A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate $(C)$ or defect $(D)$ unconditionally. The updated in random sequence have chance adopt one of neighboring strategies probability depending payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, we study density $c$ cooperators stationary state. This system exhibits continuous transition between absorbing states...

Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists various disciplines. Here we present simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation public goods games. This natural extension leads rock--scissors--paper type cyclic dominance of the three strategies cooperate, defect loner i.e. those unwilling participate enterprise. In spatial settings with...

The effects of payoffs and noise on the maintenance cooperative behavior are studied in an evolutionary Prisoner's Dilemma game with players located sites different two-dimensional lattices. This system exhibits a phase transition from mixed state cooperators defectors to homogeneous one where only remain alive. Using systematic Monte Carlo simulations levels generalized mean-field approximations we have determined boundaries (critical points) separating two phases plane temperature (noise)...

Evolutionary game theory is designed to capture the essentials of characteristic interactions among individuals. Its most prominent application quest for origins and evolution cooperation. The effects population structures on performance behavioral strategies became apparent only in recent years marks advent an intriguing link between apparently unrelated disciplines. structured populations reveals critical phase transitions that fall into universality class directed percolation square...

Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of two pure strategies (cooperation or defection) distributed on a two-dimensional lattice. rate strategy adoption from randomly chosen neighbors is controlled by payoff difference and two-value pre-factor w characterizing whom learned from. reduced teaching activity concentrations ν at beginning fixed further on. Numerical analytical calculations...

We study the evolution of cooperation in public goods games on different regular graphs as a function noise level underlying strategy adoptions. focus effects that are brought about by group sizes which individuals participate, revealing larger groups players may induce qualitatively behavior when approaching deterministic limit adoption. While pairwise interactions an intermediate uncertainty adoptions ensure optimal conditions for survival cooperators at specific graph topology, warrant...

The efficiency of institutionalized punishment is studied by evaluating the stationary states in spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool punishers as three competing strategies. Fines costs are considered two main parameters determining distributions strategies on square lattice. Each player collects a payoff from five five-person games, evolution subsequently governed imitation based pairwise comparisons at low level noise. impact...

Situations where individuals have to contribute joint efforts or share scarce resources are ubiquitous. Yet, without proper mechanisms ensure cooperation, the evolutionary pressure maximize individual success tends create a tragedy of commons (such as over-fishing destruction our environment). This contribution addresses number related puzzles human behavior with an game theoretical approach it has been successfully used explain other biological species many times, from bacteria vertebrates....

We have studied an evolutionary prisoner's dilemma game with players located on two types of random regular graphs a degree 4. The analysis is focused the effects payoffs and noise (temperature) maintenance cooperation. When varying level and/or highest payoff, system exhibits second-order phase transition from mixed state cooperators defectors to absorbing where only remain alive. For graph (and Bethe lattice) behavior similar those found previously square lattice nearest neighbor...

We study the evolution of cooperation in spatial public goods games where, besides classical strategies (C) and defection (D), we consider punishing cooperators (PC) or defectors (PD) as an additional strategy. Using a minimalist modeling approach, our goal is to separately clarify identify consequences two strategies. Since punishment costly, lose evolutionary competition case well-mixed interactions. When interactions are taken into account, however, outcome can be strikingly different,...

Voluntary participation in public good games has recently been demonstrated to be a simple yet effective mechanism avoid deadlocks states of mutual defection and promote persistent cooperative behavior. Apart from cooperators defectors third strategical type is considered: the risk averse loners who are unwilling participate social enterprise rather rely on small but fixed earnings. This results rock-scissors-paper cyclic dominance three strategies. In prisoner's dilemma, effects voluntary...

We study the evolution of cooperation within spatial prisoner's dilemma game on a square lattice where fraction players $\ensuremath{\mu}$ can spread their strategy more easily than rest due to predetermined larger teaching capability. In addition, characterized by capability are allowed temporarily link with distant opponents same kind probability $p$, thus introducing shortcut connections among distinguished players. show that these additional temporary able sustain throughout whole range...

Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share an amount money, unfair offers rare and their acceptance rate small. While empathy spatiality may lead evolution fairness, thus far considered continuous strategies precluded observation solutions would be driven by pattern formation. Here we introduce a spatial with discrete strategies, show this simple alteration opens gate fascinatingly rich dynamical behavior. In addition...

Aging is always present, tailoring our interactions with others, and postulating a finite lifespan during which we are able to exercise them. We consider the prisoner's dilemma game on square lattice examine how quenched age distributions different aging protocols influence evolution of cooperation when taking life experience knowledge accumulation into account as time passes. In agreement previous studies, find that assignment players, introducing heterogeneity game, substantially promotes...

We have studied the evolution of strategies in spatial public goods games where both individual (peer) and institutional (pool) punishments are present beside unconditional defector cooperator strategies. The strategy distribution is governed by imitation based on random sequential comparison neighbors' payoff for a fixed level noise. Using numerical simulations we evaluated frequencies phase diagrams when varying synergy factor, punishment cost, fine. Our attention focused two extreme cases...

We study the evolution of cooperation in spatial public goods games with four competing strategies: cooperators, defectors, punishing and defectors. To explore robustness cooperation-promoting effect costly punishment, besides usual strategy adoption dynamics we also apply mutations. As expected, frequent mutations create kind well-mixed conditions, which support spreading However, when mutation rate is small, final stationary state does not significantly differ from mutation-free model,...

Abstract The evolution of cooperation among unrelated individuals in human and animal societies remains a challenging issue across disciplines. In this context, two models have attracted most attention: the prisoner's dilemma for pairwise interactions public goods game group interactions. games share many features as demonstrated by close linkage their cores. spatially structured systems with arranged on lattice we investigate effects size geometry success cooperators defectors compulsory...

Maintenance of cooperation was studied for a two-strategy evolutionary prisoner's dilemma game where the players are located on one-dimensional chain and their payoff comes from games with nearest- next-nearest-neighbor interactions. The applied host geometry makes it possible to study impacts two conflicting topological features. rule involves some noise affecting strategy adoptions between interacting players. Using Monte Carlo simulations extended versions dynamical mean-field theory we...

The spatial rock-scissors-paper game (or cyclic Lotka–Volterra system) is extended to study how the spatiotemporal patterns are affected by rewired host lattice providing uniform number of neighbours (degree) at each site. On square this system exhibits a self-organizing pattern with equal concentration competing strategies (species). If quenched background constructed substituting random links for nearest-neighbour bonds then limit cycle occurs when portion exceeds threshold value. This...

Competition among cooperative, defective, and loner strategies is studied by considering an evolutionary prisoner's dilemma game for different partnerships. In this each player can adopt one of its coplayer's strategy with a probability depending on the difference payoffs coming from games corresponding coplayers. Our attention focused effects annealed quenched randomness in partnership fixed number It shown that only loners survive if four coplayers are chosen randomly (mean-field limit)....

We studied spatial Prisoner's Dilemma and Stag Hunt games where both the strategy distribution players' individual noise level could evolve to reach higher payoff. Players are located on sites of different two-dimensional lattices gain their payoff from with neighbors by choosing unconditional cooperation or defection. The way adoption can be characterized a single $K$ (temperaturelike) parameter describing how strongly adoptions depend difference. If we start system random many player...

An evolutionary prisoner's dilemma (PD) game is studied with players located on a hierarchical structure of layered square lattices. The can follow two strategies [$D$ (defector) and $C$ (cooperator)] their income comes from PD games the ``neighbors.'' adoption one neighboring allowed probability dependent payoff difference. Monte Carlo simulations are performed to study how measure cooperation affected by number levels $(Q)$ temptation defect. According highest frequency be observed at top...

We study a six-species Lotka-Volterra-type system on different two-dimensional lattices when each species has two superior and inferior partners. The invasion rates from predator sites to randomly chosen neighboring prey site depend the predator-prey pair, whereby cyclic symmetries within three-species defensive alliances are conserved. Monte Carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival difference alliance-specific rates. This behavior is qualitatively...