William H. Sandholm is a contemporary economist and game theorist at the University of Wisconsin–Madison, specializing in evolutionary game theory and population games. His work rigorously examines the dynamic stability properties of evolutionary processes, including when and why replicator dynamics fail to converge to equilibrium. He is best known for his comprehensive treatment of population games and their relationship to Nash and evolutionarily stable equilibria.
Authored Population Games and Evolutionary Dynamics (2010), a foundational text in evolutionary game theory
Demonstrated conditions under which replicator dynamics fail to converge to evolutionarily stable states
Developed the theory of potential games and their stability properties under evolutionary dynamics
Extended evolutionary game theory to continuous population and large-game settings
Contributed formal foundations for connecting individual decision rules to aggregate population dynamics