Evolutionarily stable strategy and invader strategy in matrix games

2012 ◽  
Vol 66 (1-2) ◽  
pp. 383-397 ◽  
Author(s):  
Zhanwen Ding ◽  
Shuxun Wang ◽  
Honglin Yang
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Stable Strategy ◽  
Matrix Games ◽  
Evolutionarily Stable

scholarly journals Best Reply Player Against Mixed Evolutionarily Stable Strategy User

2021 ◽  
Vol 84 (1) ◽  
Author(s):  
József Garay ◽  
Tamás F. Móri
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Payoff Matrix ◽  
Matrix Game ◽  
Stable Strategy ◽  
Matrix Games ◽  
Basic Assumptions ◽  
Population Games ◽  
Previous Round ◽  
The Mean ◽  
Evolutionarily Stable

AbstractWe consider matrix games with two phenotypes (players): one following a mixed evolutionarily stable strategy and another one that always plays a best reply against the action played by its opponent in the previous round (best reply player, BR). We focus on iterated games and well-mixed games with repetition (that is, the mean number of repetitions is positive, but not infinite). In both interaction schemes, there are conditions on the payoff matrix guaranteeing that the best reply player can replace the mixed ESS player. This is possible because best reply players in pairs, individually following their own selfish strategies, develop cycles where the bigger payoff can compensate their disadvantage compared with the ESS players. Well-mixed interaction is one of the basic assumptions of classical evolutionary matrix game theory. However, if the players repeat the game with certain probability, then they can react to their opponents’ behavior. Our main result is that the classical mixed ESS loses its general stability in the well-mixed population games with repetition in the sense that it can happen to be overrun by the BR player.

SOME REMARKS ON EVOLUTIONARY STABILITY IN MATRIX GAMES

2013 ◽  
Vol 15 (04) ◽  
pp. 1340024 ◽  
Author(s):  
K. S. MALLIKARJUNA RAO ◽  
A. J. SHAIJU
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Sufficient Conditions ◽  
Direct Proof ◽  
Evolutionary Stability ◽  
Stable Strategy ◽  
Matrix Games ◽  
Pure Strategies ◽  
Evolutionarily Stable

In this article, we revisit evolutionary stability in matrix games. We provide a new direct proof to characterize a pure evolutionarily stable strategy (ESS), in games with exactly two pure strategies, as a strategy that is evolutionarily stable against multiple mutations. This direct proof yields generalizations to k × k games which explains why such a characterization is not possible in general. Furthermore, we prove other necessary/sufficient conditions for evolutionary stability against multiple mutations.

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.

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