Commitment to Cooperation and Peer Punishment: Its Evolution Tatsuya Sasaki, Isamu Okada, Satoshi Uchida and Xiaojie Chen This file includes: Supplementary Text, Sections S1 and S2 Supplementary Figures, Figure S1 S1. Replicator Dynamics in Donation Games with Deposit-Based Commitment We analyze the replicator dynamics in the case of deposit-based commitment to costly peer punishment. Let xS an...

Garay and Hofbauer (SIAM J. Math. Anal. 34 (2003)) proposed sufficient conditions for robust permanence and impermanence of the deterministic replicator dynamics. We reconsider these conditions in the context of the stochastic replicator dynamics, which is obtained from its deterministic analogue by introducing Brownian perturbations of payoffs. When the deterministic replicator dynamics is per...

In this paper we study the properties of complex systems based on replicator dynamics. Vector field analysis is used to reveal new properties of the dynamical system. Spectral problem has been considered and Lyaponov function has been derived from the algebraic properties of the system under consideration. New mathematical model with multi-agent interaction is developed and general properties o...

Many complex systems in mathematical biology and other areas can be described by the replicator equation. We show that solutions of a wide class of replicator equations minimize the KL-divergence of the initial and current distributions under time-dependent constraints, which in their turn, can be computed explicitly at every instant due to the system dynamics. Therefore, the Kullback principle...

We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed points of the dynamics and the Nash equilibria. Except for the special case of zero-sum games one finds a transition as a function of the so-called co-operati...

This article studies the replicator dynamics in the presence of shocks. I show that under these dynamics, strategies that do not survive the iterated deletion of strictly dominated strategies are eliminated in the long run, even in the presence of nonvanishing perturbations. I also give an example that shows that the stochastic dynamics in this article have equilibrium selection properties that...

Template-dependent replication at the molecular level is the basis of reproduction in nature. A detailed understanding of the peculiarities of the chemical reaction kinetics associated with replication processes is therefore an indispensible prerequisite for any understanding of evolution at the molecular level. Networks of interacting self-replicating species can give rise to a wealth of diffe...