Georgia Institute of Technology College of Sciences

The concept of "strategic equilibrium," where each player's strategy is optimal against those of the other players, was introduced by John Nash in his Ph.D. thesis in 1950. Throughout the years, Nash equilibrium has had a most significant impact in economics and many other areas. However, more than 60 years later, its dynamic foundations - how are equilibria reached in long-term interactions - are still not well established. In this talk we will overview a body of work of the last decade on dynamical systems in multi-player environments. On the one hand, the natural informational restriction that each participant may not know the payoffs and utilities of the other participants - "uncoupledness" - turns out to severely limit the possibilities to converge to Nash equilibria. On the other hand, there are simple adaptive heuristics - such as "regret matching" - that lead in the long run to correlated equilibria, a concept that embodies full rationality. We will also mention connections to behavioral and neurobiological studies, to computer science concepts, and to engineering applications.