_terms: D005075:Biological Evolution; D003163:Competitive Behavior; D005716:Game Theory; D056084:Genetic Fitness; D008954:Models, Biological; D012098:Reproduction; D012201:Reward
keywords: auction theory; evolutionarily stable strategy; evolutionary dynamics; evolutionary game theory