scholarly journals Instability of cooperation in finite populations

2019 ◽  
Author(s):  
Chai Molina ◽  
David J. D. Earn
Keyword(s):  
Finite Population ◽  
Selection Process ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Evolution Of Cooperation ◽  
Implicit Assumption ◽  
Stable Strategy ◽  
Infinite Population ◽  
Snowdrift Game ◽  
Evolutionarily Stable

AbstractEvolutionary game theory has been developed primarily under the implicit assumption of an infinite population. We rigorously analyze a standard model for the evolution of cooperation (the multi-player snowdrift game) and show that in many situations in which there is a cooperative evolutionarily stable strategy (ESS) if the population is infinite, there is no cooperative ESS if the population is finite (no matter how large). In these cases, contributing nothing is a globally convergently stable finite-population ESS, implying that apparent evolution of cooperation in such games is an artifact of the infinite population approximation. The key issue is that if the size of groups that play the game exceeds a critical proportion of the population then the infinite-population approximation predicts the wrong evolutionary outcome (in addition, the critical proportion itself depends on the population size). Our results are robust to the underlying selection process.

scholarly journals Evolutionary Stable Strategies in Games with Fuzzy Payoffs

2020 ◽  
pp. 63-71
Author(s):  
Haozhen Situ
Keyword(s):  
Fuzzy Set ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Evolutionary Stability ◽  
Fuzzy Decision ◽  
Stable Strategy ◽  
New Approach ◽  
Fuzzy Payoff ◽  
Evolutionarily Stable ◽  
The Membership Function

Evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory. ESS provides an evolutionary stability criterion for biological, social and economical behaviors. In this paper, we develop a new approach to evaluate ESS in symmetric two player games with fuzzy payoffs. Particularly, every strategy is assigned a fuzzy membership that describes to what degree it is an ESS in presence of uncertainty. The fuzzy set of ESS characterize the nature of ESS. The proposed approach avoids loss of any information that happens by the defuzzification method in games and handles uncertainty of payoffs through all steps of finding an ESS. We use the satisfaction function to compare fuzzy payoffs, and adopts the fuzzy decision rule to obtain the membership function of the fuzzy set of ESS. The theorem shows the relation between fuzzy ESS and fuzzy Nash equilibrium. The numerical results illustrate the proposed method is an appropriate generalization of ESS to fuzzy payoff games.

A dynamic programming approach to evolutionarily stable strategy theory

1980 ◽  
Vol 12 (1) ◽  
pp. 3-5 ◽  
Author(s):  
C. Cannings ◽  
D. Gardiner
Keyword(s):  
Dynamic Programming ◽  
Density Function ◽  
Evolutionarily Stable Strategy ◽  
Programming Approach ◽  
Stable Strategy ◽  
War Of Attrition ◽  
Dynamic Programming Approach ◽  
The Individual ◽  
Image Position ◽  
Evolutionarily Stable

In the war of attrition (wa), introduced by Maynard Smith (1974), two contestants play values from [0, ∞), the individual playing the longer value winning a fixed prize V, and both incurring a loss equal to the lesser of the two values. Thus the payoff, E(x, y) to an animal playing x against one playing y, is A more general form (Bishop and Cannings (1978)) has and it was demonstrated that with and there exists a unique evolutionarily stable strategy (ess), which is to choose a random value from a specified density function on [0, ∞). Results were also obtained for strategy spaces [0, s] and [0, s).

scholarly journals Intraspecific competition and coordination in the evolution of lateralization

2008 ◽  
Vol 364 (1519) ◽  
pp. 861-866 ◽  
Author(s):  
Stefano Ghirlanda ◽  
Elisa Frasnelli ◽  
Giorgio Vallortigara
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Population Level ◽  
Neural Circuitry ◽  
Brain Lateralization ◽  
Stable Strategy ◽  
Cooperative Interactions ◽  
Strategic Factors ◽  
Left And Right ◽  
Predator Interactions ◽  
Evolutionarily Stable

