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.     

COEXISTENCE OR EXCLUSION IN A COMPETITIVE COMMON-POOL FISHERY: A REVISIONIST VIEW

ABSTRACT. One of the earliest applications of game theory to renewable resource modeling was Colin Clark's analysis, in 1980, of the competitive exploitation of a common-pool resource. His model described the dynamics of a single Gordon-Schaeffer fish stock, being harvested non-cooperatively by two or more independently managed fleets. He showed that aggressive harvesting by all fleets (a Nash equilibrium) would lead to stock drawdown to a level which would successively eliminate all of the less efficient harvesters. Furthermore, when the fleets were closely matched, the survivor(s) of this aggressive competition would be forced, by the threat of competitors' reentry, to hold the stock in its severely degraded state, and hence to harvest at only marginal profitability. This outcome has often been compared to the open access “tragedy of the commons.” and to the outcome of the well-known “prisoners' dilemma” game. In this article I will argue that, for closely matched fleets, a more likely outcome is that the fleets will tacitly agree, without overt communication, to focus simultaneously on a specific set of coordinated policies which will permit their continuing coexistence and profitable operation. This policy profile also forms a Nash equilibrium, one which is secured by the mutual ability of the fleets to quickly recognize and credibly punish any unilateral deviations from the anticipated actions. Thus the dynamic harvesting game more nearly resembles the repeated prisoners' dilemma than it does the classical single stage version.     

Decentralized Interaction and Co-Adaptation in the Repeated Prisoner&2018;s Dilemma

A Prisoner&2018;s dilemma that is repeated indefinitely has many equilibria; the problem of selecting among these is often approached using evolutionary models. The background of this paper is a number of earlier studies in which a specific type of evolutionary model, a genetic algorithm (GA), was used to investigate which behavior survives under selective pressure. However, that normative instrument searches for equilibria that may never be attainable. Furthermore, it aims for optimization and, accordingly, says what people should do to be successful in repeated prisoner&2018;s dilemma (RPD) type situations. In the current paper, I employ simulation to find out what people would do, whether this makes them successful or not. Using a replication of Miller&2018;s (1988) GA study for comparison, a model is simulated in which the population is spatially distributed across a torus. The agents only interact with their neighbors and locally adapt their strategy to what they perceive to be successful behavior among those neighbors. Although centralized GA-evolution may lead to somewhat better performance, this goes at the cost of a large increase in required computations while a population with decentralized interactions and co-adaptation is almost as successful and, additionally, endogenously learns a more efficient scheme for adaptation. Finally, when the agents&2018; perceptive capabilities are limited even further, so that they can only perceive how their neighbors are doing against themselves, rather than against all those neighbors&2018; opponents&2014;which essentially removes reputation as a source of information&2014;cooperation breaks down.     

Preplay negotiations and the prisoner's dilemma

In order to improve outcomes of one shot noncooperative games a formal procedure for conducting preplay negotiations is proposed. For the prisoners' dilemma game it is shown that all the perfect equilibrium in the induced game (the game with the preplays) yield the cooperative pay-off. For another game it is shown that all perfect equilibrium payoffs converge to be Pareto optimal as the number of preplays increases.     

Arms races as iterated prisoner's dilemma games

Many important aspects of arms races are captured by the iterated prisoner's dilemma (IPD) game. In this analysis, strategies are developed and analyzed for IPD games which most resemble arms races; those which are finite, uncertain and time varying in length. It is shown that, under certain conditions, it can be rational to unilaterally cooperate following a series of mutual defection. A number of conclusions concerning arms race behavior are drawn.     

Coordination and Cooperation in Dyadic Relationships

A Markov model with a coordination parameter isdeveloped to depict coordination and cooperation decisionprocesses in 2 × 2 game relationships. The parameters ofthe model can be used to define and measure various forms ofinfluence. The model is applied to data collected using aprisoner's dilemma payoff structure to represent thesuperior-subordinate relationship. The results demonstrate theusefulness of the model and the measures of influence. Superiorsand subordinates are more likely to coordinate following mutualcooperation, achieving matching behaviors more frequently thanan independent-decisions model would predict. Subordinates showslightly more influence over leaders' behaviors than vice versa.     

Prisoner's dilemma game on adaptive networks under limited foresight

We study the emergence of cooperation in an environment where players in prisoner's dilemma game (PDG) not only update their strategies but also change their interaction relations. Different from previous studies in which players update their strategies according to the imitation rule, in this article, the strategies are updated with limited foresight. We find that two absorbing states—full cooperation and full defection—can be reached, assuming that players can delete interaction relations unilaterally, but new relations can only be created with the mutual consent of both partners. Simulation experiments show that high levels of cooperation in large populations can be achieved when the temptation to defect in PDG is low. Moreover, we explore the factors which influence the level of cooperation. These results provide new insights into the cooperation in social dilemma and into corresponding control strategies. © 2012Wiley Periodicals, Inc. Complexity, 2012     

Modelling a social dilemma of mode choice based on commuters’ expectations and social learning

This study attempts to apply an agent-based approach to modelling a social dilemma of travel mode choice considering psychological and sociological aspects. A traveller is modelled to have expectations, which shows the traveller’s beliefs about the influence of other group members on his action, as decision-making rules. Social interaction using a group-based interaction is hypothesized to be important. We apply an imitation game based on social learning mechanisms to the model. Two kinds of mechanism are used: payoff-biased and conformist transmission. The model reveals the conditions that make cooperation as a possible outcome are optimistic bandwagon expectations, group-based interactions, and strong conformist transmissions.     

