具有联盟结构的对称资源开采博弈中的均衡

I. Sylenko
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引用次数: 0

摘要

资源开采/资本积累博弈是一个随机的非零和无限视界博弈,是将著名的最优增长模型推广到m个共同拥有可再生资源的战略竞争主体。在博弈的不同(通常是对称的)框架中,纳什均衡的存在在这一主题的科学文献中受到了极大的关注。本文的重点是将联合分量引入对称问题。具体地说,我们考察了具有固定联盟结构的博弈是否对有利可图的联盟偏差具有稳定性。假设所有参与者的集合被划分成不相交且在整个博弈中保持一致的联盟。每个联盟的成员能够以合作的方式协调他们的行动并执行联合偏差。这种环境包含了一种自然的社会关系概念,这可能反映了在实际应用中出现的潜在背景。本文中相应的均衡概念被表示为一个位置,在这个位置上,集合中的任何一个联盟都不能偏离该位置以增加其成员的总回报。在具有无界效用的对称资源抽取博弈模型下,研究了它的存在性。该模型在文献[12;13],得出了对称和非对称博弈结构下的平稳马尔可夫完美均衡的存在性。该模型的第一个特征是,参与者的偏好被认为是严格凹幂函数形式的等弹性。此外,不同状态间的运动规律与玩家的共同投资相关,遵循几何随机游走。我们证明了在公式化设置内的博弈对于智能体集合上的任何分区都具有对抗有利联盟偏差的稳定性。该方法为建立相应的平稳策略提供了一种算法,可用于实际目的。最后,我们使用两个具有不同数值配置的例子来说明玩家的个人奖励如何根据游戏开始时设置的联盟结构而变化的可能模式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Equilibrium in a Symmetric Game of Resource Extraction with Coalitional Structure
The game of resource extraction / capital accumulation is a stochastic nonzero-sum infinite horizon game, obtained as an extension of the well-known optimal growth model to m strategically competing players, who jointly posses a renewable resource. The existence of a Nash equilibrium in different, often symmetric, frameworks of the game received a significant attention in the scientific literature on the topic. The focus of this paper is to introduce the coalitional component to the symmetric problem. Specifically, we examine whether the game with a fixed coalitional structure admits stability against profitable coalitional deviations.It is assumed that the set of all players is partitioned into coalitions which do not intersect and remain consistent throughout the game. The members of each coalition are able to coordinate their actions and perform joint deviations in a cooperative manner. Such setting incorporates a natural concept of established social ties, which may reflect a potential context appearing in practical applications. The corresponding notion of equilibrium in the paper is expressed as a position, from which none of the set coalitions can deviate in a manner to increase a total reward of its members. Its existence is studied in the context of a certain symmetric resource extraction game model with unbounded utilities of the players. This model was studied in [12; 13], concluding a Stationary Markov Perfect Equilibrium existence in both symmetric and non-symmetric game structure. The first feature of the model is that the preferences of the players are considered to be isoelastic in the form of strictly concave power functions. Furthermore, the law of motion between states is set to follow a geometric random walk in relation to players' joint investments. We prove that the game within the formulated settings admits stability against profitable coalitional deviations for any partition on the set of agents. The method provides an algorithm for building the corresponding stationary strategies, which can be useful for practical purposes. Finally, we use two examples with different numerical configurations to illustrate possible patterns of how the individual rewards of the players vary depending on a coalitional structure, which is set at the beginning of the game.
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