Behavior in a Shared Resource Game with Cooperative, Greedy, and Vigilante Players
Christopher Griffin, George Kesidis

TL;DR
This paper analyzes the complex dynamics of resource sharing in a distributed system involving cooperative, greedy, and vigilante players, revealing conditions for equilibrium existence and oscillatory behaviors due to strategic interactions.
Contribution
It introduces a novel model capturing the interactions among different player types and demonstrates the impact of jump discontinuities on equilibrium and system dynamics.
Findings
Best response function for greedy players has a jump discontinuity.
No Nash equilibrium exists under certain conditions.
Fictitious play may oscillate indefinitely without convergence.
Abstract
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…
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Taxonomy
TopicsGame Theory and Applications · Evolutionary Game Theory and Cooperation · Distributed Control Multi-Agent Systems
