The Co‐evolution of cooperation and complexity in a multi‐player,local‐interaction prisoners' dilemma

Agents located on a 20 × 20 toroidal lattice play a Prisoners' Dilemma game with their Moore neighbors, adopting policies of cooperation and defection that depend only on their own action and the number of cooperators in the neighborhood in the last round of the game. These policies (“characters”) are encoded in 19‐bit strings, which are subjected to evolution according to a genetic algorithm, with selection based on the cumulative scores of the agents in the neighborhood over 10 rounds of the basic game. Simulations examine the evolution of the population of characters over 1000 generations. Even with selection disabled, the genetic algorithm organizes the population into a small number of surviving characters clustered in spatially homogeneous regions. Selection for fitness rapidly achieves uniform cooperation. The characters evolved cooperate on the initial play, continue to cooperate when five or more of their neighbors cooperate, tend to defect defensively when they have cooperated and most of their neighbors have defected, and switch back to cooperation when five or more neighbors cooperate. When selection operates at the level of the whole society, however, the diversity of the population rapidly collapses, a single character predominates, and the cooperativeness of the dominating character is a matter of chance, so that there is no systematic tendency to evolve cooperation. © 2001 John Wiley & Sons, Inc.     

A model for processes combining competition with cooperation

Cooperative processes are usually treated separately from competitive processes. Such separation is often artificial, for there are a number of processes, at all levels, where cooperation intertwines with competition. A class of processes of this kind involving two component systems is described. The components are assumed to cooperate until they attain an optimum level, and to hinder each other's growth from then on. The model boils down to a system of non-linear equations which are solved in closed form for the most interesting case, the one where the process does not even get started unless there is cooperation.     

COMPETITION AND COOPERATION IN A DYNAMICAL MODEL OF NATURAL RESOURCES

Abstract In this paper, we propose a model describing the commercial exploitation of a common renewable resource by a population of strategically interacting agents. Players can cooperate or compete; cooperators maximize the payoff of their group while defectors maximize their own profit. The partition of the players into two groups, defectors and cooperators, results from the players' choices, so it is not predetermined. This partition is decided as a Nash equilibrium of a static game. It is shown that different types of players can exist in an equilibrium; more precisely, depending on the parameter values such as resource stock, cost, and so on, there might be equilibria only with defectors, cooperators, or with a combination of cooperators and defectors. In any case the total harvest depends on the renewable resource stock, so it influences agents' positions. It is assumed that at each time period the agents harvest according to Nash equilibrium, which can be combined with a dynamic model describing the evolution of fish population. A complete analysis of the equilibria is presented and their stability is analysed. The effect of the different Nash equilibria on the stability of the fish stock, showing that full cooperation is the most stable case, is examined.     

基于演化博弈的大运河文化带城市间合作发展策略研究

目前我国正向纵深推进大运河文化带建设,合作发展是推进其建设的重要手段。文章引入经济环境、城市间资源互补性、收益分配比例、机会主义收益、惩罚成本等影响因子,运用演化博弈研究大运河文化带沿线城市间合作的形成机制。结果表明良好的宏观经济环境或城市间资源互补性强时,带来高合作超额收益,从而提高城市间向合作演化的可能性;机会收益与惩罚成本之间的差额越小,越能提高合作可能性;相反,合作成本限制了双方的合作;此外,超额收益在城市间的配比影响合作,且影响方向取决于双方投入成本与收益分配比例。因此,当前亟需政府采取各种政策鼓励城市间,特别是资源互补性强的城市间利用良好的经济建设环境加强合作,同时提高监查力度。合作城市在合作中要重视诸如利益分配、违约惩罚机制等管理机制的设计。     

A cooperative strategy for solving dynamic optimization problems

Optimization in dynamic environments is a very active and important area which tackles problems that change with time (as most real-world problems do). In this paper we present a new centralized cooperative strategy based on trajectory methods (tabu search) for solving Dynamic Optimization Problems (DOPs). Two additional methods are included for comparison purposes. The first method is a Particle Swarm Optimization variant with multiple swarms and different types of particles where there exists an implicit cooperation within each swarm and competition among different swarms. The second method is an explicit decentralized cooperation scheme where multiple agents cooperate to improve a grid of solutions. The main goals are: firstly, to assess the possibilities of trajectory methods in the context of DOPs, where populational methods have traditionally been the recommended option; and secondly, to draw attention on explicitly including cooperation schemes in methods for DOPs. The results show how the proposed strategy can consistently outperform the results of the two other methods.     

