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CS 364 A : Algorithmic Game Theory Lecture # 16 : Best-Response Dynamics ∗

Affirmative answers to these questions are important because they justify equilibrium analysis. Properties of equilibria, such as a near-optimal objective function value, are not obviously relevant when players fail to find one. More generally, proving that natural learning algorithms converge quickly to an equilibrium lends plausibility to the predictive power of an equilibrium concept. To reason about the three questions above, we require a behavioral model — “dynamics” — for players when not at an equilibrium. Thus far, we’ve just assumed that equilibria persist and that non-equilibria don’t. This lecture focuses on variations of “best-response dynamics,” while the next two lectures study dynamics based on regret-minimization. No concrete model of learning will be fully convincing. We aspire toward simple and natural learning algorithms that lead to concrete and non-trivial predictions. Ideally, we would like to reach the same conclusion via multiple different learning processes. Then, even though we might not literally believe in any of the specific learning algorithms, we can have some confidence that the conclusion is robust, and not an artifact of the details of a particular learning process.