Prisoner's Game Research Articles

Research on Evolutionary Game Analysis of Spatial Cooperation for Social Governance of Basin Water Pollution

Given that the two institutional arrangements of government regulation and market allocation cannot effectively solve the conflict between individual and collective interests in the process of water pollution control, this work presents a useful attempt on the third institutional arrangement of environmental governance—social governance—to overcome the dilemma. Based on common pool resource theory and multi-person prisoner game analysis framework, it incorporates environmental damage function, spatial network structure, and strategy update based on a learning mechanism into the analysis framework. In addition, it constructs a set of spatial cooperative evolution game models of basin water pollution social governance, so as to test the guarantee effect of the spontaneous collective action conditions of basin polluters on the long-term survival of the new system. This work adopts the Monte Carlo numerical simulation method to conduct the simulation experiment research. The experimental results show it is possible to successfully form collective actions entirely dependent on emitters, which yet requires a large initial scale of cooperation, that is, a majority of the emitter group autonomously abides by credible commitments. In this process, transparent full information and active organizational mobilization have a positive effect on the collective action development. The organic combination can better guide emitters to abide by credible commitments to achieve the optimal collective interests. The study results can provide a theoretical and practical reference for the social governance mechanism at a large-scale basin.

The effect of perceptions competition and learning costs on cooperation in spatial evolutionary multigames

It is a great challenge to correctly understand the evolution and incentives of cooperation. In recent years, the spatial evolutionary multigames have attracted extensive attention from researchers. Actually, for players, not only themselves but also their neighbors will affect their perceptions, which has not been considered in previous works. In addition, changing perceptions has a learning process, which will cause some costs. Inspired by the above facts, we explore the impact of perceptions competition mechanisms and learning costs on the evolution of cooperation in the multigames dilemma, which consists of prisoner game and snowdrift game. Especially, we further explore how different groups can coexist in such a setting. It is found that the heterogeneity of payoffs contributes to network reciprocity and can maintain cooperative behaviors even under unfavorable conditions. Compared with the static multigames mechanism, our perceptions competition mechanism has a higher proportion of cooperators under the same temptation value b and sucker payoff θ, and the cooperators can survive within a larger range of parameters. At the same time, a small cost can effectively maintain a high proportion of cooperators, while an appropriate cost will keep players at a high level of both the proportion of cooperators and the coexistence range. The continuous increase of costs will make our evolutionary mechanism ineffective and turn to static multigames. We also find that the introduction of costs will help different types of players coexist, and with the increase of costs, the coexistence area will first decrease and then increase. Moreover, our main findings are equally applicable to complex networks such as BA networks and random networks.

Natural Selection Between Two Games with Applications to Game Theoretical Models of Cancer.

Evolutionary game theory has been used extensively to study single games as applied to cancer, including in the context of metabolism, development of resistance, and even games between tumor and treatment. However, the situation when several games are being played against each other at the same time has not yet been investigated. Here, we describe a mathematical framework for analyzing natural selection not just between strategies, but between games. We provide theoretical analysis of situations of natural selection between the games of Prisoner's dilemma and Hawk-Dove, and demonstrate that while the dynamics of cooperators and defectors within their respective games is as expected, the distribution of games changes over time due to natural selection. We also investigate the question of mutual invasibility of games with respect to different strategies and different initial population composition. We conclude with a discussion of how the proposed approach can be applied to other games in cancer, such as motility versus stability strategies that underlie the process of metastatic invasion.

Does information of how good or bad your neighbors are enhance cooperation in spatial Prisoner's games?

Network reciprocity is one of the key mechanisms to solve social dilemmas, and has attracted many researchers for the last decade. Here, we explore what happens if network reciprocity is dovetailed with indirect reciprocity. This is motivated by the idea that a player may utilize observed information to evaluate his neighbors. Simulations based on our minimal model reveal that adding indirect reciprocity does not always increase the level of cooperation beyond the level of model without indirect reciprocity. This implies that the combination of two different reciprocity mechanisms, each enhancing cooperation if applied independently, can lead negative interference effect on cooperation. The details of this depend on type of action assessment system determining what is good and bad. Interestingly, we found that a high level of information is not always superior to low levels of information.

Resilient cooperators stabilize long-run cooperation in the finitely repeated Prisoner\u2019s Dilemma

Learning in finitely repeated games of cooperation remains poorly understood in part because their dynamics play out over a timescale exceeding that of traditional lab experiments. Here, we report results of a virtual lab experiment in which 94 subjects play up to 400 ten-round games of Prisoner’s Dilemma over the course of twenty consecutive weekdays. Consistent with previous work, the typical round of first defection moves earlier for several days; however, this unravelling process stabilizes after roughly one week. Analysing individual strategies, we find that approximately 40% of players behave as resilient cooperators who avoid unravelling even at significant cost to themselves. Finally, using a standard learning model we predict that a sufficiently large minority of resilient cooperators can permanently stabilize unravelling among a majority of rational players. These results shed hopeful light on the long-term dynamics of cooperation, and demonstrate the importance of long-run experiments.

Research on the Water Resource Manegement Based on Game Model

It is a principal-agent relationship in the process of the implementation of water resource management in China, which causes the game between the different governments inevitably. Game theory is a method that explains the decision makers’ behavior under different conditions. Traditionally, in the finite repeated prisoner's game, the Nash equilibrium of the “prisoner dilemma” is the only equilibrium of prisoners. This result seems to be inconsistent with the true choices in the water resource governance. From analyzing the game model with complete information and incomplete information, it finds the Nash equilibrium under the different conditions between the central government and the local governments. In order to strengthen the cooperation of all levels of government, it is absolutely essential that the central government provide complete information and increase the punishment probability, improve the incentive mechanism and reform the local government's performances evaluation in the future.

