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Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one's own…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
Starting from a heuristic learning scheme for N-person games, we derive a new class of continuous-time learning dynamics consisting of a replicator-like drift adjusted by a penalty term that renders the boundary of the game's strategy space…
We consider a network of coupled agents playing the Prisoner's Dilemma game, in which players are allowed to pick a strategy in the interval [0,1], with 0 corresponding to defection, 1 to cooperation, and intermediate values representing…
We study a model in which two players with opposing interests try to alter a status quo through instability-generating actions. We show that instability can be used to secure longer-term durable changes, even if it is costly to generate and…
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how…
Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study…
It is known from both theory and experiments that introducing time delays into the communication network of mobile-agent swarms produces coherent rotational patterns. Often such spatio-temporal rotations can be bistable with other swarming…
Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of…
Here we consider a game theoretic model of multilevel selection in which individuals compete based on their payoff and groups also compete based on the average payoff of group members. Our focus is on multilevel social dilemmas: games in…
Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists in particular the question is often how such behaviors can arise \textit{de novo}…
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…
One could observe drastically different dynamics of zero-sum and non-zero-sum games under replicator equations. In zero-sum games, heteroclinic cycles naturally occur whenever the species of the population supersede each other in a cyclic…
We compare games under delayed control and delay games, two types of infinite games modelling asynchronicity in reactive synthesis. In games under delayed control both players suffer from partial informedness due to symmetrically delayed…
The hawk-dove game admits two types of equilibria: an asymmetric pure equilibrium in which players in one population play hawk and players in the other population play dove, and an inefficient symmetric mixed equilibrium, in which hawks are…
In games with continuous strategy spaces, if a rest point of the replicator dynamics is asymptotically stable then the rest point must be finitely supported (van Veelen, M., Spreij, P., 2009. Evolution in games with a continuous action…
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a…
We study the asymptotic behavior of deterministic, continuous-time imitation dynamics for population games over networks. The basic assumption of this learning mechanism -- encompassing the replicator dynamics -- is that players belonging…
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…