Cooperating and Non-cooperating Firms in Inventive and Absorptive Research

We consider a duopoly competing in quantity, where firms can invest in both innovative and absorptive research and development to reduce their unit production cost, and where they benefit from free spillovers between them. We analyze the case where firms act non-cooperatively and the case where they cooperate by forming a research joint venture. We show that, in both modes of play, there exists a unique symmetric solution. We find that the level of investment in innovative research and development is always the highest and that the efficiency of investment in absorptive research has almost no impact on the equilibrium solution.     

Equilibrium computation of the Hart and Mas-Colell bargaining model

The 8-th problem raised by [Hart, S., Mas-Colell, A., 2010. Bargaining and cooperation in strategic form games. Journal of the European Economics Association 8 (1), 7–33], is solved. To be specific, I show that the set of SP equilibria can be determined by a finite number of systems of linear inequalities, which are efficiently solvable when there are two players. This is more or less surprising because the Hart and Mas-Colell bargaining model and the SP equilibrium both seem to be rather complicated, and it is well known that an arbitrary Nash equilibrium is hard to compute, even when there are only two players. Using this algorithm, it is shown that players of Prisoners’ Dilemma can cooperate to some extent in the Hart and Mas-Colell bargaining, and full cooperation is attainable as ρ$\rho$, a parameter of this model, approaches to 1. Quantitative efficiency, i.e. price of anarchy, is also analyzed.     

Resource allocation on condition of random resource demand of network activities

A general network model is considered. Each activity may require several storable and productive resources. Fixed amounts of storable resources are delivered at fixed times. The capacities of the productive resources are assumed to be constant. A general resource allocation problem is derived in order to optimize the cost for the execution of the network activities, In the main, the case is considered where the resource demands of the activities are random variables. For this case, the means of resource demands are estimated and a method is presented to obtain a vector of start times and durations of the activities so that a cost function is minimized and the probability that, at any time, there appears no lack of resources is maximized.     

Strategic interactions in traditional franchise systems: Are franchisors always better off?

The effects of price competition and advertising spillover on franchisees’ decision to cooperate and on franchisor’s contractual preferences are investigated. We show that the franchisees’ decision to cooperate or not depends on the type of franchise contracts. Under exclusive territory contracts, any mode of play between franchisees give the same profits to the franchisees and franchisor. Contracts that allow price competition and well targeted local advertising offer a good ground for horizontal cooperation, which may or may not benefit the franchisor depending on whether the prices are strategic substitutes or strategic complements. Contracts in which price competition is allowed and the burden of advertising decisions is totally transferred to the franchisor lead to cooperation between franchisees at the expense of the franchisor. Franchisees do not cooperate to the benefit of the franchisor if local advertising is predatory and price competition is not allowed in the contract, but franchisees are given the responsibility to undertake local advertising. Also, the franchisor endorses cooperation between franchisees when local advertising has a public good nature, but such a cooperation may never occur when the impact of local advertising on demand is significant. We finally show that while some contracts always dominate others, the choice of a franchise contract may also depend on local competition and/or the franchise goodwill.     

LEARNING BY DOING IN THE PRESENCE OF AN OPEN ACCESS RENEWABLE RESOURCE: IS GROWTH SUSTAINABLE?

ABSTRACT. We examine the relationship between growth, resource abundance and trade when the natural resource is renewable and open access and there is inter‐industry learning by doing. We find growth is not sustainable in the closed economy and can be sustained in the open economy only so long as the labor forced engaged in resource extraction shrinks over time. Comparisons of steady state welfare in autarky and free trade reveal that for very high or low world prices of the resource‐based good, it is possible for the economy to gain from trade. However if the price is intermediate, it may instead lose.     