The X-Factor

This article addresses practices of reflexivity, drawing on a number of stimuli, including Zizek’s formulation of Lacan’s “prisoners game,” whereby different circumstances generate a typology of reflexive responses from the prisoners in their competitive efforts to win freedom. The article also draws on reflexive performances based on literature and in history, and more extensively on the art of Rene Magritte. These various reflexive performances are then related to the reflexive “praxes” of the authors’ doctoral study. We conclude that reflexivity is always part of a necessary uncertainty, whose “remainder” between the visible and the invisible, the present and the absent, generates an inescapably qualitative symbolon.

Release the prisoners game

This article presents the mathematical approach of the optimal strategy to win the ‘Release the prisoners’ game and the integration of this analysis in a math class. Outline lesson plans at three different levels are given, where simulations are suggested as well as theoretical findings about the probability distribution function and its mean value.

Interrelationships among noncooperative and coalition stability concepts

Insightful theorems are established on interrelationships among coalition and noncooperative stability concepts defined within the paradigm of the Graph Model for Conflict Resolution. More specifically, the newly defined coalition stability definitions that are considered are coalition Nash stability (CNash), coalition general metarationality (CGMR), coalition symmetric metarationality (CSMR) and coalition sequential stability (CSEQ), along with their earlier-defined noncooperative versions. A range of interesting new theorems are derived to establish connections among these coalition stability concepts as well as between noncooperative and coalition stability definitions. Applications with respect to the games of Prisoner’s Dilemma and Chicken, as well as a groundwater contamination dispute, demonstrate how the various stability definitions can be applied in practice and confirm the validity of some of the theorems as well as point out, by example, certain types of relationships which cannot hold.

Constructing quantum games from nonfactorizable joint probabilities

A probabilistic framework is developed that gives a unifying perspective on both the classical and quantum versions of two-player games. We suggest exploiting peculiar joint probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct a quantum game when the corresponding classical game is obtained from factorizable joint probabilities. We analyze how nonfactorizability changes Nash equilibria in three well-known games of prisoner's dilemma, stag hunt, and chicken. In this framework we find that for the game of prisoner's dilemma even nonfactorizable EPR joint probabilities cannot be helpful to escape from the classical outcome of the game. For a particular version of the chicken game, however, we find that the two nonfactorizable sets of joint probabilities, which maximally violate the Clauser-Holt-Shimony-Horne sum of correlations, indeed result in new Nash equilibria.

QUANTUM OCTAL GAMES

Quantum games offer situations where quantum information theory may help in solving or improving games with lack of information. For example, one may rely upon properties of entanglement for showing the superiority of a quantum player who is allowed to use quantum operations against a classical player (penny flipover [5]). Quantum communication properties enter into play in cooperative games (prisoners game, [3], guessing number [10]). An introduction to this field and an overview of important results are proposed in [7, 8]. But games may also help to make notions easier to understand, and new ways of reasoning to apprehend. The objective of this paper is to formalize and study a simple game with qubits using quantum notions of measurement and superposition, while keeping a simple formalism so that knowing quantum mechanics is not necessary to play the game. We generalize Conway's classical octal games to quantum octal games, and we solve the quantum combinatorial game QO.07 by giving a winning strategy for it. A playable version of the studied qubit game is available at the address .

Evolutionary prisoner’s dilemma game on a square lattice

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing state when varying the value of temptation to defect. In the limits $c \to 0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.

Great-Power Cooperation under Conditions of Limited Reciprocity: From Empirical to Formal Analysis

Theorists of cooperation argue that reciprocity combined with cooperative initiatives can allow cooperation to emerge between self-interested actors caught in collective goods dilemmas and lacking binding authority. Cooperation among the world's great powers is a key testing ground for such theories. Using U.S.-Chinese relations as a focus, this article develops a formal, decision-theoretic, model of great-power relations. The model is based on the empirical evidence from the Three-Way Street study of the U.S.-Soviet-Chinese triangle during the Cold War. The empirical results are used to construct stylized conditions that restrict the model in ways corresponding to our best empirical knowledge of great-power relations. These restrictions allow the model to be simplified (becoming decision-theoretic rather than game-theoretic), without losing empirical realism. The restrictions also allow the model to be generalized in several ways; it allows for graduated play along a scale of cooperation-conflict and for limited (partial) reciprocity in response to movements along that scale. Payoffs are defined along a scale of severity (relative incentives to defect vs. cooperate) in games of Prisoner's Dilemma, Stag Hunt, Chicken, Deadlock, or Harmony. The model implies that limited reciprocity is surprisingly effective in creating the conditions for cooperation to emerge, under a range of payoff structures and realistic discounting of future outcomes.

Some New Sources of Social Conflict: Transformations of Mixed-Motive Games

Some New Sources of Social Conflict: Transformations of Mixed-Motive Games

TIT FOR TAT in sticklebacks and the evolution of cooperation.

The problems of achieving mutual cooperation can be formalized in a game called the Prisoner's Dilemma in which selfish defection is always more rewarding than cooperation. If the two protagonists have a certain minimum probability of meeting again a strategy called TIT FOR TAT is very successful. In TIT FOR TAT the player cooperates on the first move and thereafter does whatever the opponent did on the previous move. I have studied the behaviour of fish when confronting a potential predator, because conflicts can arise within pairs of fish in these circumstances which I argue resemble a series of games of Prisoner's Dilemma. Using a system of mirrors, single three-spined sticklebacks (Gasterosteus aculeatus) approaching a live predator were provided with either a simulated cooperating companion or a simulated defecting one. In both cases the test fish behaved according to TIT FOR TAT supporting the hypothesis that cooperation can evolve among egoists.