We show that the success of cooperation in an evolutionary prisoner's dilemma on a complex network can be predicted by a simple, quantitative network analysis using mean field parameters. The criterion is shown to be accurate on a wide variety of networks with degree distributions ranging from regular to Poisson to scale-free. The network analysis uses a parameter that allows for comparisons of networks with both similar, and distinct, topologies. Furthermore, we establish the criterion here as a natural network analogue of Hamilton's classical rule for kin selection, despite arising in an entirely different context. The result is a network-based evolutionary rule for altruism that parallels Hamilton's genetic rule.
We introduce the stochastic Network-Iterated Prisoner's Dilemma (NIPD) model, a network of players playing the Prisoner's Dilemma with their neighbours, each with a memory-one strategy which they constantly and locally update to improve their success. This process is non-deterministic, and mirrors societal interactions in many relevant aspects. We use it to assess the flexibility, noise tolerance and real-world adaptability of some well-known strategies. Furthermore, in the model a new strategy naturally emerges which proves way more successful than those. We also derive some theoretical param…
This manuscript explores the research topics and collaborative behaviour of authors in the field of the Prisoner's Dilemma using topic modeling and a graph theoretic analysis of the co-authorship network. The analysis identified five research topics in the Prisoner's Dilemma which have been relevant over the course of time. These are human subject research, biological studies, strategies, evolutionary dynamics on networks and modeling problems as a Prisoner's Dilemma game. Moreover, the results demonstrated the Prisoner's Dilemma is a field of continued interest, and that it is a collaborative…
Game theory is fundamental to understanding cooperation between agents. Mainly, the Prisoner's Dilemma is a well-known model that has been extensively studied in complex networks. However, although the emergence of cooperation has been investigated before, the influence of memory in its evolution is not well understood. This paper presents a detailed study of cooperation dynamics in which agents have memory. We simulate the evolutionary Prisoner's dilemma game on random, scale-free and networks presenting degree-degree correlation. Through extensive simulations, we show that assortativity can …
The Iterated Prisoner's Dilemma (IPD) is a well studied framework for understanding direct reciprocity and cooperation in pairwise encounters. However, measuring the morality of various IPD strategies is still largely lacking. Here, we partially address this issue by proposing a suit of plausible morality metrics to quantify four aspects of justice. We focus our closed-form calculation on the class of reactive strategies because of their mathematical tractability and expressive power. We define reactive means as a tool for studying how actors in the IPD and Iterated Snowdrift Game (ISG) behave…
Evolutionary Dynamics of Reputation-Based Voluntary Prisoner's Dilemma Games
Kyushu University（九州大学）；Teesside University（蒂斯赛德大学）；CSSC Systems Engineering Research Institute（中国船舶系统工程研究院）；CSSC Intelligent Innovation Research Institute（中国船舶智能创新研究院）；Yunnan University of Finance and Economics（云南财经大学）；University of Maribor（马里博尔大学）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔阿道夫·德罗尔克博士社区健康中心）；Kyung Hee University（庆熙大学）；Korea University（高丽大学）；Northwestern Polytechnical University（西北工业大学）
Understanding the role of network structure in the evolution of cooperation is a key research goal at the intersection between physics and biology. Recent studies have particularly focused on multiplex networks given that multiple social domains are interrelated and cannot be represented by single-layer networks. However, the role of network multiplexity is not fully understood when combined with another important network characteristic: network dynamics. In the present study, we investigated evolutionary prisoner's dilemma games played on dynamic two-layer multiplex networks in which the payo…
We investigate the repeated prisoner's dilemma game where both players alternately use reinforcement learning to obtain their optimal memory-one strategies. We theoretically solve the simultaneous Bellman optimality equations of reinforcement learning. We find that the Win-stay Lose-shift strategy, the Grim strategy, and the strategy which always defects can form symmetric equilibrium of the mutual reinforcement learning process amongst all deterministic memory-one strategies.
We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoners' dilemma game. We provide a necessary condition for memory-two deterministic strategies to form symmetric equilibria. We then provide three examples of memory-two deterministic strategies which form symmetric mutual reinforcement learning equilibria. We also prove that mutual reinforcement learning equilibria formed by memory-two strategies are also mutual reinforcement learning equilibria when both players use…
On the existence of fair zero-determinant strategies in the periodic prisoner's dilemma game
Graduate School of Sciences and Technology for Innovation, Yamaguchi University（山口大学创新科学技术研究生院）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理系）
We analyze an extended model of the Iterated Prisoner's Dilemma where agents decide to play based on the data from their limited memory or recommendations. The cooperators can decide whether to play with the matched opponent or not. The agents' decisions are directly linked to their level of optimism since they decide to play if they believe the opponent has a high probability of cooperating. Optimism is precisely tuned by parameters optimism threshold and tolerance. Our experiment showed that being optimistic is better for cooperators as it leads to more accurate exploration in the multi-agen…
A Round-Robin Tournament of the Iterated Prisoner's Dilemma with Complete Memory-Size-Three Strategies
在本文中，一个囚犯的困境罗宾轮比赛的模拟结果。在锦标赛中，每个参与策略都扮演一个迭代的囚徒困境，与其他策略（循环赛）和作为一个变体也与自己对抗。锦标赛的参与者都是确定性的策略，并且对自己和对手过去的动作具有相同大小的记忆：对手最多三个最近的动作和自己最多两个最近的动作。一个重点是设置在调查的影响，迭代次数，支付矩阵的细节，和内存大小的影响。主要结果是，对于这里进行的锦标赛，不同的策略出现作为赢家不同的收益矩阵，即使不同的收益矩阵是相似的判断，如果他们满足关系T + S = P + R或2R > T + S。由于这一结果，它建议，每当迭代囚徒困境是用来模拟一个真正的系统，不明确固定的支付矩阵，应该检查，如果结论仍然有效，当使用不同的支付矩阵。
