Game Theoretic Models

Abstract

Abstract Thus far, frequency-dependent interactions have been assumed not to be present, although they are undoubtedly important in nature (Clarke 1969, 1979; Endler 1986, 1988; Sherratt and Harvey 1993; Sinervo and Calsbeek 2006; Bond 2007). Putative examples of traits under frequency-dependent selection in natural populations are resource polymorphisms (Smith and Skulason 1996), mating polymorphisms (Sinervo and Lively 1996), color polymorphisms (Bond 2007), plant defenses (NÙñez-Farfa´n et al. 2007), and blood group antigen genes (Fumagalli et al. 2009). Analysis of models involving frequency-dependence is the domain of game theory. In a general sense, game theory is concerned with interactions between individuals: The basic scenario is one in which two individuals, called the players, meet and interact and either suffer a loss in fitness or an increase in fitness, called in either case the payoff. The important element of game theory is the Payoff matrix, which designates the increase or decrease in fitness to each player. Analysis consists in locating the Evolutionarily Stable Strategy (ESS), which, as previously noted, is defined as that strategy (or phenotype) which if adopted by all members of a population cannot be invaded by a mutant strategy (or phenotype) (Maynard Smith 1982). In general, game theoretic models are frequency-dependent but this is not an essential element of such models. Kokko (2007) gives an example of a frequency-independent model that involves the optimal growth rate of two neighboring trees. This case is considered in detail in Scenario 1. Here I shall examine the general elements of the analysis.