The emergence of cooperation in tie strength models

In this paper, we propose a tie strength model to explain the emergence of cooperation in spatial prisoner's dilemma games, assuming that cooperators preferentially allocate their investments to friends with strong ties. Two types of prisoner's dilemma models are examined in this study: the traditional two-strategy model considering only cooperators and defectors; the expanded three-strategy model consisting cooperators, defectors and extortioners. The results show that tie strength model contributes to the promotion of cooperation in both types of prisoner's dilemma games. However, we point out that the influence of the investment preference is quite different in the two prisoner's dilemma game settings. In the two-strategy prisoner's dilemma game, only small preference contributes to the promotion of cooperation. Once this preference exceeds a critical value, cooperation will be prohibited. We explain this phenomenon by arguing that extremely strong investment preference undermines the ability of cooperative clusters to resist defectors. Moreover, we extend the analysis into the three-strategy case and discover that the catalytic effect of extortioners can eliminate this first up and then down trend in the two-strategy model. The equilibrium fraction of cooperators is always positively correlated to the level of investment preference in three-strategy models.     

A note on uncertainty and cooperation in a finitely repeated prisoner's dilemma

An intuitive expectation is that in a finitely repeated prisoner's dilemma, the players will achieve mutual cooperation in at least some periods. Existing explanations for equilibrium cooperation (with agents perfectly informed of one another's characteristics) require that the number of repetitions be unknown, which is in many cases an uncomfortably strong uncertainty assertion. This paper demonstrates that if agents have private information concerning the number of repetitions (as opposed to being completely uninformed), equilibrium mutual cooperation can occur in a finitely repeated game. This appears to be a weaker and more palatable assumption then that of complete uncertainty, and hence provides a natural and useful alternative foundation for mutual cooperation.     

On some variants of dynamical systems

A dynamical system motivated by discrete physics is studied. Fuzzy dynamical systems are used to study fuzzy discrete replicator dynamics of hawk–dove (HD) and prisoner's dilemma (PD) games. New solutions are obtained. Finally a preliminary study for fuzzy predator–prey model is studied and a new equilibrium is found.     

New equilibria for noncooperative two‐person games

New equilibrium concepts for noncooperative two‐person games are introduced and examined. Although these equilibria coincide with the Nash equilibria in all constant‐sum games, they differ significantly in other cases. In particular, for finite repetitions of the prisoner's dilemma, some cooperating strategy combinations become equilibria.     

A dynamic analysis of the repeated prisoner's dilemma game

A new dynamic model for the repeated prisoner's dilemma game is analyzed.     

A non-equilibrium analysis of the finitely-repeated prisoner's dilemma

We follow a non-equilibrium approach to the finitely repeated prisoner's dilemma with trigger strategies. Each player has a probability distribution which gives the probability with which he thinks the other player first plans to cheat in any given period. We show that, provided that this probability distribution assigns some minimum weight to all periods, the players will cooporate for most of the game if it is repeated enough times.     

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.     

Prisoner's dilemma and clusters on small‐world networks

The structure of interaction plays an important role in the outcome of evolutionary games. This study investigates the evolution of stochastic strategies of the prisoner's dilemma played on structures ranging from lattices to small world networks. Strategies and payoffs are analyzed as a function of the network characteristics of the node they are playing on. Nodes with lattice‐like neighborhoods tend to perform better than the nodes modified during the rewiring process of the construction of the small‐world network. © 2007 Wiley Periodicals, Inc. Complexity 12:22–36, 2006     

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     

Structural heterogeneity mediates the effect of community structure on cooperation