Noncooperative farsighted stable set in an <Emphasis Type="Italic">n</Emphasis>-player prisoners’ dilemma

We examine an n-player prisoners’ dilemma game in which only individual deviations are allowed, while coalitional deviations (even non-binding ones) are not, and every player is assumed to be sufficiently farsighted to understand not only the direct outcome of his own deviation but also the ultimate outcome resulting from a chain of subsequent deviations by other players. We show that there exists a unique, noncooperative farsighted stable set (NFSS) and that it supports at least one (partially and/or fully) cooperative outcome, which is individually rational and Pareto-efficient. We provide a sufficient condition for full cooperation. Further, we discuss the relationship between NFSS and other “stable set” concepts such as the (myopic) von Neumann–Morgenstern stable set, Harsanyi (1974)’s strictly stable set, Chwe (1994)’s largest consistent set, and the cooperative farsighted stable set examined by Suzuki and Muto (2005). The author is very grateful to Professor Eiichi Miyagawa, the editor and the associate editor of this journal for their insightful comments and suggestions. He also acknowledges the financial support of Japan Society for the Promotion of Science [Grant-in-Aid for Scientific Research (C), No. 18530175].     

Explaining cooperation in the finitely repeated simultaneous and sequential prisoner’s dilemma game under incomplete and complete information

Explaining cooperation in social dilemmas is a central issue in behavioral science, and the prisoner’s dilemma (PD) is the most frequently employed model. Theories assuming rationality and selfishness predict no cooperation in PDs of finite duration, but cooperation is frequently observed. We therefore build a model of how individuals in a finitely repeated PD with incomplete information about their partner’s preference for mutual cooperation decide about cooperation. We study cooperation in simultaneous and sequential PDs. Our model explains three behavioral regularities found in the literature: (i) the frequent cooperation in one-shot and finitely repeated N-shot games, (ii) cooperation rates declining over the course of the game, and (iii) cooperation being more frequent in the sequential PD than in the simultaneous PD.     

The survival of inefficient and efficient norms: Equilibria with and without meta-norms in a repeated norm enforcing game

ABSTRACT

Although meta-norms have been considered as the key to sustaining cooperation norms, this study argues that the meta-norms also facilitate the survival of inefficient norms. The opportunistic norm violation strategy is proposed as an alternative mechanism to motivate costly punishments. A repeated norm enforcing game, in which the externality of the normative action can be negative or positive, is analyzed. This game is equivalent to a social dilemma if the externality is large enough. The ranges of externalities that support tit-for-tat, meta-norm, and opportunism equilibria are compared. The meta-norm equilibrium has the highest stability; however, it can persist in negative externalities. Finally, the opportunism equilibrium is more stable than the tit-for-tat equilibrium, but it breaks down when the externality is small.     

Evolutionary prisoner’s dilemma games with local interaction and best-response dynamics

This paper studies the long run behavior in evolutionary prisoner’s dilemma games. All players are assumed to sit around a circle and to interact only with their neighbors. It is known that full-defection is the unique long run equilibrium as the probability of players’ experimentation (or mutation) tends to zero in the best response dynamics. Here, it is shown that full-cooperation could emerge in the long run if one also cares for his neighbors in the bestresponse dynamics.     

Interaction dynamics of two reinforcement learners

The paper investigates a stochastic model where two agents (persons, companies, institutions, states, software agents or other) learn interactive behavior in a series of alternating moves. Each agent is assumed to perform “stimulus-response-consequence” learning, as studied in psychology. In the presented model, the response of one agent to the other agent's move is both the stimulus for the other agent's next move and part of the consequence for the other agent's previous move. After deriving general properties of the model, especially concerning convergence to limit cycles, we concentrate on an asymptotic case where the learning rate tends to zero (“slow learning”). In this case, the dynamics can be described by a system of deterministic differential equations. For reward structures derived from [2×2] bimatrix games, fixed points are determined, and for the special case of the prisoner's dilemma, the dynamics is analyzed in more detail on the assumptions that both agents start with the same or with different reaction probabilities.     

