Algorithmic Game Theory: Computational Evolutionary Game Theory

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Abstract

This chapter examines the intersection of evolutionary game theory and theoretical computer science. We will show how techniques from each field can be used to answer fundamental questions in the other. In addition, we will analyze a model that arises by combining ideas from both fields. First, we describe the classical model of evolutionary game theory and analyze the computational complexity of its central equilibrium concept. Doing so involves applying techniques from complexity theory to the problem of finding a game-theoretic equilibrium. Second, we show how agents using imitative dynamics, often considered in evolutionary game-theory, converge to an equilibrium in a routing game. This is an instance of an evolutionary game-theoretic concept providing an algorithm for finding an equilibrium. Third, we generalize the classical model of evolutionary game theory to a graph-theoretic setting. Finally, this chapter concludes with directions for future research. Taken as a whole, this chapter describes how the fields of theoretical computer science and evolutionary game theory can inform each other. 29.1 Evolutionary Game Theory Classical evolutionary game theory models organisms in a population interacting and competing for resources. The classical model assumes that the population is infinite. It models interaction by choosing two organisms uniformly at random, who then play a 2-player, symmetric game. The payoffs that these organisms earn represent an increase or a loss in fitness, which either helps or hinders the organisms ability to reproduce. In this model, when an organism reproduces, it does so by making an exact replica of itself, thus a child will adopt the same strategy as its parent. One of the fundamental goals of evolutionary game theory is to characterize which strategies are resilient to small mutant invasions. In the classical model of evolutionary game theory, a large fraction of the population, called the incumbents, all adopt the same strategy. The rest of the population, called the mutants, all adopt some other strategy. The incumbent strategy is considered to be stable if the incumbents retain a higher fitness than the mutants. Since the incumbents are more fit, they reproduce