Problem
Research questions and friction points this paper is trying to address.
network allocation games
anonymous preferences
stable allocations
swap-based stability
jump-based stability
Network Allocation Games with Anonymous Preferences
🤖 AI Summary
This study addresses the problem of stable assignments for anonymous agents on graph structures, where each agent’s utility depends solely on the number of like-type neighbors. Integrating tools from game theory, graph theory, and computational complexity, the work systematically investigates the existence and computational tractability of stable assignments under various notions of stability based on swaps and jumps. The main contributions are twofold: first, it delineates sharp conditions—based on the form of the utility function and the underlying graph topology—that determine whether stable assignments exist; second, it establishes that, under nearly all standard stability definitions, both welfare-maximizing assignment and verification of Pareto optimality are strongly NP-hard, thereby precisely characterizing the computational intractability of associated optimization and decision problems.
📝 Abstract
We study network allocation games in which a set of agents must be allocated to (a subset of) the vertices of a graph topology. The agents are anonymous and strategic: Each of them aims to maximize her utility, which is a function of the number of agents in the neighborhood of their allocated vertex. We focus on the existence and the computation of stable allocations under various notions of stability. More specifically, we study swap-based stability notions, where agents can exchange locations between them, and jump-based stability notions, where agents can jump to an empty vertex of the graph. For almost all stability notions we consider, we provide dichotomies between existence and intractability that depend on the structure of the utility functions of the agents and the topology. In addition, we prove strong intractability results for computing welfare-maximizing allocations and for verifying whether a given allocation is Pareto optimal.
Innovation
Methods, ideas, or system contributions that make the work stand out.
network allocation games
anonymous preferences
swap-based stability
jump-based stability
computational dichotomy
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