一种惩罚机制下一次性n人囚徒困境的合作性

为解决一次性n人囚徒困境中局中人如何走出困境的问题,引进了背叛惩罚函数及其严厉度和参与人的背叛愿意度等概念,并用数学论证法证明了如下结果:(1)参与人的背叛愿意度都不超过1.(2)背叛愿意度越大,这个参与人越愿意背叛;(3)背叛愿意度为0零时,这个参与人是否背叛其赢得一样;(4)当背叛愿意度取负数时,其绝对值越大,参与人的合作积极性越大.得到博弈结果的判定法:(1)计算各参与人的背叛愿意度.(2)若至少有一个参与人愿意背叛,则全体参与人都背叛.(3)若全体参与人都愿意合作,则合作成功.例子表明,本结果在理论上可有效地解决中局中人如何走出困境和在给定惩罚机制下博弈结果的预测问题.     

基于参与主体异质性条件下囚徒困境合作演化博弈模型研究

利用演化博弈理论,对参与主体异质性条件下的囚徒困境模型进行了探讨,求出了满足不同条件下的演化稳定策略,并对种群中个体异质性对演化稳定策略的影响进行了分析,得出种群中选择相同策略的个体异质性差异越大,参与个体选择合作行为作为演化稳定策略的可能性就越大.极端地,当个体的异质性趋向于无穷大时,合作成为唯一的演化稳定占优策略,为现实大多数合作系统中能保持长期的一种合作稳定状态提供了合理地解释.     

Properties of learning models in collective action: Rationality of backward-looking players

This article intends to clarify properties of learning models in simulation studies and to conduct a comparison of preceding learning models. Learning models are often used in many simulation studies, but there is no uniform rule of learning. We introduce three technical properties (monotonicity, condition of probability, neutrality) and three rational properties (rationality is fixed situations, rationality in first order stochastic domination, rationality with risk preference in stocahstic situations). We examine Michael Macy's model, the Erev & Roth model, and some others. We find that these models have different properties. Though learning is treated as one of the solutions of social dilemma from the results of Macy's model (Kollock, 1998), Macy's model is peculiar learning model. Learning is not always a solution of social dilemma. A comparison of learning models from a uniform point of view clarifies the properties of each model, and helps to probe conformity of a learning model and human behavior.     

On the prisoner’s dilemma in R&D with input spillovers and incentives for R&D cooperation

This paper considers a standard model of strategic R&D with spillovers in R&D inputs, and extends the result that duopoly firms engaged in a standard two-stage game of R&D and Cournot competition end up in a prisoner’s dilemma situation for their R&D decisions, whenever spillover effects and R&D costs are relatively low. In terms of social welfare, this prisoner’s dilemma always works to the advantage of both consumers and society. This result allows a novel and enlightening perspective on some issues of substantial interest in the innovation literature. In particular, the incentive firms face towards R&D cooperation in the form of an R&D cartel is shown to be maximal for the case of zero spillovers, which is when the prisoner’s dilemma has the largest scope.     

阈值风险下的多企业合作治理污染的演化博弈分析

针对环境污染具有跨区域性,环境资源的公共物品属性,由单一产污企业治理污染物难以取得有效成果,辖区内多个产污企业合作治理是环境保护的必由之路。 本文从演化博弈论的研究视角探讨了多个排污企业之间的决策演化过程,建立了多主体演化博弈模型,并考虑了污染排放总量超过总量阈值时的环境恶化风险,研究阈值风险对产污企业合作治理污染策略选择的影响。 研究结果表明,较高的治理成本很大地约束了逐利企业治理污染的行为选择,造成公地悲剧的社会问题。 企业治污成本较大背景下,环境阈值风险发生概率越高,越能有效促进合作治理环境策略的演化稳定,合作治理占优于不治理。 出于对企业自身初始禀赋的保护,产污企业初始禀赋越大、排污收费率越高,越能有效促进企业治理污染物的积极性。 最后,为促进辖区内污染企业合作治理污染提出了政策建议。     

On the existence and efficiency of the von Neumann-Morgenstern stable set in a n-player prisoners' dilemma

We show that there exist von Neumann-Morgenstern (vN-M) stable sets in a n-player version of the prisoners' dilemma game with preplay negotiations in which every player can deviate unilaterally from the currently proposed combination of actions but can not do so jointly with other players, and that every vN-M stable set includes at least one Pareto-efficient outcome. The negotiation among the players is formulated as the “individual contingent threats situation” within the framework of the theory of social situations due to Greenberg (1990). The method of proving the existence also provides us with a step-by-step method of constructing the vN-M stable set. Final version June 2001     

PREFERENCE AND EVOLUTION IN THE ITERATED PRISONER''S DILEMMA

Game theory is extensively used to study strategy-making and actions of play-ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner's dilemma. In this article, a pref-erence parameter k was introduced in the payoff matrix, wherein the value of k denotes the player's degree of egoism and altruism (preference). Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how prefer-ence influences the evolutionary equilibrium and behaviors of players. The authors get the general results: egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.