Statistical physics of the spatial Prisoner’s Dilemma with memory-aware agents

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• 作者：Marco Alberto Javarone
• 关键词：Statistical and Nonlinear Physics
• 刊名：The European Physical Journal B - Condensed Matter
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：89
• 期：2
• 全文大小：787 KB
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• 作者单位：Marco Alberto Javarone (1) (2)
  
  1. Department of Mathematics and Computer Science, University of Cagliari, 09123, Cagliari, Italy
  2. DUMAS – Department of Humanities and Social Sciences, University of Sassari, 07100, Sassari, Italy
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Condensed Matter
  Physics
  Complexity
  Fluids
  Solid State Physics and Spectroscopy
  Superconductivity, Superfluidity and Quantum Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1434-6036

文摘

We introduce an analytical model to study the evolution towards equilibrium in spatial games, with ‘memory-aware’ agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner’s Dilemma, as it constitutes an emblematic example of a game whose Nash equilibrium is defection. Previous investigations showed that, under opportune conditions, it is possible to reach, in the evolutionary Prisoner’s Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms like motion may lead a population to become cooperative. In the proposed model, we map agents to particles of a gas so that, on varying the system temperature, they randomly move. In doing so, we are able to identify a relation between the temperature and the final equilibrium of the population, explaining how it is possible to break the classical Nash equilibrium in the spatial Prisoner’s Dilemma when considering agents able to increase their payoff over time. Moreover, we introduce a formalism to study order-disorder phase transitions in these dynamics. As result, we highlight that the proposed model allows to explain analytically how a population, whose interactions are based on the Prisoner’s Dilemma, can reach an equilibrium far from the expected one; opening also the way to define a direct link between evolutionary game theory and statistical physics. Keywords Statistical and Nonlinear Physics