  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.
