Evolutionary-game theory has been developed as a mathematical framework to study the interaction among rational biological agents in a population [152]. In evolutionary-game theory, the agent adapts (i.e., evolves) the chosen strategy based on its fitness (i.e., payoff). In this way, both static and dynamic behavior (e.g., equilibrium) of the game can be analyzed.

Evolutionary-game theory has the following advantages over the traditional non-cooperative game theory we have studied in the previous chapters:

• As we have seen, the Nash equilibrium is the most common solution concept for non-cooperative games. An N-tuple of strategies in an N-player game is said to be in Nash equilibrium if an agent (player) cannot improve his payoff by moving to another strategy, given that the other players stay with their strategies at Nash equilibrium. Specifically, the strategy of a player at Nash equilibrium is the best response to the strategies of the other players, again at Nash equilibrium. However, the Nash equilibrium is not necessarily efficient, as it would be possible for all players to benefit from a collective behavior. Also, there could be multiple Nash equilibria in a game, and if the agent is restricted to adopting only pure strategies, the Nash equilibrium may not exist. In this case, the solution of the evolutionary game (i.e., evolutionarily stable strategies (ESS) or evolutionary equilibrium) can serve as a refinement to the Nash equilibrium, especially when multiple Nash equilibria exist.

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