Dynamic Selection in Normal-Form Games

This paper investigates a class of dynamic selection processes for n-person normal-form games which includes the Brown-von Neumann-Nash dynamics. For (two-person) zero-sum games and for (n-person) potential games every limit set of these dynamics is a subset of the set of Nash-equilibria. Furthermore, under these dynamics the unique Nash-component of a zero-sum game is minimal asymptotically stable and for a potential game a smoothly connected component which is a local maximizer is minimal asymptotically stable.

[1]  Klaus Ritzberger,et al.  From evolutionary to strategic stability , 2000, J. Econ. Theory.

[2]  J. Hofbauer.  From Nash and Brown to Maynard Smith: Equilibria, Dynamics and ESS , 2001 .

[3]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Jeroen M. Swinkels.  Adjustment Dynamics and Rational Play in Games , 1993 .

[5]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[6]  J. Neumann,et al.  SOLUTIONS OF GAMES BY DIFFERENTIAL EQUATIONS , 1950 .

[7]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

[8]  J. Weibull,et al.  Evolutionary Selection in Normal-Form Games , 1995 .

[9]  S. Hart,et al.  Uncoupled Dynamics Cannot Lead to Nash Equilibrium ∗ , 2002 .

[10]  E. I. Vilkas,et al.  Axiomatic Definition of the Value of a Matrix Game , 1963 .

[11]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[12]  L. Shapley,et al.  REGULAR ARTICLEPotential Games , 1996 .

[13]  J. Jordan.  Three Problems in Learning Mixed-Strategy Nash Equilibria , 1993 .

[14]  S. Hart,et al.  Uncoupled Dynamics Do Not Lead to Nash Equilibrium , 2003 .

[15]  D. Friedman.  EVOLUTIONARY GAMES IN ECONOMICS , 1991 .

[16]  P. Taylor.  Evolutionarily stable strategies with two types of player , 1979, Journal of Applied Probability.

[17]  Fabrizio Germano,et al.  On (un)knots and dynamics in games , 2002, Games Econ. Behav..

[18]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

[19]  L. Samuelson,et al.  Evolutionary Stability in Asymmetric Games , 1992 .

[20]  Josef Hofbauer,et al.  The theory of evolution and dynamical systems , 1988 .

[21]  J. Neumann.  Zur Theorie der Gesellschaftsspiele , 1928 .