Strategic Coalitions in Networked Contest Games

TL;DR

This paper analyzes how bilateral resource transfers in networked contest games can lead to mutually beneficial coalitions, providing conditions for their existence and methods to identify optimal coalition structures.

Contribution

It characterizes network conditions for beneficial bilateral transfers and introduces gradient-based dynamics to find advantageous coalitional arrangements.

Findings

Beneficial transfers depend on mild connectivity conditions.

Sufficient conditions for mutually beneficial transfers are provided.

Gradient-based methods can identify optimal coalitional structures.

Abstract

In competitive resource allocation formulations multiple agents compete over different contests by committing their limited resources in them. For these settings, contest games offer a game-theoretic foundation to analyze how players can efficiently invest their resources. In this class of games the resulting behavior can be affected by external interactions among the players. In particular, players could be able to make coalitions that allow transferring resources among them, seeking to improve their outcomes. In this work, we study bilateral budgetary transfers in contest games played over networks. Particularly, we characterize the family of networks where there exist mutually beneficial bilateral transfer for some set of systems parameters. With this in mind, we provide sufficient conditions for the existence of mutually beneficial transfers. Moreover, we provide a constructive argument that guarantees that the benefit of making coalitions only depends on mild connectivity conditions of the graph structure. Lastly, we provide a characterization of the improvement of the utilities as a function of the transferred budget. Further, we demonstrate how gradient-based dynamics can be utilized to find desirable coalitional structures. Interestingly, our findings demonstrate that such collaborative opportunities extend well beyond the typical "enemy-of-my-enemy" alliances.