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University of Hawaii

Electrical Engineering

Refinements of Nash Equilibrium and Their Computation

Date: 2019-05-31           Add to Google Calendar
Time: 11:00am - 12:00pm
Location: Holmes Hall 389
Speaker: Dr Chuangyin Dang, Acting Head and Professor in Department of Systems Engineering and Engineering Management, City University of Hong Kong

As a powerful mechanism for conflict modeling and analysis, game theory has been successfully applied in a variety of fields. The concept of Nash equilibrium is one of the most important and elegant ideas in game theory. Nevertheless, a game can have many Nash equilibria and some of these equilibria may be inconsistent with our intuitive notions about what should be the outcome of a game. To reduce this ambiguity and eliminate some of these counterintuitive equilibria, the concepts of perfect equilibrium and proper equilibrium were introduced in game theory. The introductions of perfect equilibrium and proper equilibrium have significantly advanced the development of game theory and its applications. The computation of perfect equilibrium and proper equilibrium plays an important role in the applications of game theory. This talk will present our recent developments of smooth path-following approaches to computing a perfect equilibrium and a proper equilibrium of a finite n-person game in normal form. The basic idea of the approaches is to formulate an artificial game by incorporating a quadratic term into each player’s payoff function with a smooth nonlinear function of an extra variable. The emphasis is on fully exploiting differentiability of the problem. The equilibrium system of the artificial game establishes the existence of a smooth path that starts from a totally mixed strategy profile and leads to a perfect equilibrium or proper equilibrium. An efficient predictor-corrector method is adapted for numerically following the path. Numerical results show that the approaches are effective and efficient.

Prof. Chuangyin Dang received PhD in Operations Research/Economics from Tilburg University, The Netherlands, in 1991. He currently is Acting Head and Professor in Department of Systems Engineering and Engineering Management, City University of Hong Kong. Prior to this, Prof. Dang held faculty positions at the University of California at Davis, Delft University of Technology, and the University of Auckland, and was research fellow at the Cowles Foundation for Research in Economics, Yale University. He is best known for the inventions of the D1-triangulation of the Euclidean space and simplicial path-following methods for integer programming. Prof. Dang received Outstanding Research Achievements Award from Tilburg University in 1990. His research interests include game theory and applications, systems modeling and optimization, economics and computation, pattern recognition and machine learning. His recent research interests include energy systems, intelligent transportation systems, optimization, algorithms, and understanding the benefit of prediction in system design.