具有合作、贪婪和警戒的共享资源博弈中的行为
Behavior in a Shared Resource Game with Cooperative, Greedy, and Vigilante Players
摘要：
我们研究了一个分布式系统中的信任问题，其中一个共同的资源是由多方共享。在这种自然的信息有限的环境中，各方遵守一个行为协议，导致资源的公平共享。然而，贪婪的玩家可能会从合作协议中叛逃，并获得比公平份额更大的资源，通常不会对自己产生重大的不利后果。在本文中，我们研究了几个义务警员的球员谁也从合作资源共享协议的缺陷，但只在响应感知贪婪的行为的作用。对于一个简单的参与模型，我们展示了贪婪和义务警员之间令人惊讶的复杂动态。我们表明，最佳反应函数的贪婪的球员在我们的制定有一个跳跃的不连续性，这导致的条件下，没有纳什均衡。为了研究这一性质，我们制定了一个精确的表示的情况下，贪婪的球员最佳对策函数时，有一个贪婪的球员，一个义警球员和$N-2$合作的球员。我们用这个公式来说明纳什均衡存在的条件。我们还证明了在不存在纳什均衡的情况下，由虚拟博弈产生的离散动力系统将不会收敛，而会由于跳跃的不连续性而无限振荡.多个义务警员和贪婪的球员的情况下进行了数值研究。最后，我们探讨了虚拟游戏和更好的响应动力学（梯度下降）之间的关系，并说明了这个动力系统可以有一个不动点，即使离散动力系统所产生的虚拟游戏没有。
英文摘要：
We study a problem of trust in a distributed system in which a common resource is shared by multiple parties. In such naturally information-limited settings, parties abide by a behavioral protocol that leads to fair sharing of the resource. However, greedy players may defect from a cooperative protocol and achieve a greater than fair share of resources, often without significant adverse consequences to themselves. In this paper, we study the role of a few vigilante players who also defect from a cooperative resource-sharing protocol but only in response to perceived greedy behavior. For a simple model of engagement, we demonstrate surprisingly complex dynamics among greedy and vigilante players. We show that the best response function for the greedy-player under our formulation has a jump discontinuity, which leads to conditions under which there is no Nash equilibrium. To study this property, we formulate an exact representation for the greedy player best response function in the case when there is one greedy player, one vigilante player and $N-2$ cooperative players. We use this formulation to show conditions under which a Nash equilibrium exists. We also illustrate that in the case when there is no Nash equilibrium, then the discrete dynamic system generated from fictitious play will not converge, but will oscillate indefinitely as a result of the jump discontinuity. The case of multiple vigilante and greedy players is studied numerically. Finally, we explore the relationship between fictitious play and the better response dynamics (gradient descent) and illustrate that this dynamical system can have a fixed point even when the discrete dynamical system arising from fictitious play does not.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