Does cooperation in auditing matter? A comparison of a non-cooperative and a cooperative game model of auditing

A game model of auditing including internal control investigation and substantive testing is analysed as a non-cooperative game. It is shown that in order for the presumed socially desirable outcome of high and honest effort by all to be obtained, it is necessary to adjust the cost structure to ameliorate the costs of not-qualifying erroneous accounts if the auditor can prove he or she has worked hard. Comparison with a cooperative game analysis of the model shows that there is a region of parameters where both cooperative and non-cooperative versions of the game lead to this socially desirable outcome. The significance of this result is that whilst society expects an ‘independent’ auditor not to cooperate with the auditee, the practical realities of auditing require a considerable degree of cooperation. This leads to an ‘expectations gap’ between what society expects and what actually happens, except in those cost regions where both the cooperative and non-cooperative versions of the audit game lead to the same solution.     

Optimal server resource reservation policies for priority classes of users under cyclic non-homogeneous markov modeling

Resource availability optimization is studied on a server–client system where different users are partitioned into priority classes. The aim is to provide higher resource availability according to the priority of each class. For this purpose, resource reservation is modeled by a homogeneous continuous time Markov chain (CTMC), but also by a cyclic non-homogeneous Markov chain (CNHMC) as there is a cyclic behavior of the users’ requests for resources. The contribution of the work presented consists in the formulation of a multiobjective optimization problem for both the above cases that aims to determine the optimal resource reservation policy providing higher levels of resource availability for all classes. The optimization problem is solved either with known methods or with a proposed kind of heuristic algorithm. Finally, explicit generalized approximate inverse preconditioning methods are adopted for solving efficiently sparse linear systems that are derived, in order to compute resource availability.     

A systematic analysis of the N‐person chicken game

We report computer simulation experiments based on our agent‐based simulation tool to model the multiperson Chicken dilemma game for the case when the agents are greedy simpletons who imitate the action of that of their neighbors who received the highest payoff for its previous action. The individual agents may cooperate with each other for the collective interest or may defect, i.e., pursue their selfish interests only. After a certain number of iterations the proportion of cooperators stabilizes to either a constant value or oscillates around such a value. The payoff (reward/penalty) functions are given as two straight lines: one for the cooperators and another for the defectors. The payoff curves are functions of the ratio of cooperators to the total number of agents. Even for linear payoff functions, we have four free parameters that determine the payoff functions that have the following properties: (1) Both payoff functions increase with the increasing number of cooperators. (2) In the region of low cooperation the cooperators have a higher reward than the defectors. (3) When the cooperation rate is high, there is a higher payoff for defecting behavior than for cooperating behavior. (4) As a consequence, the slope of the D function is greater than that of the C function and the two payoff functions intersect. (5) All agents receive a lower payoff if all defect than if all cooperate. We have investigated the behavior of the agents systematically. The results show that the solutions have predictable tendencies but they are nontrivial and quite irregular. The solutions show drastic changes in the parameter ranges 0.6 ≤ R ≤ 0.65 for all values of S and 0 ≤ S ≤ 0.2 when R < 0.6 (R is the reward for mutual cooperation and S is the sucker's payoff to a lonely cooperator). © 2010 Wiley Periodicals, Inc. Complexity, 2010     

Combining evolutionary game theory and network theory to analyze human cooperation patterns

As natural systems continuously evolve, the human cooperation dilemma represents an increasingly more challenging question. Humans cooperate in natural and social systems, but how it happens and what are the mechanisms which rule the emergence of cooperation, represent an open and fascinating issue. In this work, we investigate the evolution of cooperation through the analysis of the evolutionary dynamics of behaviours within the social network, where nodes can choose to cooperate or defect following the classical social dilemmas represented by Prisoner’s Dilemma and Snowdrift games. To this aim, we introduce a sociological concept and statistical estimator, “Critical Mass”, to detect the minimum initial seed of cooperators able to trigger the diffusion process, and the centrality measure to select within the social network. Selecting different spatial configurations of the Critical Mass nodes, we highlight how the emergence of cooperation can be influenced by this spatial choice of the initial core in the network. Moreover, we target to shed light how the concept of homophily, a social shaping factor for which “birds of a feather flock together”, can affect the evolutionary process. Our findings show that homophily allows speeding up the diffusion process and make quicker the convergence towards human cooperation, while centrality measure and thus the Critical Mass selection, play a key role in the evolution showing how the spatial configurations can create some hidden patterns, partially counterbalancing the impact of homophily.     

