Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied “heavy ball with friction” optimization method. By exploiting a well-known link between the replicator dynamics and the Shahshahani geometry on the space of mixed strategies, the dynamics are stated in a Riemannian geometric framew...

The replicator-mutator equations from evolutionary dynamics serve as a model for the evolution of language, behavioral dynamics in social networks, and decision-making dynamics in networked multi-agent systems. Analysis of the stable equilibria of these dynamics has been a focus in the literature, where symmetry in fitness functions is typically assumed. We explore asymmetry in fitness and show...

We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed due to non-uniqueness of solutions, but is amenable to a natural selection principle that picks a unique solution. The model allows us to make specific statem...

The paper explores the implications of melioration learning—an empirically significant variant of reinforcement learning—for game theory. We show that in games with invariable pay-offs melioration learning converges to Nash equilibria in a way similar to the replicator dynamics. Since melioration learning is known to deviate from optimizing behavior when an action’s rewards decrease with increa...

Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multi-player replicator dynamics in a constant environment. The two-player terms correspond to the time-averaged payoffs, while the three and four-player terms arise from the adaptation of the morphs to their varying environment. Such mult...

This paper is the ...rst attempt of applying the Easley Rustichini (Econometrica, 1999, 5) Replicator dynamics framework to simple one-period security markets, with a ...nite set of actions for traders. In two and three action environments, the examples developed here show that even with very simple (objective) state spaces and straightforward Replicator Dynamics, prices may not necessarily con...

Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multiplayer replicator dynamics in a constant environment. The two-player terms correspond to the time-averaged payoffs, while the three- and four-player terms arise from the adaptation of the morphs to their varying environment. Such mult...

We derive both the finite and infinite population spatial replicator dynamics as fluid limit of a stochastic cellular automaton. The is identical to model used by Vickers our derivation justifies addition diffusion replicator. form generalizes results Durett Levin on games. study differences in two equations they pertain one-dimensional rock-paper-scissors game.

This paper proposes and analyzes a model of stochastic evolution in finite populations. The expected motion in our model resembles the standard replicator dynamic when the population is large, but is qualitatively different when the population size is small, due to the difference between maximizing payoff and maximizing relative payoff. Moreover, even in large populations the asymptotic behavio...

We analyze evolutionary games with replicator dynamics that have frequency dependent stage games. In such an evolutionary game, the payoffs of a strategy at any point in time are functions of the strategy shares given by the players’ strategy choices at that time. This framework is suited to model feedback effects between population variables and individual incentives, indirect network effects,...