Evolutionary Selection Dynamics Research Articles

Evolution and correlated equilibrium

Given a normal form game and a signal generating process, we construct an expanded game in the spirit of Aumann (Econometrica 55(1):1–18, 1987) in which agents condition their strategic choices on perceived signals. We collect results on evolutionary selection dynamics of Ritzberger and Weibull (Econometrica 63(6):1371–1399, 1995), Swinkels (J Econ Theory 57(2):306–332, 1992b) and Samuelson and Zhang (J Econ Theory 57:363–391, 1992) to apply them to normal form games with payoff irrelevant signals. We suggest a selection dynamic for the evolution of signals and characterize the set of signal distributions and induced payoffs for sets that are asymptotically stable with respect to this evolutionary selection on signals.

IS MORE MEMORY IN EVOLUTIONARY SELECTION (DE)STABILIZING?

We investigate the effects of memory on the stability of evolutionary selection dynamics based on a multinomial logit model in a simple asset pricing model with heterogeneous beliefs. Whether memory is stabilizing or destabilizing depends in general on three key factors: (1) whether or not the weights on past observations are normalized; (2) the ecology or composition of forecasting rules, in particular the average trend extrapolation factor and the spread or diversity in biased forecasts; and (3) whether or not costs for information gathering of economic fundamentals have to be incurred.

Evolutionary Selection against Dominated Strategies

A class of evolutionary selection dynamics is defined, and the defining property, convex monotonicity, is shown to be sufficient and essentially necessary for the elimination of strictly dominated pure strategies. More precisely: (1) all strictly dominated strategies are eliminated along all interior solutions in all convex monotonic dynamics, and (2) for all selection dynamics where the pure-strategy growth rates are functions of their current payoffs, violation of convex monotonicity implies that there exist games with strictly dominated strategies that survive along a large set of interior solutions. The class of convex monotonic dynamics is shown to contain certain selection dynamics that arise in models of social evolution by way of imitation.Journal of Economic LiteratureClassification Number: C72.

Evolutionary Selection in Normal-Form Games

This paper investigates stability properties of evolutionary selection dynamics in normal-form games. The analysis is focused on deterministic dynamics in continuous time and on asymptotic stability of sets of population states, more precisely of faces of the mixed-strategy space. The main result is a characterization of those faces which are asymptotically stable in all dynamics from a certain class, and we show that every such face contains an essential component of the set of Nash equilibria, and hence a strategically stable set in the sense of Kohlberg and Mertens (1986).

The ‘as if’ approach to game theory: Three positive results and four obstacles

The usual justifications of non-cooperative solution criteria are rationalistic in nature, building on individual rationality and expectation-coordination postulates. In contrast, the ‘as if’ approach to game-theoretic rationality is evolutionary, arguing that even if strategically interacting agents do not meet these epistemic conditions, their long-run aggregate behavior will nevertheless conform with them because of the workings of biological or social selection processes. The present essay discusses three implications of evolutionary selection dynamics in favour of the ‘as if’ paradigm, and four potential obstacles to the general validity of these implications.