Adapting Game Theory To Evolutionary Games
On reflection Maynard Smith realised that in an evolutionary version of Game Theory it is not really a requirement that players be rational – it is only required that they have a strategy. The results of the game will test how good that strategy is. That is what Evolution does – it tests alternative strategies for the ability to survive and reproduce. In Biology, strategies are genetically inherited traits that control an individuals action – and strategies are algorithmic – just like computer programs. The key point in the Evolutionary Game Theory model is that the success of a strategy is not just determined by how good the strategy is in itself, it is a question on how good the strategy is in the presence of other alternative strategies, and on the frequency that other strategies are employed within a competing population. It is also a question of how good a strategy plays against itself, because in the biological world a successful strategy will eventually dominate a population and competing individuals in it end up facing identical strategies to their own.
The object of the evolutionary game is to become more fit than competitors – to produce as many replicas of oneself as one can and the payoff is in units of Fitness (relative worth in being able to reproduce). It is always a multi-player game with a very large population of competitors. Rules describe the contest as in classical Game Theory but for evolutionary games rules include the element of replicator dynamics, in other words the general rules say exactly how the fitter players will spawn more replicas of themselves into the population and the less fit will be culled out of the player population (expressed in a Replicator Equation). The replicator dynamics in essence models the heredity mechanism, but for simplicity leaves out mutation. Similarly, Evolutionary Game Theory only uses asexual reproduction for the sake of simplicity. Games are run repetitively with no terminating conditions. The results that are studied include the dynamics of changes in the population, the success/survival of strategies and any equilibrium states reached in a competing. Unlike classical Game Theory players do not choose their strategy or have the ability to change it, they are born with that strategy and their offspring will inherit that same identical strategy.
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