Replicator Dynamics

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Replicator dynamics track changing population shares on a simplex: strategies or features that perform better than the average tend to grow, while weaker ones shrink. Researchers use evolutionary game theory to study equilibria and stability, extend the equations to delayed or learning agents, and connect them to optimization methods such as majorization-minimization. Applications include social norms and coordination in games, feature weighting, graph optimization, and competitive routing in associative memory. A central tension is that convergence guarantees depend on assumptions about fitness, transfer, and delay, and mathematical persistence alone does not establish that an outcome is fair or authorized.

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Bayesian Replicator Dynamics and the Inversion of Strict Dominance in Bimatrix Games
Oct 26, 2026Jaime Ruiz-Serra, Nihat Ay, Michael HarréGame Theory Replicator Dynamics
Centre for Complex Systems, The University of Sydney, Sydney, Australia · Institute for Data Science Foundations, Hamburg University of Technology, Hamburg, Germany
Delayed Repression and Emergent Instability in Adaptive Multi-Agent Systems
May 28, 2026Igor ItkinDynamical Systems Replicator Dynamics
Independent Researcher, Tel Aviv, Israel
Evolutionary Data Theory: On the Similarities between Data Problems and Evolutionary Games
May 26, 2026Philipp WissgottReplicator Dynamics
danube.ai solutions gmbh, 1040 Vienna, Austria
The fitness landscape of social norms in social dilemmas
May 13, 2026Maximilian Puelma TouzelSocial Dilemmas Game Theory
Mila - Quebec AI Institute Montréal, Canada
A general classification of the replication dynamics with a unique fixed point in the interior of simplex $S_N$
May 11, 2026Hongju Daisy Chen, Bin Yi, Zhanshan Sam MaDynamical Systems Game Theory
School of Mathematics and Statistics, Guilin University of Technology, Guilin, Guangxi, China · Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin, Guangxi, China · Computational Biology and Medical Ecology Lab Biostatistics and Image Genetics Lab Kunming Institute of Zoology, Chinese Academy of Sciences, Kunming, China +2
Graph Normalization: Fast Binarizing Dynamics for Differentiable MWIS
May 6, 2026Laurent GuiguesDynamical Systems Replicator Dynamics
Emergent Self-Attention from Astrocyte-Gated Associative Memory Dynamics
Apr 28, 2026Arnau Vivet, Alex ArenasSoftmax Attention Dynamical Systems
1Departament d’Enginyeria Inform`atica i Matem`atiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain · 2Complexity Science Hub Vienna, Metternichgasse 8, 1030 Vienna, Austria
The Axiom of Consent: Authorization, Friction, and Multi-Agent Coordination
Jan 10, 2026Murad FarzullaMulti-Agent Coordination Replicator Dynamics
Dissensus, London, UK · King’s College London, London, UK
The Replicator-Optimization Mechanism: A Scale-Relative Formalism for Persistence-Conditioned Dynamics with a Conditional Consent-Friction Instantiation
Jan 10, 2026Murad FarzullaDynamical Systems Replicator Dynamics
Dissensus, London, UK · King’s College London, London, UK
Feature weighting for data analysis via evolutionary simulation
Nov 9, 2025Aris Daniilidis, Alberto Domínguez Corella, Philipp WissgottReplicator Dynamics Importance Weighting
Institut für Stochastik und Wirtschaftsmathematik, Variational Analysis, Dynamics and Operations Research Unit E105-04, Technische Universität Wien, Wiedner Hauptstraße 8, 1040 Vienna, Austria · Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstraße 36, A-8010 Graz, Austria · danube.ai solutions gmbh, 1040 Vienna, Austria

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Bayesian Replicator Dynamics and the Inversion of Strict Dominance in Bimatrix Games

Jaime Ruiz-Serra, Nihat Ay, Michael Harré

Centre for Complex Systems, The University of Sydney, Sydney, Australia · Institute for Data Science Foundations, Hamburg University of Technology, Hamburg, Germany

Game Theory Replicator Dynamics Evolutionary Game Theory

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Replicator dynamics, the central model of evolutionary game theory, describe populations evolving under selection and agents learning by trial and error. They also admit a third use: continuous-time Bayesian inference, in which an agent planning against an opponent accumulates evidence for each candidate strategy. Here we show that this use divides all two-player games into two classes. With the standard expected-utility payoff, the dynamics can be expressed as Bayesian updating only in games (with any number of actions) where no player has a dominant strategy. The logarithmic payoff of Ay and Erb admits the Bayesian representation in every game. Coordination, anti-coordination, and cyclic games share qualitative dynamics under both payoff definitions, with equilibria displaced and selection thresholds shifted. In contrast, the flows of every game with a dominant strategy are reversed between the payoff definitions, with the strictly dominant strategy eliminated under logarithmic payoffs. Cooperation therefore emerges in the Prisoner's Dilemma, and games of common interest converge to mutual defection. For two-action games the classification is complete and rests on an exact Hamiltonian structure shared by both payoff definitions. The structure gives a behavioural test: cycles in the classic Matching Pennies game have amplitude-independent period (isochronous) under logarithmic payoffs, but not under expected utility. Logarithmic evidence integration thus determines which strategic outcomes dynamical selection can reach, wherever learning approximates Bayesian updating.