The Limitations of Equilibrium Concepts in Evolutionary Games

In evolutionary games, equilibrium concepts adapted from classical game theory—typically, refinements of the Nash equilibrium—are employed to identify the probable outcomes of evolutionary processes. Over the years, various negative results have been produced demonstrating limitations to each proposed refinement. These negative results rely on an undefined notion of evolutionary significance. We propose an explicit and novel definition of the notion of evolutionary significance in line with what is assumed in these results. This definition enables a comprehensive analysis of the limitations of the proposed equilibrium concepts. Taken together, the results show that even under favorable assumptions as to the underlying dynamics and stability concept—the replicator dynamics and asymptotic stability—all equilibrium concept makes errors of either omission or commission; typically both

The Limitations of Equilibrium Concepts in Evolutionary Games

In evolutionary games, equilibrium concepts adapted from classical game theory—typically, refinements of the Nash equilibrium—are employed to identify the probable outcomes of evolutionary processes. Over the years, various negative results have been produced demonstrating limitations to each proposed refinement. These negative results rely on an undefined notion of evolutionary significance. We propose an explicit and novel definition of the notion of evolutionary significance in line with what is assumed in these results. This definition enables a comprehensive analysis of the limitations of the proposed equilibrium concepts. Taken together, the results show that even under favorable assumptions as to the underlying dynamics and stability concept—the replicator dynamics and asymptotic stability—all equilibrium concept makes errors of either omission or commission; typically both

Selection-Mutation Dynamics of Signaling Games

We study the structure of the rest points of signaling games and their dynamic behavior under selection-mutation dynamics by taking the case of three signals as our canonical example. Many rest points of the replicator dynamics of signaling games are not isolated and, therefore, not robust under perturbations. However, some of them attract open sets of initial conditions. We prove the existence of certain rest points of the selection-mutation dynamics close to Nash equilibria of the signaling game and show that all but the perturbed rest points close to strict Nash equilibria are dynamically unstable. This is an important result for the evolution of signaling behavior, since it shows that the second-order forces that are governed by mutation can increase the chances of successful signaling