Multilevel selection has been indicated as an essential factor for the evolution of complexity in interacting RNA-like replicator systems. There are two types of multilevel selection mechanisms: implicit and explicit. For implicit multilevel selection, spatial self-organization of replicator populations has been suggested, which leads to higher level selection among emergent mesoscopic spatial ...

In (Viossat, 2006, “The replicator dynamics does not lead to correlated equilibria”, forthcoming in Games and Economic Behavior), it was shown that the replicator dynamics may eliminate all pure strategies used in correlated equilibrium, so that only strategies that do not take part in any correlated equilibrium remain. Here, we generalize this result by showing that it holds for an open set of...

Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through environment-mediated interactions. An application to rock-scissors-paper game inte...

We study a class of evolutionary game dynamics under which the population state moves in the direction that agrees most closely with current payoffs. This agreement is defined by means of a Riemannian metric which imposes a geometric structure on the set of population states. By supplying microfoundations for our dynamics, we show that the choice of geometry provides a state-dependent but payof...

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...

We propose a simple model of network co–evolution in a game–dynamical system of interacting agents that play repeated games with their neighbors, and adapt their behaviors and network links based on the outcome of those games. The adaptation is achieved through a simple reinforcement learning scheme. We show that the collective evolution of such a system can be described by appropriately define...

Models of evolutionary dynamics are often approached via the replicator equation, which in its standard form is given by ẋi = xi ( fi (x)−φ) , i = 1, . . . ,n, where xi is the frequency, or relative abundance, of strategy i, fi is its fitness, and φ = ∑i=1 xi fi is the average fitness. A game-theoretic aspect is introduced to the model via the payoff matrix A, where Ai, j is the expected payoff...