Biological auctions with multiple rewards

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.

The War against the Taliban

Operation Enduring Freedom was hampered by a chronic shortage of attack helicopters available to ISAF forces in Afghanistan. Tactical operations into Taliban-held territory were launched even though close air support capable of dealing with “danger close” situations could not be assigned in advance. It led to significant ISAF casualties if the Taliban decided to fight back rather than withdraw. Departing from a Clausewitz-style, i.e. second-mover advantage, mixed-strategy equilibrium and taking account of the “Irregular Warfare” nature of the pay-offs, the paper looks into the existence of strategic moves. In particular, as playing a mixed strategy if rotary wing air support is unavailable merely incentivises a more aggressive Taliban response to any kind of operation due to the information asymmetry, it is argued that by moving away from the mixed-strategy equilibrium ISAF casualties in properly supported operations could be reduced, thus handing a first-mover advantage to ISAF.

Mixed Equilibrium in a Pure Location Game: The Case of n≥4$$n \ge 4$$ Firms

The Hotelling game of pure location allows interpretations in spatial competition, political theory, and strategic forecasting. In this paper, the doubly symmetric mixed-strategy equilibrium for