Emergence of cooperation in evolutionary prisoner's dilemma game strongly depends on the topology of underlying interaction network. We explore this dependence using community networks with different levels of structural heterogeneity, which are generated by a tunable upper‐bound on the total number of links that any vertex can have. We study the effect of community structure on cooperation by analyzing a finite population analogue of the evolutionary replicator dynamics. We find that structural heterogeneity mediates the effect of community structure on cooperation. In the community networks with low level of structural heterogeneity, community structure has negative effect on cooperation. However, the positive effect of community structure on cooperation appears and enhances with increasing structural heterogeneity. Our work may be helpful for understanding the complexity of cooperative behaviors in social networks. © 2011 Wiley Periodicals, Inc. Complexity, 2012     

Zones of cooperation in demographic prisoner's dilemma

The emergence of cooperation in prisoner's dilemma (PD) games is generally assumed to require repeated play (and strategies such as Tit for Tat, involving memory of previous interactions) or features (“tags”) permitting cooperators and defectors to distinguish one another. In the demographic PD, neither assumption is made: Agents with finite vision move to random sites on a lattice and play a fixed culturally-inherited zero-memory strategy of cooperate (C) or defect (D) against neighbors. Agents are indistinguishable to one another—they are “tagless.” Positive payoffs accrue to agents playing C against C, or D against C. Negative payoffs accrue to agents playing C against D, or D against D. Payoffs accumulate. If accumulated payoffs exceed some threshold, agents clone offspring of the same strategy onto neighboring sites and continue play. If accumulated payoffs are negative, agents die and are removed. Spatial zones of cooperation emerge. © 1998 John Wiley & Sons, Inc.     

On an N-person noncooperative Markov game with a metric state space

We consider a noncooperative N-person discounted Markov game with a metric state space, and define the total expected discounted gain. Under some conditions imposed on the objects in the game system, we prove that our game system has an equilibrium point and each player has his equilibrium strategy. Moreover in the case of a nondiscounted game, the total expected gain up to a finite time can be obtained, and we define the long-run expected average gain. Thus if we impose a further assumption for the objects besides the conditions in the case of the discounted game, then it is proved that the equilibrium point exists in the nondiscounted Markov game. The technique for proving the nondiscounted case is essentially to modify the objects of the game so that they become objects of a modified Markov game with a discounted factor which has an equilibrium point in addition to the equilibrium point of the discounted game.     

Edgeworthian economies

We present a model of an Edgeworthian exchange economy where two goods are traded in a random meeting market place. The novelty of our model is that we associate a greediness factor to each participant which brings up a game alike the prisoner's dilemma into the usual Edgeworthian exchange economy. Along the time, random pairs of participants are chosen, and they trade or not according to their greediness. Furthermore, we let the greediness of the participants evolve along the trades according to one of the following rules: (a) the greediness of the participants decreases if they were able to trade and increases otherwise; (b) the greediness of the participants increases if they were able to trade and decreases otherwise. We observe that for rule (a) the greediness of each participant converges to one of two possible values, and that for rule (b) the greediness of all participants converges to a single value. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cooperation by indirect revelation through strategic behavior

The paper deals with a one-shot prisoners' dilemma when the players have an option to go to court but cannot verify their testimonies. To solve the problem a second stage is added to a game. At the first stage the players are involved in the prisoners' dilemma and at the second stage they play another game in which their actions are verifiable. In such a setup the information about the actions chosen at the prisoners' dilemma stage can be revealed through strategic behavior of the players during second stage. A mechanism for such revelation in the extended game is described. It provides an existence of a unique sequential equilibrium, which may be obtained by an iterative elimination of dominated strategies and has a number of desirable properties.     

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.     

Social Motives and Expectations in One-Shot Asymmetric Prisoner's Dilemmas

We propose a formal-behavioral framework with 3 components: nonselfish motives, expectations about others' nonselfish motives, and a game-theoretic component. For nonselfish motives, 3 nonstandard utility models representing altruism, inequality aversion, and norms are considered. Expectations are modeled as certain versus uncertain expectations. The game-theoretic component predicts behavior of actors and actors' expectations about behaviors of others. This framework is applied to asymmetric one-shot prisoner's dilemmas; predictions are tested experimentally. Formal analyses show that asymmetry provides new predictions through which nonstandard utility-expectation models can be distinguished. Empirical tests show that the inequality aversion model does considerably worse than altruistic and normative variants. Statistical tests for own motives, expected motives, and the association between the two are provided, while accounting for decision noise.     

