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.

The behaviour of strategy-frequencies in Parker's model

1980 ◽  
Vol 12 (1) ◽  
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 I1, I2, ···, In where Ij is the strategy ‘play value mj′ and m1 < m2 < ··· < mn. 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[Ii, Ij] is the expected payoff for playing Ii against Ij. We also assume that A is regular (Taylor and Jonker (1978)) i.e. that all its rows are independent.

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).

On the local stability of an evolutionarily stable strategy in a diploid population

1984 ◽  
Vol 21 (02) ◽  
pp. 215-224 ◽  
Author(s):  
W. G. S. Hines ◽  
D. T. Bishop
Keyword(s):  
Local Stability ◽  
Evolutionarily Stable Strategy ◽  
Payoff Matrix ◽  
Stable Strategy ◽  
Diploid Population ◽  
Haploid Population ◽  
The Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations

The evolutionarily stable strategy for a given payoff matrix contest, although originally determined in terms of a haploid population, has been shown elsewhere to correspond to an equilibrium of the mean strategy of a diploid population. In this note, the equilibrium is shown to be locally stable for diploid populations. This local stability is demonstrated primarily by relating the behaviour of the perturbed diploid population to one, or in some cases two, associated haploid populations.

The allocation of resources in a multiple-trial war of attrition conflict

1996 ◽  
Vol 28 (3) ◽  
pp. 933-964 ◽  
Author(s):  
J. C. Whittaker
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Pure Strategy ◽  
Allocation Of Resources ◽  
Stable Strategy ◽  
Fixed Amount ◽  
War Of Attrition ◽  
Evolutionarily Stable

We consider a model in which players must divide a fixed amount of resource between a number of trials of an underlying contest, with the underlying contest based on the War of Attrition. We are able to find the unique ES set (a simple generalisation of the idea of an evolutionarily stable strategy) in certain circumstances: in particular we find the conditions under which the ES set may contain a pure strategy.

Algorithm for Evolutionarily Stable Strategies against Pure Mutations

2018 ◽  
Author(s):  
Sam Ganzfried
Keyword(s):  
Game Theory ◽  
Positive Result ◽  
Evolutionarily Stable Strategy ◽  
Solution Concept ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
Mutation Strategy ◽  
Important Solution ◽  
Pure Strategies ◽  
Evolutionarily Stable

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.

A dynamic programming approach to evolutionarily stable strategy theory

1980 ◽  
Vol 12 (01) ◽  
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).

The allocation of resources in a multiple-trial war of attrition conflict

1996 ◽  
Vol 28 (03) ◽  
pp. 933-964 ◽  
Author(s):  
J. C. Whittaker
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Pure Strategy ◽  
Allocation Of Resources ◽  
Stable Strategy ◽  
Fixed Amount ◽  
War Of Attrition ◽  
Evolutionarily Stable

We consider a model in which players must divide a fixed amount of resource between a number of trials of an underlying contest, with the underlying contest based on the War of Attrition. We are able to find the unique ES set (a simple generalisation of the idea of an evolutionarily stable strategy) in certain circumstances: in particular we find the conditions under which the ES set may contain a pure strategy.

On the local stability of an evolutionarily stable strategy in a diploid population

1984 ◽  
Vol 21 (2) ◽  
pp. 215-224 ◽  
Author(s):  
W. G. S. Hines ◽  
D. T. Bishop
Keyword(s):  
Local Stability ◽  
Evolutionarily Stable Strategy ◽  
Payoff Matrix ◽  
Stable Strategy ◽  
Diploid Population ◽  
Haploid Population ◽  
The Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations

The evolutionarily stable strategy for a given payoff matrix contest, although originally determined in terms of a haploid population, has been shown elsewhere to correspond to an equilibrium of the mean strategy of a diploid population. In this note, the equilibrium is shown to be locally stable for diploid populations. This local stability is demonstrated primarily by relating the behaviour of the perturbed diploid population to one, or in some cases two, associated haploid populations.

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.

Sign in / Sign up

Export Citation Format

Share Document