Constrained swap dynamics over a social network in distributed resource reallocation

Abstract

We examine a resource allocation problem where each agent is to be assigned exactly one object. Agents are initially endowed with a resource that they can swap with one another. However, not all exchanges are plausible: we represent required connections between agents with a social network. Agents may only perform pairwise exchanges with their neighbors and only if it brings them preferred objects. We analyze this distributed process through two dual questions. Could an agent obtain a certain object if the swaps occurred favourably? Can an agent be guaranteed a certain level of satisfaction regardless of the actual exchanges? These questions are investigated through parameterized complexity, focusing on budget constraints such as the number of exchanges an agent may be involved in or the total duration of the process.