Emergence of cooperation among interacting individuals

Chiappin, José Raymundo Novaes; Oliveira, Mário J. de

doi:10.1103/physreve.59.6419

Cited by 26 publications

(23 citation statements)

References 11 publications

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“…The existence of absorbing state(s) implies the appearance of critical phase transitions that is realized by the extinction of one or two strategies when tuning the parameters. These critical phase transitions exhibit general features and belong to the directed percolation universality class [34,48,49].…”

Section: Simulation Results For the Imitation Rulementioning

confidence: 99%

Payoff components and their effects in a spatial three-strategy evolutionary social dilemma

et al. 2015

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We study a three-strategy spatial evolutionary prisoner's dilemma game with imitation and logit update rules. Players can follow the always-cooperating, always-defecting or the win-stay-lose-shift (WSLS) strategies and gain their payoff from games with their direct neighbors on a square lattice. The friendliness parameter of the WSLS strategy-characterizing its cooperation probability in the first round-tunes the cyclic component of the game determining whether the game can be characterized by a potential. We measured and calculated the phase diagrams of the system for a wide range of parameters. When the game is a potential game and the logit rule is applied, the theoretically predicted phase diagram agrees very well with the simulation results. Surprisingly, this phase diagram can be accurate even in the nonpotential case if there are only two surviving strategies in the stationary state; this result harmonizes with the fact that all 2 × 2 games are potential games. For the imitation dynamics, we found that the effects of spatiality combined with the presence of two cooperative strategies are so strong that they suppress even substantial changes in the payoff matrix, thus the phase diagrams are independent of the cyclic component's intensity. At the same time, this type of strategy update mechanism supports the formation of cooperative clusters that results in a cooperative society in a wider parameter range compared to the logit dynamics.

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Section: Simulation Results For the Imitation Rulementioning

confidence: 99%

Payoff components and their effects in a spatial three-strategy evolutionary social dilemma

et al. 2015

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“…We consider the spatial version of the prisoner's dilemma [1,[25][26][27]30,[34][35][36][37], placing the interacting elements in the vertices of a d-dimensional array, usually a hypercube, with periodic boundary conditions. The results presented here are for d = 2.…”

Section: The Modelmentioning

confidence: 99%

Disordered environments in spatial games

2001

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The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in heterogeneous ecosystems in spatial evolutionary games by considering site diluted lattices. The main result is that due to disorder, the fraction of cooperators in the population is enhanced. Moreover, the system presents a dynamical transition at ρ * , separating a region with spatial chaos from one with localized, stable groups of cooperators.

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“…Consequently, this system becomes equivalent to a branching and annihilating random walk [17] which exhibits a transition belonging to the directed percolation (DP) universality class [12,18,19,20]. According to MC simulations for r → r C from above, the frequency of C is proportional to (r − r C ) β with r C = 4.526(1) and β = 0.55(3) for σ = 1 and K = τ = 0.1.…”

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confidence: 99%

Phase Transitions and Volunteering in Spatial Public Goods Games

Szabó

Hauert²

2002

Phys. Rev. Lett.

609

453

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Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists in various disciplines. Here we present a simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games. This natural extension leads to rock-scissors-paper type cyclic dominance of the three strategies cooperate, defect and loner i.e. those unwilling to participate in the public enterprise. In spatial settings with players arranged on a regular lattice this results in interesting dynamical properties and intriguing spatio-temporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two-and three-strategy states which are either in the class of directed percolation or show interesting analogies to Ising-type models. Although volunteering is incapable of stabilizing cooperation, it efficiently prevents successful spreading of selfish behavior and enables cooperators to persist at substantial levels. PACS numbers: 05.50.+q, 87.23.Cc In behavioral sciences and more recently in economics the evolution of cooperation among unrelated individuals represents one of the most stunning phenomena [1,2]. The prisoner's dilemma (PD) has long established as a paradigm to explain cooperative behavior through pairwise interactions [3]. While the PD attracted attention from biologists and social scientists, most studies in experimental economics focused on the closely related but more general public goods game (PGG) for group interactions [4]. In typical PGG experiments, an experimenter endows e.g. four players with $ 10 each. The players then have the opportunity to invest part or all of their money into a common pool. They know that the total amount in the pool is doubled and equally divided among all participants irrespective of their contributions. If everybody cooperates and contributes their money, each player ends up with $ 20. However, every player faces the temptation to defect and to free-ride on the other player's contributions by withholding the money since every invested dollar returns only 50 cents to the investor. Obviously, defection represents the dominating strategy leading to the 'rational' equilibrium where no one increases its initial capital. Such strategical behavior prescribed to homo oeconomicus is frequently at odds with experimental findings [5] and lead to the decline of this rationality concept.Note that for pairwise encounters with a fixed investment amount, the PGG reduces to the PD. PGG interactions are abundant in animal and human societies [6,7,8]. Consider for example predator inspection behavior, alarm calls and group defense as well as health insurance, public transportation or environmental issues, to name only a few.Recently it was demonstrated that voluntary participation in such public enterprises may provide an escape hatch out of economic stalemate and results in a substantial and persistent * Present address:Department of Zoology, Uni...

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Emergence of cooperation among interacting individuals

Cited by 26 publications

References 11 publications

Payoff components and their effects in a spatial three-strategy evolutionary social dilemma

Payoff components and their effects in a spatial three-strategy evolutionary social dilemma

Disordered environments in spatial games

Phase Transitions and Volunteering in Spatial Public Goods Games

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