Stationary,completely mixed and symmetric optimal and equilibrium strategies in stochastic games

In this paper, we address various types of two-person stochastic games—both zero-sum and nonzero-sum, discounted and undiscounted. In particular, we address different aspects of stochastic games, namely: (1) When is a two-person stochastic game completely mixed? (2) Can we identify classes of undiscounted zero-sum stochastic games that have stationary optimal strategies? (3) When does a two-person stochastic game possess symmetric optimal/equilibrium strategies? Firstly, we provide some necessary and some sufficient conditions under which certain classes of discounted and undiscounted stochastic games are completely mixed. In particular, we show that, if a discounted zero-sum switching control stochastic game with symmetric payoff matrices has a completely mixed stationary optimal strategy, then the stochastic game is completely mixed if and only if the matrix games restricted to states are all completely mixed. Secondly, we identify certain classes of undiscounted zero-sum stochastic games that have stationary optima under specific conditions for individual payoff matrices and transition probabilities. Thirdly, we provide sufficient conditions for discounted as well as certain classes of undiscounted stochastic games to have symmetric optimal/equilibrium strategies—namely, transitions are symmetric and the payoff matrices of one player are the transpose of those of the other. We also provide a sufficient condition for the stochastic game to have a symmetric pure strategy equilibrium. We also provide examples to show the sharpness of our results.     

Optimal replacement policies with minimal repair and age-dependent costs

In this paper, we study a modified minimal repair/replacement problem that is formulated as a Markov decision process. The operating cost is assumed to be a nondecreasing function of the system's age. The specific maintenance actions for a manufacturing system to be considered are whether to have replacement, minimal repair or keep it operating. It is shown that a control limit policy, or in particular a (t, T) policy, is optimal over the space of all possible policies under the discounted cost criterion. A computational algorithm for the optimal (t, T) policy is suggested based on the total expected discounted cost.     

On the optimal management of project risk

The uncertainty of project networks has been mainly considered as the randomness of duration of the activities. However, another major problem for project managers is the uncertainty due to the randomness of the amount of resources required by each activity which can be expressed by the randomness of its cost. Such randomness can seriously affect the discounted cost of the project and it may be strongly correlated with the duration of the activity.In this paper, a model considering the randomness of both the cost and the duration of each activity is introduced and the problem of project scheduling is studied in terms of the project's discounted cost and of the risk of not meeting its completion time. The adoption of the earliest (latest) starting time for each activity decreases (increases) the risk of delays but increases (decreases) the discounted cost of the project. Therefore, an optimal compromise has to be achieved. This problem of optimization is studied in terms of the probability of the duration and of the discounted cost of the project falling outside the acceptable domain (Risk function) using the concept of float factor as major decision variable. This last concept is proposed to help the manager to synthetize the large number of the decision variables representing each schedule for the studied project. Numerical results are also presented for a specific project network.     

A finite step algorithm via a bimatrix game to a single controller non-zero sum stochastic game

Given a non-zero sum discounted stochastic game with finitely many states and actions one can form a bimatrix game whose pure strategies are the pure stationary strategies of the players and whose penalty payoffs consist of the total discounted costs over all states at any pure stationary pair. It is shown that any Nash equilibrium point of this bimatrix game can be used to find a Nash equilibrium point of the stochastic game whenever the law of motion is controlled by one player. The theorem is extended to undiscounted stochastic games with irreducible transitions when the law of motion is controlled by one player. Examples are worked out to illustrate the algorithm proposed.The work of this author was supported in part by the NSF grants DMS-9024408 and DMS 8802260.