A simple model of imperfect competition,where 4 are few and 6 are many

The theory presented in this paper investigates the connection between the number of competitors and the tendency to cooperate within the context of a symmetric Cournot model with linear cost and demand, supplemented by specific institutional assumptions about the possibilities of cooperation. Cooperative forms of behavior are modelled as moves in a non-cooperative game. The proposition that few suppliers will maximize their joint profits whereas many suppliers are likely to behave non-cooperatively does not appear as an assumption but as a conclusion of the theory. For the simple model analyzed in this paper a definite answer can be given to the question where a “small group” of competitors ends and a “large group” begins: 5 is the dividing line between “few” and “many”.     

COLLECTIVE DECISION MAKING IN AN INTERNATIONAL RIVER POLLUTION MODEL

In this paper, we study international river pollution problems. We introduce a model in which countries located along a river from upstream to downstream derive benefits from causing pollution, but also incur environmental costs from experiencing its own pollution and the pollution of all its upstream countries. The total welfare, being the sum of all benefits minus the sum of all costs, is maximized when all countries cooperate. Several principles from international water law are applied to find reasonable and fair distributions of the total welfare that can be obtained under full cooperation. Such a distribution of the welfare at efficient pollution levels can be implemented by monetary compensations.     

A partial cooperation model for non-unique linear two-level decision problems

This paper examines a linear static Stackelberg game where the follower's optimal reaction is not unique. Traditionally, the problem has been approached using either an optimistic or a pessimistic framework, respectively, representing the two extreme situations of full cooperation and zero cooperation from the follower. However, partial cooperation from the follower is a viable option. For partial cooperation, the leader's optimal strategy may be neither optimistic nor pessimistic. Introducing a cooperation index to describe the degree of follower cooperation, we first formulate a partial cooperation model for the leader. The two-level problem is then reformulated into a single-level model. It is shown that the optimistic and pessimistic situations are special cases of the general model, and that the leader's optimal choice may be an intermediate solution.     

Share functions for cooperative games with levels structure of cooperation

In a standard TU-game it is assumed that every subset of the player set N can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure of Aumann and Drèze (1974). They assumed that the player set is partitioned into unions and that players can only cooperate within their own union. Owen (1977) introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter (1989) extended this value to games with levels structure of cooperation, which consists of a game and a finite sequence of partitions defined on the player set, each of them being coarser than the previous one.     

The impact of disaster on the strategic interaction between company and government

A company allocates a resource between safety effort and production. The government earns taxes on production. The disaster probability is modeled as a contest between the disaster magnitude and the two players’ safety efforts. The model illustrates that safety efforts are strategic substitutes and inverse U shaped in the disaster magnitude. The company’s safety effort increases, and the government’s safety effort decreases, in taxation. Taxation can ameliorate companies’ free riding on governments’ safety efforts. With sufficiently large production, the government prefers, and the company does not prefer, raising taxation above 0%. For the government, an upper limit usually exists above which taxation cannot be profitably increased. The model shows how both or no players exert safety efforts when the disaster magnitude is small and large respectively, and how they free ride on each other’s safety efforts when the disaster magnitude is intermediate. The company free rides when the unit production cost is low so that the large profits outweigh the negative impact of the disaster. With endogenized taxation determined by the government, the tax rate decreases in the disaster magnitude, the unit production cost, the government’s unit cost of safety effort, and how the company is negatively affected by the disaster. The tax rate increases in the company’s resource and how the government is negatively affected by the disaster. The tax rate is weakly U shaped in the company’s unit safety effort. The model is illustrated with numerical examples and with the oil spill disasters by BP in 2010 and by Exxon Valdez in 1989.     

产能约束下的闭环供应链制造商合作策略研究

构建了一个由制造商、回收商和零售商组成的闭环供应链模型,运用Stackelberg博弈对产能约束下制造商的合作策略进行了研究。研究发现:制造商始终有与回收商或零售商合作的经济动机,且当产能较小时,更倾向于与零售商合作;反之,则更倾向与回收商进行合作。此外,相对于无合作模式,不同合作策略对于回收率、供应链整体利润、新产品与再制品总体环境影响程度以及消费者剩余的影响会随着制造商产能大小的变化发生改变,而不同合作策略对于总体环境影响程度的影响与制造商的再制造水平也存在关联。