Related papers: Nonlinear Dynamics of the Rock-Paper-Scissors Game…
Stability of evolutionary dynamics of non-repeated Prisoner's Dilemma game with non-uniform interaction rates [1], via benefit and cost dilemma is studied . Moreover, the stability condition (b+c/b-c)2 < r1r3 is derived in case of…
When faced with an imminent risk of predation, many animals react to escape consumption. Antipredator strategies are performed by individuals acting as a group to intimidate predators and minimize the damage when attacked. We study the…
We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the…
We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…
This paper treats a random collision model of three species, which is represented by the random time change of three standard Poisson processes. The prey-predator relation in the random collision model looks like paper-scissors-stone game,…
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…
Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of…
We study the evolutionary robustness of strategies in infinitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator…
Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This…
We describe a new system for the simulation of simultaneous moves between noncolocational players. This has applications in the burgeoning Rock-Paper-Scissors by mail movement.
Feedbacks between strategies and the environment are common in social-ecological, evolutionary-ecological, and even psychological-economic systems. Utilizing common resources is always a dilemma for community members, like tragedy of the…
The prototype of a cyclic dominant system is the so-called rock-scissors-paper game, but similar relation among competing strategies can be identified in several other models of evolutionary game theory. In this work we assume that a…
A central goal in ecology is to understand how biodiversity is maintained. Previous theoretical works have employed the rock-paper-scissors (RPS) game as a toy model, demonstrating that population mobility is crucial in determining the…
Understanding the emergence and stability of cooperation in public goods games is important due to its applications in fields such as biology, economics, and social science. However, a gap remains in comprehending how mutations, both…
Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\sigma^2I$. The…
We study a system of ordinary differential equations in R5 that is used as a model both in population dynamics and in game theory, and is known to exhibit a heteroclinic network consisting in the union of four types of elementary…
The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…
We study the rock-paper-scissors game in structured populations, where the invasion rates determine individual payoffs that govern the process of strategy change. The traditional version of the game is recovered if the payoffs for each…
A co-evolving and adaptive Rock (R)-Paper (P)-Scissors (S) game (ARPS) in which an agent uses one of three cyclically dominating strategies is proposed and studied numerically and analytically. An agent takes adaptive actions to achieve a…
We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two…