Flow methods for cooperative games with generalized coalition configuration

TL;DR

This paper introduces a new class of cooperative games with generalized coalition configurations, providing flow-based solution methods, axiomatic characterizations, and decomposition techniques for these complex cooperative scenarios.

Contribution

It defines and characterizes flow methods for cooperative games with generalized coalition configurations, including a novel construction procedure and flow decomposition results.

Findings

Flow methods are constructed via a two-step Owen-inspired procedure.

Associated flows can be decomposed into two flows with specific axiomatic characterizations.

The framework extends cooperative game analysis to restricted and structured coalition settings.

Abstract

This paper introduces the class of cooperative games with generalized coalition configuration. This new class of games corresponds to cooperative games with coalition configuration and restricted cooperation. A coalition configuration is a collection of coalitions covering the agent set. The restriction of cooperation between agents is represented by a set system on each element of the coalition configuration. A coalition profile is a list of feasible coalitions, one for each element of the coalition configuration. A coalition profile function associates a worth with each coalition profile. Based on this framework, we define and axiomatically characterize marginal values whose coefficients induce a unitary flow on the product digraph obtained from these set systems. Next, we propose a two-step procedure, inspired by Owen's procedure, to construct flow methods as above. Then, we show that the associated flow is decomposable into two flows. Finally, we use two axioms to characterize the flows that can be decomposed in this way, and hence the flow methods constructed using our procedure.