Jeff Shamma (Georgia Institute of Technology)
Exploring Bounded Rationality in Game Theory
Solution concepts in game theory, such as Nash equilibrium, traditionally ignore the processes and associated computational costs of how agents go about deriving strategies. The notion of bounded rationality seeks to address such issues through a variety of alternative formulations. This talk presents two settings motivated by bounded rationality. First, we consider incomplete information dynamic games. A Nash equilibrium in this setting requires each agent to solve a partially observed Markov decision problem that requires knowledge of a possibly extensive environment as well as the strategies of other agents. We introduce an alternative notion, called “empirical evidence equilibria”, in which agents form naive models with available measurements. These models reflect an agent’s limited awareness of its surroundings, and the level of naivety or sophistication can be different for each agent. We show that such equilibria are guaranteed to exist for any profile of agent rationality and compare the concept to mean field equilibria. Second, we investigate learning in evolutionary games, where the focus is on the dynamic behaviors away from equilibrium rather than characterizations of equilibrium. A lingering issue in this framework is what constitutes “natural” versus “concocted” learning rules. Building on prior work on so-called “stable games”, we introduce a class of dynamics motivated by control theoretic passivity theory. We show how passivity theory both captures and extends selected prior work on evolutionary games and offers a candidate for what constitutes natural learning.