Recent studies have revealed a variety of left–right asymmetries among vertebrates and invertebrates. In many species, left- and right-lateralized individuals coexist, but in unequal numbers (‘population-level’ lateralization). It has been argued that brain lateralization increases individual efficiency (e.g. avoiding unnecessary duplication of neural circuitry and reducing interference between functions), thus counteracting the ecological disadvantages of lateral biases in behaviour (making individual behaviour more predictable to other organisms). However, individual efficiency does not require a definite proportion of left- and right-lateralized individuals. Thus, such arguments do not explain population-level lateralization. We have previously shown that, in the context of prey–predator interactions, population-level lateralization can arise as an evolutionarily stable strategy when individually asymmetrical organisms must coordinate their behaviour with that of other asymmetrical organisms. Here, we extend our model showing that populations consisting of left- and right-lateralized individuals in unequal numbers can be evolutionarily stable, based solely on strategic factors arising from the balance between antagonistic (competitive) and synergistic (cooperative) interactions.

constraints from handedness on the evolution of brain lateralization

2005 ◽  
Vol 28 (4) ◽  
pp. 603-604 ◽  
Author(s):  
maryanne martin ◽  
gregory v. jones
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Brain Lateralization ◽  
Stable Strategy ◽  
Evolutionarily Stable

can we understand brain lateralization in humans by analysis in terms of an evolutionarily stable strategy? the attempt to demonstrate a link between lateralization in humans and that in, for example, fish appears to hinge critically on whether the isomorphism is viewed as a matter of homology or homoplasy. consideration of human handedness presents a number of challenges to the proposed framework.

Strategy stability in complex randomly mating diploid populations

1982 ◽  
Vol 19 (03) ◽  
pp. 653-659 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Convex Hull ◽  
Lyapunov Functions ◽  
Evolutionarily Stable Strategy ◽  
Stable Strategy ◽  
Convergence In Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations ◽  
Better Than

A class of Lyapunov functions is used to demonstrate that strategy stability occurs in complex randomly mating diploid populations. Strategies close to the evolutionarily stable strategy tend to fare better than more remote strategies. If convergence in mean strategy to an evolutionarily stable strategy is not possible, evolution will continue until all strategies in use lie on a unique face of the convex hull of available strategies. The results obtained are also relevant to the haploid parthenogenetic case.

The behaviour of strategy-frequencies in Parker's model

1980 ◽  
Vol 12 (01) ◽  
pp. 5-7
Author(s):  
D. Gardiner
Keyword(s):  
Finite Number ◽  
Evolutionarily Stable Strategy ◽  
Pure Strategy ◽  
Payoff Matrix ◽  
Stable Strategy ◽  
Expected Payoff ◽  
Pure Strategies ◽  
Image Position ◽  
Evolutionarily Stable

Parker's model (or the Scotch Auction) for a contest between two competitors has been studied by Rose (1978). He considers a form of the model in which every pure strategy is playable, and shows that there is no evolutionarily stable strategy (ess). In this paper, in order to discover more about the behaviour of strategies under the model, we shall assume that there are only a finite number of playable pure strategies I 1, I 2, ···, I n where I j is the strategy ‘play value m j ′ and m 1 < m 2 < ··· < m n . The payoff matrix A for the contest is then given by where V is the reward for winning the contest, C is a constant added to ensure that each entry in A is non-negative (see Bishop and Cannings (1978)), and E[I i , I j ] is the expected payoff for playing I i against I j . We also assume that A is regular (Taylor and Jonker (1978)) i.e. that all its rows are independent.

scholarly journals Biological auctions with multiple rewards

2015 ◽  
Vol 282 (1812) ◽  
pp. 20151041 ◽  
Author(s):  
Johannes G. Reiter ◽  
Ayush Kanodia ◽  
Raghav Gupta ◽  
Martin A. Nowak ◽  
Krishnendu Chatterjee
Keyword(s):  
Mixed Strategy ◽  
Evolutionarily Stable Strategy ◽  
Fundamental Characteristic ◽  
Stable Strategy ◽  
Bidding Strategies ◽  
Multiple Resources ◽  
Mixed Strategy Equilibrium ◽  
Strategy Equilibrium ◽  
Evolutionarily Stable ◽  
Competition For Resources

The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.

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