human language, over its evolutionary history, has emerged as one of the fundamental defining characteristic of the modern man. however, this milestone evolutionary process through natural selection has not left any ’linguistic fossils’ that may enable us to trace back the actual course of development of language and its establishment in human societies. lacking analytical tools to fathom the cr...

Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system initially has a large number of species (diversity). The extinction dynamics shows several significant features such as a power law in basin size distribution, indu...

This paper analyzes the dynamic stability of moral codes in a two population trust game. Guided by a moral code, members of one population, the Trustors, are willing to punish members of the other population, the Trustees, who defect. Under replicator dynamics, adherence to the moral code has unstable oscillations around an interior Nash Equilibrium (NE), but under smoothed best response dynami...

This chapter begins with some basic terminology, introducing elementary game theoretic notions such as payoff, strategy, best reply, Nash equilibrium pairs etc. Players who use strategies which are in Nash equilibrium have no incentive to deviate unilaterally. Next, a population viewpoint is introduced. Players meet randomly, interact according to their strategies, and obtain a payoff. This pay...

This paper studies how a matching rule affects the evolution of fairness in an ultimatum mini game. Gale et al. [1995] show that only selfish behaviour survives in the deterministic replicator dynamics under the random matching rule. In contrast, this paper shows that, under an assortative matching rule, the fair behaviour may survive at an asymptotically stable state.

Human language, over its evolutionary history, has emerged as one of the fundamental defining characteristic of the modern man. However, this milestone evolutionary process through natural selection has not left any ’linguistic fossils’ that may enable us to trace back the actual course of development of language and its establishment in human societies. Lacking analytical tools to fathom the cr...

The replicator dynamics of players choosing either mixed or pure strategies are usually regarded as equivalent, as long as strategies are played with identical frequencies. In this paper we show that a population of pure strategies can be invaded by mixed strategies in any two-player game with equilibrium coexistence upon the addition of an arbitrarily small amount of noise in the replication p...

It is shown that, under the replicator dynamics, all strategies played in correlated equilibrium may be eliminated, so that only strategies with zero marginal probability in all correlated equilibria survive. This occurs in particular in a family of 4 × 4 games built by adding a strategy to a Rock-Paper-Scissors game.  2006 Elsevier Inc. All rights reserved. JEL classification: C73

We simulate the prisoner’s dilemma and hawk-dove games on a real social acquaintance network. Using a discrete analogue of replicator dynamics, we show that surprisingly high levels of cooperation can be achieved, contrary to what happens in unstructured mixing populations. Moreover, we empirically show that cooperation in this network is stable with respect to invasion by defectors.

We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T . Taking T as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems and present an analysis of the resulting limit cycles using Lindstedt’s me...