Universal scaling for the dilemma strength in evolutionary games

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.     

Reciprocal cooperation in the Prisoner's Dilemma repeated with random horizon

Summary A standard assumption on the Iterated Prisoner's Dilemma is that the probability of further interaction is constant. Then, cooperation via reciprocity can be guaranteed if and only if this probability is sufficiently high. In this paper we analyze a more realistic model: a discrete random variable, not necessarily geometric, governs the number of interactions. We obtain necessary conditions and sufficient conditions for reciprocal cooperation based on the use of TFT strategy by both players. The obtained conditions are particularized to classes of distributions with monotonous failure rate and to some relevant probability models.     

Motif structure and cooperation in real-world complex networks

Networks of dynamical nodes serve as generic models for real-world systems in many branches of science ranging from mathematics to physics, technology, sociology and biology. Collective behavior of agents interacting over complex networks is important in many applications. The cooperation between selfish individuals is one of the most interesting collective phenomena. In this paper we address the interplay between the motifs’ cooperation properties and their abundance in a number of real-world networks including yeast protein-protein interaction, human brain, protein structure, email communication, dolphins’ social interaction, Zachary karate club and Net-science coauthorship networks. First, the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated. To this end, the evolutionary dynamics of the Prisoner’s Dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time. Then, the three- to six-node motifs are extracted for each network. The significance of the abundance of a motif, represented by a Z-value, is obtained by comparing them with some properly randomized versions of the original network. We found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and Z-value, i.e. the more the Z-value the less the amount of cooperativity. This suggests that networks composed of well-structured units do not have good cooperativity properties.     

Non-factorizable joint probabilities and evolutionarily stable strategies in the quantum prisoner's dilemma game

The well-known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein-Podolsky-Rosen type setting. Earlier results report that in this scheme the classical NE remains intact as the unique solution of the quantum PD game. In contrast, we show here that interestingly in this scheme a non-classical solution for the ESS emerges for the quantum PD.     

Commons dilemma and the “Tragedy of the Commons”

There are a lot of studies on commons dilemma. But few studies succeed to formulate it adequately. Moreover, although there are some situations where the dilemma does not occur, these studies focuses only the case that the dilemma does occur. In the present paper, we formulate the commons dilemma as an N‐person game and examine what situations our formulation represents. We show that there are six regions with respect to the value decrement induced by one additional animal and that commons dilemma does not occur in some of these regions.     

重复囚徒困境博弈中的社会行为仿真

大多数经济行为都可以看作博弈论的一个特殊案例.本文通过计算机仿真对重复囚徒困境博弈的特点进行了分析,建立基于累积期望差异评价策略的重复囚徒困境博弈模型,并对仿真结果进行了分析.分析结果表明,它能够对社会群体行为随着时间的推移提供动态描述,同时对于重复博弈问题的研究有着重要的辅助作用.     

演化博弈与自组织合作

主要研究复杂网络上的演化博弈.首先研究具有社团结构的无标度网络上的演化囚徒困境博弈及Newman-Watts小世界网络中异质性对合作演化的影响.然后考察了在不同合作者和作弊者初始分布配置情况下,不同的初始比例条件对合作水平的影响,且在社会网络上研究了雪堆博弈中的合作演化.进一步地,讨论了网络拓扑和博弈动力学的共同演化问题和网络上演化囚徒困境中的强化学习问题.最后给出了复杂网络上演化博弈论的未来发展方向与应用前景.     

Effects of Inertia on Evolutionary Prisoner's Dilemma Game

Considering the inertia of individuals in real life,we propose a modified Fermi updating rule,where the inertia of players is introduced into evolutionary prisoner's dilemma game(PDG) on square lattices.We mainly focus on how the inertia affects the cooperative behavior of the system.Interestingly,we find that the cooperation level has a nonmonotonic dependence on the inertia:with small inertia,cooperators will soon be invaded by defectors;with large inertia,players are unwilling to change their strategies and the cooperation level remains the same as the initial state;while a moderate inertia can induce the highest cooperation level.Moreover,effects of environmental noise and individual inertia are studied.Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.     

Modeling Reputation Management System on Online C2C Market

This paper discusses the effectiveness of sharing information concerning the reputations of buyers and sellers making online transactions in a consumer-to-consumer (C2C) market. We developed a computer simulation model that describes online transactions with a reputation management system that shares information concerning the reputations of consumers. The model takes an agent-based approach in which agents' actions are based on the iterated prisoner's dilemma. No model exists to analyze C2C markets even though there are many case studies concerning the effectiveness of sharing reputation information among participants in a market. The simulation results revealed that a positive reputation system can be more effective than a negative reputation system for an online transaction, even though the negative one can work for a traditional transaction. The result should be an important consideration when designing practical reputation management systems for online transactions.     

Effects of Inertia on Evolutionary Prisoner's Dilemma Game

Considering the inertia of individuals in real life, we propose a modified Fermi updating rule, where the inertia of players is introduced into evolutionary prisoner's dilemma game (PDG) on square lattices. We mainly focus on how the inertia affects the cooperative behavior of the system. Interestingly, we find that the cooperation level has a nonmonotonic dependence on the inertia: with small inertia, cooperators will soon be invaded by defectors; with large inertia, players are unwilling to change their strategies and the cooperation level remains the same as the initial state; while a moderate inertia can induce the highest cooperation level. Moreover, effects of environmental noise and individual inertia are studied. Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.