Stochasticity, Selection, and the Evolution of Cooperation in a Two-Level Moran Model of the Snowdrift Game

The Snowdrift Game, also known as the Hawk-Dove Game, is a social dilemma in which an individual can participate (cooperate) or not (defect) in producing a public good. It is relevant to a number of collective action problems in biology. In a population of individuals playing this game, traditional evolutionary models, in which the dynamics are continuous and deterministic, predict a stable, interior equilibrium frequency of cooperators. Here, we examine how finite population size and multilevel selection affect the evolution of cooperation in this game using a two-level Moran process, which involves discrete, stochastic dynamics. Our analysis has two main results. First, we find that multilevel selection in this model can yield significantly higher levels of cooperation than one finds in traditional models. Second, we identify a threshold effect for the payoff matrix in the Snowdrift Game, such that below (above) a determinate cost-to-benefit ratio, cooperation will almost surely fix (go extinct) in the population. This second result calls into question the explanatory reach of traditional continuous models and suggests a possible alternative explanation for high levels of cooperative behavior in nature.

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Dominant Cubic Coefficients of the ‘1/3-Rule’ Reduce Contest Domains

Mathematics ◽

10.3390/math7060491 ◽

2019 ◽

Vol 7 (6) ◽

pp. 491 ◽

Cited By ~ 1

Author(s):

Paul F. Slade

Keyword(s):

Population Size ◽

Probability Function ◽

Social Dilemma ◽

Payoff Matrix ◽

Fixation Probability ◽

Random Genetic Drift ◽

Selection Differential ◽

Maclaurin Series ◽

Third Order ◽

Moran Model

Antagonistic exploitation in competition with a cooperative strategy defines a social dilemma, whereby eventually overall fitness of the population decreases. Frequency-dependent selection between two non-mutating strategies in a Moran model of random genetic drift yields an evolutionary rule of biological game theory. When a singleton fixation probability of co-operation exceeds the selectively neutral value being the reciprocal of population size, its relative frequency in the population equilibrates to less than 1/3. Maclaurin series of a singleton type fixation probability function calculated at third order enables the convergent domain of the payoff matrix to be identified. Asymptotically dominant third order coefficients of payoff matrix entries were derived. Quantitative analysis illustrates non-negligibility of the quadratic and cubic coefficients in Maclaurin series with selection being inversely proportional to population size. Novel corollaries identify the domain of payoff matrix entries that determines polarity of second order terms, with either non-harmful or harmful contests. Violation of this evolutionary rule observed with non-harmful contests depends on the normalized payoff matrix entries and selection differential. Significant violations of the evolutionary rule were not observed with harmful contests.

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EVOLUTIONARY GAMES IN MULTI-AGENT SYSTEMS OF WEIGHTED SOCIAL NETWORKS

International Journal of Modern Physics C ◽

10.1142/s0129183109013923 ◽

2009 ◽

Vol 20 (05) ◽

pp. 701-710 ◽

Cited By ~ 16

Author(s):

WEN-BO DU ◽

XIAN-BIN CAO ◽

HAO-RAN ZHENG ◽

HONG ZHOU ◽

MAO-BIN HU

Keyword(s):

Cooperative Behavior ◽

Social Systems ◽

Evolutionary Game ◽

Evolutionary Games ◽

Evolution Of Cooperation ◽

Multi Agent Systems ◽

Snowdrift Game ◽

Cooperation Level ◽

The Social ◽

Multi Agent

Much empirical evidence has shown realistic networks are weighted. Compared with those on unweighted networks, the dynamics on weighted network often exhibit distinctly different phenomena. In this paper, we investigate the evolutionary game dynamics (prisoner's dilemma game and snowdrift game) on a weighted social network consisted of rational agents and focus on the evolution of cooperation in the system. Simulation results show that the cooperation level is strongly affected by the weighted nature of the network. Moreover, the variation of time series has also been investigated. Our work may be helpful in understanding the cooperative behavior in the social systems.

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Baumard et al.'s moral markets lack market dynamics

Behavioral and Brain Sciences ◽

10.1017/s0140525x12000945 ◽

2013 ◽

Vol 36 (1) ◽

pp. 89-90 ◽

Cited By ~ 1

Author(s):

Daniel M. T. Fessler ◽

Colin Holbrook

Keyword(s):

Cooperative Behavior ◽

Partner Choice ◽

Evolution Of Cooperation ◽

Market Dynamics ◽

Market Models

AbstractMarket models are indeed indispensable to understanding the evolution of cooperation and its emotional substrates. Unfortunately, Baumard et al. eschew market thinking in stressing the supposed invariance of moral/cooperative behavior across circumstances. To the contrary, humans display contingent morality/cooperation, and these shifts are best accounted for by market models of partner choice for mutually beneficial collaboration.

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Punishment Leads to Cooperative Behavior in Structured Societies

Evolutionary Computation ◽

10.1162/evco_a_00062 ◽

2012 ◽

Vol 20 (2) ◽

pp. 301-319 ◽

Cited By ~ 8

Author(s):

Shade T. Shutters

Keyword(s):

Social Structure ◽

Computer Simulations ◽

Degree Distribution ◽

Cooperative Behavior ◽

Evolution Of Cooperation ◽

Scale Free ◽

Structured Population ◽

Altruistic Punishment ◽

Costly Punishment ◽

Scale Free Networks

Altruistic punishment occurs when an agent incurs a cost to punish another but receives no material benefit for doing so. Despite the seeming irrationality of such behavior, humans in laboratory settings routinely pay to punish others even in anonymous, one-shot settings. Costly punishment is ubiquitous among social organisms in general and is increasingly accepted as a mechanism for the evolution of cooperation. Yet if it is true that punishment explains cooperation, the evolution of altruistic punishment remains a mystery. In a series of computer simulations I give agents the ability to punish one another while playing a continuous prisoner's dilemma. In simulations without social structure, expected behavior evolves—agents do not punish and consequently no cooperation evolves. Likewise, in simulations with social structure but no ability to punish, no cooperation evolves. However, in simulations where agents are both embedded in a social structure and have the option to inflict costly punishment, cooperation evolves quite readily. This suggests a simple and broadly applicable explanation of cooperation for social organisms that have nonrandom social structure and a predisposition to punish one another. Results with scale-free networks further suggest that nodal degree distribution plays an important role in determining whether cooperation will evolve in a structured population.

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