Effect of space in the game “war of attrition”
Journal article, 2012

Spatial dynamics has in many cases been invoked as a mechanism that can promote the evolution of coexistence and cooperation, although the precise conditions for this to occur have not yet been characterised. In an effort to address this question we have analyzed an alternative version of the theoretical game “war of attrition,” which exhibits unusual behavior: The well-mixed system exhibits quasistationary coexistence and a relaxation time that scales exponentially with the system size, while the spatial system shows a relaxation time that is considerably smaller and scales with a power α≈1.4 of the system size. Further, the spatial system exhibits a first-order phase transition in the strategy distribution at a consolation prize of k≈1/3. Close to this point the relaxation time diverges with an exponent γ≈1.2. This analysis shows that the effect of space is highly dependent on the type of game considered.

spatial

war of attrition

game theory

Author

Philip Gerlee

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Torbjörn Lundh

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

1539-3755 (ISSN)

Vol. 85 4 Art. no. 041115- 041115

Subject Categories

Computational Mathematics

Biological Sciences

Roots

Basic sciences

Areas of Advance

Life Science Engineering

DOI

10.1103/PhysRevE.85.041115