Strategic Coalitions in Networked Contest Games

TL;DR

The paper investigates networked contest games where multiple budget-constrained players compete over edges of a graph. It develops a per-unit-cost parametrization to characterize Nash equilibria, proves the existence of mutually beneficial budget transfers under mild connectivity conditions, and analyzes enemy-of-my-enemy alliances in a 3-node setting. It also derives a gradient-based framework for optimally designing donations between players and validates the theory through simulations on line and cycle graphs. The results show that collaborative opportunities extend beyond simple rival structures and provide a principled approach to forming and optimizing coalitions in networked adversarial resource allocation. The work advances both theoretical understanding and practical methods for coalition design in contest-based networks.

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.

Figures (12)

• Figure 1: Multiple networked contest games and their graph representation. In the contest games, it can be visualized which items (depicted as squares) each player is competing for. Equivalently, in its graph representation, an edge between two nodes indicate the existence of a bilateral contest for a common item. (a) 3-player network contest game. (b) Graph representation of the 3-player network contest game. (c) 5-player network contest game. (d) Graph representation of the 5-player network contest game.
• Figure 2: Numerical Example of Contest Game in a Network. (a) Without transfer between players. (b) With a mutually beneficial transfer.
• Figure 3: Existence results for donations in networked contest games. (a) Original conflict graph. (b) Donations between players that are not neighbors. (c) Donations between players that are neighbors. (d) Donations from a player to its only neighbor.
• Figure 4: Graph representation of a 'Enemy-of-my-Enemy' Alliance. In these alliances players $1$ and $3$ make a coalition to outperform their common adversary, player $2$.
• Figure 5: Regions with mutually beneficial 'enemy-of-my-enemy' alliances. Here, any set of parameters $B_1$, $B_2$, $B_3$ and $v_1/v_2$ inside of the shaded regions verify the existence of a mutually beneficial transfer between players $1$ and $3$.

Theorems & Definitions (10)

• Theorem 1
• Proposition 1
• Lemma 1
• Lemma 2
• Remark 1
• Lemma 3
• Remark 2
• Lemma 4
• Lemma 5
• Proposition 2