## Evolutionary Game Theory

Evolutionary game theory (EGT) is the application of game theory to games in which players interact, and change their strategy over time in response. dependent strategy evolution in populations. EGT differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibria.

Each player makes individual decisions, and the resulting payoff matrix relies upon the individual decisions of all the players. As a result, an important question in EGT is predicting the behaviour of other players engaged in any given game.

In Smith's and Price's paper, “The Logic of Animal Conflict,” a computer model was used to show why animals had not adapted a “total war” strategy. Adaptations for males focused on maximising their ability to compete with each other in order to maximise their dominance over a territory and better compete for mates. Using game theory, they were able to test a variety of evolutionary strategies to see which one emerged with the highest average payoff, explaining why animals have only evolved “limited war” strategy, in which risk of serious injury is low.

For EGT to be applicable to organisms, they cannot be following a set of random rules, but rather a specific strategy that responds to specific pressures. The value of any particular strategy is always in relation to an organism’s environment. When applied to an evolutionary context, a payoff for an outcome of a game is analogous to the fitness of an organism.

The Model assumes large populations who interact in randomly matched pairs in repeated games. The game is symmetric in two senses. The first is that players have the same set of strategies to choose from and the payoff for strategy is the same for any player or organism, irrespective of the features of the other player or organism who chooses an alternative strategy.

An important feature of the set of models under the umbrella of evolutionary game theory is repetition. If the games were not repeated, these EGT models would not be able to provide any insight into adaptive behaviours and strategies due tithe dynamic nature of the mechanisms of evolution. Further, this biological application is meaningful for economics because it provides an understanding of the adjustments that occur between two equilibrium. While game theory provides a framework within which biologists can learn and understand organisms, the observation of evolution and how these strategies are applied helps economics illuminate processes.

A strategy which can survive all "mutant" strategies is considered evolutionary stable. In the context of animal behaviour, this usually means such strategies are programmed and heavily influenced by genetics, thus making any player or organism's strategy determined by these biological factors.

The successful application of game theory to evolution has brought further insights to human behaviour. Whereas game theory traditionally assumes rational actors, in the real world this does not always describe human behaviour. EGT has predictedbehaviors in animals where strong assumptions of rationality cannot be made.

The common methodology to study the evolutionary dynamics in games is through replicator equations. These replicator equations in the context of evolutionary biology shows the growth rate of the proportion of organisms using a certain strategy and that rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole. Continuous replicator equations assume infinite populations, continuous time,complete mixing and that strategies breed true. The attractors(stable fixed points) of the equations are equivalent with evolutionarily stable states.

Evolutionary game theory has been successfully applied to many areas of evolutionary biology with a recent development in the area of co-evolution. In a paper by Carl Bergstrom and Michael Lachmann, they successfully apply evolutionary game theory models to understand the division of benefits in mutualistic interactions between organisms. Darwinian assumptions about fitness are modelled using replicator dynamics to show that the organism evolving at a slower rate in a mutualistic relationship will gain a disproportionately high share of the benefits or payoffs. This application of EGT provided an interesting and perhaps unexpected twist on the Red Queen Hypothesis which concludes evolution favored faster rates of evolution.