Correction: An evolutionarily stable strategy and the critical point of hog futures trading entities based on replicator dynamic theory: 2006-2015 data for China's 22 provinces

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).

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Intraspecific competition and coordination in the evolution of lateralization

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2008.0227 ◽

2008 ◽

Vol 364 (1519) ◽

pp. 861-866 ◽

Cited By ~ 145

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.

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constraints from handedness on the evolution of brain lateralization

Behavioral and Brain Sciences ◽

10.1017/s0140525x05370105 ◽

2005 ◽

Vol 28 (4) ◽

pp. 603-604 ◽

Cited By ~ 3

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.

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Strategy stability in complex randomly mating diploid populations

Journal of Applied Probability ◽

10.1017/s002190020003713x ◽

1982 ◽

Vol 19 (03) ◽

pp. 653-659 ◽

Cited By ~ 6

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.

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The behaviour of strategy-frequencies in Parker's model

Advances in Applied Probability ◽

10.1017/s0001867800033267 ◽

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.

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Biological auctions with multiple rewards

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2015.1041 ◽

2015 ◽

Vol 282 (1812) ◽

pp. 20151041 ◽

Cited By ~ 4

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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