Evolutionary stability in extensive two-person games

doi:10.1016/0165-4896(83)90012-4

Mathematical Social Sciences

Volume 5, Issue 3, September 1983, Pages 269-363

https://doi.org/10.1016/0165-4896(83)90012-4 Get rights and content

Abstract

The concept of an ESS (evolutionary stable strategy) has been introduced by Maynard Smith and Price for two-person games in normal form (Maynard Smith and Price, 1973). The generalization to extensive two-person games raises various conceptual and mathematical problems, like the notion of symmetry in such games. A direct translation of the normal form concept to the framework of extensive games leads to unsatisfactory consequences. Therefore, on the basis of the trembling hand approach to perfectness (Selten, 1975), the notion of a limit ESS is introduced. Several theorems on the properties of a limit ESS provide tools for the analysis of specific games. Finally, a many-period model of animal contests with ritual fights and escalated conflicts is investigated in detail.

References (26)

N.B. Davies
Territorial defence in the speckled wood butterfly (Parage aegeria): The resident always wins
Anim. Behav.
(1978)
P. Hammerstein
The role of asymmetries in animal contests
Anim. Behav.
(1981)
Wu Wen-tsün et al.
Essential equilibrium points of n-person non-cooperative games
Sci. Sinica
(1962)
G.P. Baerends
An evaluation of the conflict hypothesis as an explanatory principle for the evolution of displays
M. Beckmann et al.
Mathematik für Ökonomen II
(1973)
E.E.C. van Damme
Refinements of the Nash equilibrium concept
R. Dawkins
The Selfish Gene
(1976)
R. Dawkins et al.
Do digger wasps commit the Concorde fallacy?
Anim. Behav.
(1980)
J. Haigh
Game theory and evolution
Adv. Appl. Prob.
(1975)
J.C. Harsanyi
Oddness of the number of equilibrium points: A new Proof
Internat. J. Game Theory
(1973)

M.J.M. Jansen

Regularity and stability of equilibrium points of bimatrix games

Math. Op. Res.

(1981)

H.W. Kuhn

Extensive games and the problem of information

P. Leyhausen

Über die Funktion der relativen Stimmungshierarchie, dargestellt am Beispiel der phylogenetischen und ontogenetischen Entwicklung des Beutefangs von Raubtieren

Zeitschrift für Tierpsychologie

(1965)

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Citation Excerpt :
Some specific models are employed for building the framework to describe the interest conflicts between individuals and groups [8–10]. For example, the prisoner’s dilemma game (PDG) [11–15], served as a paradigmatic example of cooperative dilemma, has usually been used as a typical model to explore the evolution of cooperation between pairs of players. Notably, the strategy evolution in the spatial PDG is also a hot topic. [16]
A theoretical investigation on the strategy evolution in the self-organized division of labor dilemma is performed by means of evolutionary game theory. The often-used Fermi function is employed for driving the strategy updating, based on which the fixation probability of the involved strategy (performing which task) is calculated. Results about the evolution dynamics of the division of labor for two-player games are: (1) the fixation probabilityfor any selection intensity is derived; (2) the fixation probability and fixation time under weak selection are gained and a comparison with neutral selection is performed. In this case, the conditions to facilitate cooperation in division of labor are found. Then we extend the model to a multi-player one to describe the self-organized task allocation when multiple players are involved in one game. Relevant results for weak selection to favor the coexistence state of the two strategies for the multi-player games are gained. These results help understand and design effective mechanism where self-organized collective dynamics occurs in the form of maximizing the benefit of the multi-agent system.

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Mathematical Social Sciences

Abstract

References (26)

Territorial defence in the speckled wood butterfly (Parage aegeria): The resident always wins

Anim. Behav.

The role of asymmetries in animal contests

Anim. Behav.

Essential equilibrium points of n-person non-cooperative games

Sci. Sinica

An evaluation of the conflict hypothesis as an explanatory principle for the evolution of displays

Mathematik für Ökonomen II

Refinements of the Nash equilibrium concept

The Selfish Gene

Do digger wasps commit the Concorde fallacy?

Anim. Behav.

Game theory and evolution

Adv. Appl. Prob.

Oddness of the number of equilibrium points: A new Proof

Internat. J. Game Theory

Regularity and stability of equilibrium points of bimatrix games

Math. Op. Res.

Extensive games and the problem of information

Über die Funktion der relativen Stimmungshierarchie, dargestellt am Beispiel der phylogenetischen und ontogenetischen Entwicklung des Beutefangs von Raubtieren

Zeitschrift für Tierpsychologie

Cited by (148)

To outsource or not: Bike-share rebalancing strategies under the service quality deviation of a third party

Extended proper equilibrium

The evolution of taking roles

A study of the petroleum trade network of countries along “The Belt and Road Initiative”

Inefficient stage Nash is not stable

Stochastic dynamics of division of labor games in finite populations

Evolutionary stability in extensive two-person games☆

Abstract

Anim. Behav.

Anim. Behav.

Sci. Sinica

An evaluation of the conflict hypothesis as an explanatory principle for the evolution of displays

Mathematik für Ökonomen II

Refinements of the Nash equilibrium concept

The Selfish Gene

Do digger wasps commit the Concorde fallacy?

Anim. Behav.

Game theory and evolution

Adv. Appl. Prob.

Oddness of the number of equilibrium points: A new Proof

Internat. J. Game Theory

Regularity and stability of equilibrium points of bimatrix games

Math. Op. Res.

Extensive games and the problem of information

Über die Funktion der relativen Stimmungshierarchie, dargestellt am Beispiel der phylogenetischen und ontogenetischen Entwicklung des Beutefangs von Raubtieren

Zeitschrift für Tierpsychologie