Exploring Bounded Rationality in Game Theory

April 12, 2013, Webb 1100

Jeff Shamma

Georgia Tech, Electrical and Computer Engineering


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.

Speaker's Bio

Jeff Shamma is the Julian T. Hightower Chair in Systems & Control in  the School of Electrical and Computer Engineering at the Georgia Institute of Technology. Jeff received a BS in Mechanical Engineering from Georgia Tech in 1983 and a PhD in Systems Science and Engineering from MIT in 1988. Prior to returning to Georgia Tech in 2007, he held faculty positions at the University of Minnesota, UT Austin, and UCLA. Jeff is a recipient of the NSF Young Investigator Award (1992) and the American Automatic Control Council Donald P. Eckman Award (1996), and a Fellow of the IEEE (2006). He previously served on the Air Force Scientific Advisory Board (2008–2011) and is currently an Associate Editor for the IEEE Transactions on Cybernetics (2009–present) and Games (2012-present) and a Senior Editor for the newly formed IEEE Transactions on Control of Network Systems.