Interplay of Elementary Interactions Causing Social Traps in Evolutionary Games
Open Access
- 11 March 2020
- journal article
- research article
- Published by Frontiers Media SA in Frontiers in Physics
Abstract
In evolutionary games, pair interactions are defined by payoff matrices that can be decomposed into four types of orthogonal elementary games that represent fundamentally different interaction situations. The four classes of elementary interactions are formed by games with self- and cross-dependent payoffs, coordination games, and cyclic games. At the level of two-person games, social traps (dilemmas) can not occur for symmetric payoff matrices, which are combinations of coordination games and symmetrically paired self- and cross-dependent components, because individual and common interests coincide in them. In spatial evolutionary games that follow the logit evolutionary dynamics, however, the total payoff is still not maximized at certain noise levels in certain combinations of symmetric components. This phenomenon is similar to the appearance of partially ordered phases in solid state physics, which are stabilized by their higher entropy. In contrast, it is the antisymmetric part of their self- and cross-dependent components that is responsible for the emergence of traditional social dilemmas in games like the two-strategy donation game or the prisoner's dilemma. The general features of these social dilemmas are inherited by n-strategy games in the absence of cyclic components, which would prevent the existence of a potential and thus thermodynamic behavior. Using the mathematical framework of matrix decomposition, we survey the ways in which the interplay of elementary games can lead to a loss of total payoff for a society of selfish players. We describe the general features of different illustrative combinations of elementary games, including a game in which the presence of a cyclic component gives rise to the tragedy of the commons via a paradoxical effect.This publication has 61 references indexed in Scilit:
- Motion of influential players can support cooperation in Prisoner’s DilemmaZeitschrift für Physik B Condensed Matter, 2009
- A minimal model for the evolution of cooperation through evolving heterogeneous gamesEurophysics Letters, 2008
- Evolutionary games on graphsPhysics Reports, 2007
- Five Rules for the Evolution of CooperationScience, 2006
- Three-state Potts model in combination with the rock-scissors-paper gamePhysical Review E, 2005
- Volunteering as Red Queen Mechanism for Cooperation in Public Goods GamesScience, 2002
- Rock–scissors–paper and the survival of the weakestProceedings. Biological sciences, 2001
- Collective Phenomena in Spatially Extended Evolutionary GamesJournal of Theoretical Biology, 1994
- The Potts modelReviews of Modern Physics, 1982
- Some generalized order-disorder transformationsMathematical Proceedings of the Cambridge Philosophical Society, 1952