arXiv subjects

Sylvain Gibaud

Publications and source records attributed to Sylvain Gibaud.

3 recordsLinked to original sources

arXiv2021

Accumulation of individual fitness or wealth as a population game

The accumulation of individual fitness or wealth is modelled as a population game in which pairs of individuals are recurrently and randomly matched to play a game over a resource. In addition, all individuals have random access to a constant background resource, and their fitness or wealth depreciates over time. For brevity we focus on the well-known Hawk-Dove game. In the base-line model, the probability of winning a fight (that is, when both play Hawk) is the same for both parties. In an extended version, the individual with higher current fitness or wealth has a higher probability of winning. Analytical results are given for the fitness/wealth distribution at any given time, for the evolution of average fitness/wealth over time, and for the asymptotics with respect to time and population size. Long-run average fitness/wealth is non-monotonic in the value of the resource, thus providing a potential explanation of the curse of the riches.

physics.soc-ph↗

arXiv2017

Demographic Prisoner's Dilemma : a probabilistic framework

We put a probabilistic framework on the Demographic Prisoner's Dilemma. In this model, cooperating and defecting individuals are placed on a torus to move and play prisoner's dilemma game, if they are on the same site. Each individual accumulates its payoff into a quantity called wealth. If an individual becomes wealthy enough, it can have an offspring. If its wealth becomes negative, it disappears. In this framework we prove that if if the Sucker payoff is far greater than the Reward then for all initial state almost surely all cooperators will die. Moreover if the Temptation payoff (resp. Reward) are far greater than the Punition (resp. Sucker payoff) then for all initial state with positive probability cooperators and defectors live \emph{ad vitam eternam}. We also set a Mean Field model on the demographic prisoner's dilemma and prove on a linearized version of the Mean Field model that with weaker assumptions with positive probability Cooperators live \emph{ad vitam eternam}.

math.PR↗

arXiv2016

Spatialized Evolutionary prisoner's dilemma: Homogenization and propagation of chaos

Epstein introduced an agent-based model called Demographic Prisoner's dilemma. He shows, via simulations, that cooperation in this spatial evolutionary repeated game can be sustained. In order to do proves, we put on this model a particle system framework in order to prove the convergence of the spatial model to a random matching model, using homogenization techniques. Then we prove the convergence of the random matching model to a mean field model, using propagation of chaos techniques.

math.PR↗