Evolutionarily stable strategies with two types of player

1979 ◽  
Vol 16 (1) ◽  
pp. 76-83 ◽  
Author(s):  
Peter D. Taylor

A definition of ESS (evolutionarily stable strategy) is suggested for games in which there are two types of player, each with its own set of strategies, and the fitness of any strategy depends upon the strategy mix, of both types, in the population as a whole. We check that the standard ESS results hold for this definition and discuss a mate-desertion model which has appeared in the literature in which the two types are male and female.

1979 ◽  
Vol 16 (01) ◽  
pp. 76-83 ◽  
Author(s):  
Peter D. Taylor

A definition of ESS (evolutionarily stable strategy) is suggested for games in which there are two types of player, each with its own set of strategies, and the fitness of any strategy depends upon the strategy mix, of both types, in the population as a whole. We check that the standard ESS results hold for this definition and discuss a mate-desertion model which has appeared in the literature in which the two types are male and female.


Behaviour ◽  
1979 ◽  
Vol 71 (3-4) ◽  
pp. 203-244 ◽  
Author(s):  
H. Jane Brockmann ◽  
Richard Dawkins

AbstractOne suggested evolutionary origin of insect sociality is joint nesting by females of the same generation. Long before selection favoured joint nesting itself, it might have favoured some other incidental preadaptation such as the habit of 'entering' abandoned burrows, found in the usually solitary wasp Splaex ichneumoneus. We have comprehensive economic records of individually marked wasps. There is little evidence of consistent individual variation in nesting success. Wasps often abandon the nests they have dug, and other individuals adopt or 'enter' these empty burrows. 'Dig/Enter' is a good candidate for a mixed evolutionarily stable strategy : digging and entering decisions are not characteristic of particular individuals; the probability of entering is not conditional upon whether it is early or late in the season; there is no correlation between an individual's size and her tendency to dig or enter; there is no correlation between an individual's egg-laying success and her tendency to dig or enter; individuals do not choose to dig or enter on the basis of immediate past success; individuals do not dig and enter in runs, nor do they alternate; wasps do not choose to dig or enter on the basis of how long they have been searching. At one study site digging and entering decisions are roughly equally successful, but at another entering decisions are perhaps slightly more successful. Entering wasps seem not to distinguish empty, abandoned burrows from burrows that are still occupied. As a consequence of indiscriminate entering, two females sometimes co-occupy the same burrow. Co-occupation should not be called 'communal' because the wasps usually share the same brood cell, not just the same burrow. One might expect that wasps would gain some benefit from co-occupying, but they do not, for a number of reasons: only one egg is laid in a shared cell, and obviously only one of the two wasps can lay it; two wasps together do not fetch noticeably more food than one alone; two wasps together are no quicker at provisioning a cell than one wasp alone; wasps sometimes duplicate each others' efforts when they co-occupy a nest; co-occupying wasps often have costly fights. About all that can be said for joint nesting is that it may reduce parasitism. The risk of joint nesting is the price wasps pay for the advantages of taking over an already dug and abandoned burrow. A mathematical model assuming 'dig/enter' as a mixed evolutionarily stable strategy has some predictive success. If the parameters changed quantitatively, the Sphex model could come to predict selection in favour of joint nesting as such. The selection pressures would have to be very strong to overcome the demonstrated disadvantages of co-occupying. Variants of the Sphex model may be applicable to other species, and may help our understanding of the evolution of group living. The theory of evolutionarily stable strategies is relevant not just to the maintenance of behaviour but to its evolutionary change.


1980 ◽  
Vol 17 (2) ◽  
pp. 333-340 ◽  
Author(s):  
W. G. S. Hines

In addition to the concept of the evolutionarily stable strategy (ESS), developed specifically for considering intraspecific conflicts, concepts such as the Nash equilibrium from game theory and the attractor or sink from dynamical systems theory appear relevant to the problem of characterizing populations of stable composition. The three concepts mentioned are discussed for one simple standard population model. It is found that evolutionarily stable strategies of one type are necessarily Nash equilibrium strategies, although the converse is not true. The dynamical systems characterization is found to provide a model for populations susceptible to invasion by ‘co-operative' strategies, but capable of evolving back in average to the original equilibrium.


1985 ◽  
Vol 22 (1) ◽  
pp. 1-14 ◽  
Author(s):  
R. Cressman ◽  
A. T. Dash

The evolution of strategies in animal contests is examined where the dynamical equation takes into account population growth rates. This leads to a different definition of evolutionary stable strategy (ESS) from the usual one. Consequences for independent haploid species are then contrasted with the previous theory. Inheritance patterns for male–female contests with sex-dependent payoffs are considered. In particular, if males and females evolve independently to the same ESS, then so does the diploid species under random mating. Finally, the evolution of diploid populations where strategies are determined at a diallelic locus is investigated.


1983 ◽  
Vol 20 (2) ◽  
pp. 395-399 ◽  
Author(s):  
W. G. S. Hines ◽  
D. T. Bishop

A simple argument demonstrates that the mean strategy of a diploid sexual population at evolutionary equilibrium can be expected to be an evolutionarily stable strategy (ESS) in the formal sense. This result follows under a wide set of models of genetic inheritance of strategy (including sexual selection) provided that the ESS is both attainable and maintainable.


Author(s):  
Sam Ganzfried

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biology and even cancer. Finding such a strategy has been shown to be difficult from a theoretical complexity perspective. Informally an ESS is a strategy that if followed by the population cannot be taken over by a mutation strategy. We present an algorithm for the case where mutations are restricted to pure strategies. This is the first positive result for computation of ESS, as all prior results are computational hardness and no prior algorithms have been presented.


1985 ◽  
Vol 22 (01) ◽  
pp. 1-14
Author(s):  
R. Cressman ◽  
A. T. Dash

The evolution of strategies in animal contests is examined where the dynamical equation takes into account population growth rates. This leads to a different definition of evolutionary stable strategy (ESS) from the usual one. Consequences for independent haploid species are then contrasted with the previous theory. Inheritance patterns for male–female contests with sex-dependent payoffs are considered. In particular, if males and females evolve independently to the same ESS, then so does the diploid species under random mating. Finally, the evolution of diploid populations where strategies are determined at a diallelic locus is investigated.


1980 ◽  
Vol 17 (02) ◽  
pp. 333-340 ◽  
Author(s):  
W. G. S. Hines

In addition to the concept of the evolutionarily stable strategy (ESS), developed specifically for considering intraspecific conflicts, concepts such as the Nash equilibrium from game theory and the attractor or sink from dynamical systems theory appear relevant to the problem of characterizing populations of stable composition. The three concepts mentioned are discussed for one simple standard population model. It is found that evolutionarily stable strategies of one type are necessarily Nash equilibrium strategies, although the converse is not true. The dynamical systems characterization is found to provide a model for populations susceptible to invasion by ‘co-operative' strategies, but capable of evolving back in average to the original equilibrium.


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