Mathematical Game Theory

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What is new in game theory?

I went to the talk below on 9/2/2015.

Stabilityand selection in multiagent learning

Jeff S. Shamma

GeorgiaTech and KAUST

Recent years have seen significant interest in the area of multiagent ordistributed architecture control, with motivating applications ranging fromautonomous vehicle teams to communication networks to smart grid. The generalsetup is a collection of multiple decision-making elements interacting locally,perhaps striving to achieve a common collective objective. In multiagentlearning, agents dynamically adapt to the actions of other agents, therebyeffectively making the environment non-stationary from the perspective of anysingle agent. The resulting dynamics can exhibit behaviors ranging from chaosto convergence. This talk focuses on the two concerns of stability andselection---i.e., do agents converge, and if so, to what configurations? Wediscuss "stability" of population games through new connections betweenpassivity theory and evolutionary game theory. We discuss "selection"in evolutionary games using the notion of stochastic stability and demonstrateits broader applicability in various settings.

Bio: Jeff S. Shamma is the Julian T. Hightower Chairin Systems & Control (currently on leave) in the School of Electrical andComputer Engineering at the Georgia Institute of Technology (Georgia Tech) anda Professor of Electrical Engineering in the King Abdullah University ofScience and Technology (KAUST). He received a BS in Mechanical Engineering fromGeorgia Tech in 1983 and a PhD in Systems Science and Engineering from theMassachusetts Institute of Technology in 1988. He held faculty positions at theUniversity of Minnesota, University of Texas-Austin, and University ofCalifornia-Los Angeles. Prof. Shamma is a recipient of the NSF YoungInvestigator Award (1992), the American Automatic Control Council Donald P.Eckman Award (1996), and the Mohammed Dahleh Award (2013), and he is a Fellowof the IEEE (2006). Prof. Shamma's research is in the general area of feedbackcontrol and systems theory. His most recent research has been in decision andcontrol for distributed multiagent systems and the related topics of gametheory and network science, with applications to cyberphysical and societalnetwork systems.

Here are my take away from the talk:

1. For the past two decades, mathematical game theory have begun to pay attention to the dynamic and evolutionary aspects of games involving multiple players.Solution concept development seems to play a lesser role. Most papers stick to the Nash equilibrium as a solution concept

2. The dynamics studied are much more general than the differential equation based model as in differential games. Many are inspired or motivated by real life engineering development in social and communication networks where real people interact, and learning to adapt.

3. Thus, convergence to equilibria based on learning rules is a major topic of research.

4. Existence of different equilibria depending onthe use of different learning rules are also important.

5. These development can be viewed as the 6tharticle in my series of blog articles on mathematical game theory http://blog.sciencenet.cn/blog-1565-21891.html.