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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…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…
The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic…
Winners-take-all situations introduce an incentive for agents to diversify their behavior, since doing so will result in splitting an eventual price with fewer people. At the same time, when the payoff of a process depends on a parameter…
While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…
Decision-making individuals are typically either an imitator, who mimics the action of the most successful individual(s), a conformist (or coordinating individual), who chooses an action if enough others have done so, or a nonconformist (or…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
In this study, considering the importance of how to exploit renewable natural resources, we analyze a fishing model with nonlinear harvesting function in which the players at the equilibrium point do a static game with complete information…
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a…
We report on new stability conditions for evolutionary dynamics in the context of population games. We adhere to the prevailing framework consisting of many agents, grouped into populations, that interact noncooperatively by selecting…
We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…
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 strategists can be…
We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…
S. J. van Enk and R. Pike in PRA 66, 024306 (2002) argue that the equilibrium solution to a quantum game isn't unique but is already present in the classical game itself. In this work, we contest this assertion by showing that a random…
In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…
This paper further develops work from a previous article which introduced a new way of modelling evolutionary game models with an emphasis on ecological realism, concerned with how ecological factors determine payoffs in evolutionary games.…
We consider a dynamic version of sender-receiver games, where the sequence of states follows an irreducible Markov chain observed by the sender. Under mild assumptions, we provide a simple characterization of the limit set of equilibrium…
Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoner's…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…