Escalation of a local conflict into a Cold War

The Russia-Ukraine conflict of 2022 has propelled the world toward a Cold War-esque division, a trend not fully explained by rationalist models focusing on the costs and benefits of conflict and trade. Existing research suggests increased trade reduces conflict probability. This paper addresses the paradox of increasing global division despite high costs by analyzing a simple signed network game. The game models countries choosing alliances or enmities. The core argument is that one local conflict, combined with a particular strategy by one country (e.g., Russia's labeling of Ukraine supporters as "unfriendly"), is sufficient to create a global dichotomy. Specifically, if a country adopts a "friend of my enemy is my enemy" policy, the world will invariably split into two mutually antagonistic blocs. The author explores model extensions accounting for neutral states and heterogeneous preferences, acknowledging limitations such as the oversimplification of complex international dynamics and the prevalence of exceptions to the "friend of my enemy" rule. The model aims to illustrate how a local conflict can trigger a global structural shift, not to comprehensively explain all historical or predict future international relations.

The paper draws upon several key works, including Jackson and Nei (2015), which demonstrates that increased trade can prevent conflict, contrasting with the observed reality of post-2022 global divisions. Hiller (2017)'s signed network game model serves as the foundation for this analysis, extending upon earlier works such as Cartwright and Harary (1956) and Lee et al. (1994) that lack explicit incentive structures. The author differentiates their approach by focusing on the stability of coalitions under heterogeneous preference structures, acknowledging a deviation from standard Nash equilibria analysis due to communication among countries. This work contributes not through novel analytical aspects of signed network games, but in its application to current circumstances and the resulting policy implications.

The paper uses a signed network game model. The model comprises a set N of countries (n ≥ 3). Each country r adopts a strategy gr, a vector indicating positive (+1) or negative (-1) links to all other countries, representing friendly or hostile relations. The model generates a signed network G reflecting international relations. A weighted graph H assigns weights wij to links, reflecting surpluses from trade or alliances. An additive value function v(G) sums these weights, and an allocation rule Y assigns this value to countries, with Yi(g) representing country i's payoff. The model defines a signed network as stable if no coalition S can improve its payoff by changing its links. The key assumptions are: (1) a negative link exists between two specific countries (e.g., Russia and Ukraine); and (2) one country (e.g., Russia) employs a "friend of my enemy is my enemy" strategy. The author proves that under these assumptions, any constrained efficient signed network is stable, leading to a global dichotomy. The paper then explores extensions to incorporate neutral states and different payoff structures, showing that under certain conditions, the main result holds even with these complexities. The concept of stability is chosen over Nash equilibrium to reflect real-world cooperation among countries.

The core finding is that a local conflict, combined with one country's adoption of a "friend of my enemy is my enemy" strategy, inevitably leads to a stable, dichotomized global structure. Lemma 1 demonstrates that under Assumptions 1 and 2 (a negative link between two countries and the "friend of my enemy" strategy), any three-country cycle in a constrained efficient signed network is positive. Lemma 2, drawing from Davis (1967), helps establish that if countries are not enemies, they may form ties across groups. Proposition 1 builds upon these lemmas, showing that under the assumptions, any constrained efficient signed network is stable. This leads to the corollary that all stable networks exhibit a dichotomy. The model suggests that even without inherent antagonism among countries, the "friend of my enemy" policy imposes a global division. The extensions of the model show that this holds even when considering neutral states and different payoff structures, provided that surplus-sharing rules are pre-determined, location-independent, and without externalities. This key finding highlights the significant destabilizing impact of a single country adopting this specific strategy in the context of an ongoing conflict. The model also addresses the choice of 'stability' as a solution concept over Nash Equilibrium to better reflect real-world cooperation.

The findings directly address the research question by identifying a sufficient condition for a global dichotomy: a local conflict and one country's "friend of my enemy" strategy. This challenges traditional rationalist conflict models by highlighting the potential for a single country's policy to create a globally divided system regardless of other countries' preferences. The results offer crucial implications for policymakers, suggesting that ending the initial conflict or preventing the full adoption of the "friend of my enemy" strategy are key to mitigating global division. The model's limitations are acknowledged, emphasizing its illustrative nature rather than a fully comprehensive explanation of historical and future international relations. The choice of stability as a solution concept over Nash Equilibrium is justified by the reality of cooperation amongst nations.

This paper provides a simple model demonstrating how a local conflict, combined with a specific strategic policy by one country, can lead to a stable, globally dichotomized world. The results highlight the profound impact of strategic choices in international relations and offer policy prescriptions: ending the conflict or preventing the full-scale adoption of the "friend of my enemy" strategy. Future research could explore the model's robustness under more complex scenarios, including the introduction of dynamic elements and various forms of communication among countries.

The model simplifies a complex reality, abstracting away from many factors influencing international relations. The "friend of my enemy" strategy isn't universally applied; many international relationships deviate from this pattern, as exemplified by India's neutral stance in the Russia-Ukraine conflict. The assumption of an additive value function excludes complementarities, and the allocation rule is simplified. The model is static, neglecting dynamic interactions and adjustments that could influence network structures over time. The focus on stability as a solution concept, while justified by the need to reflect real-world cooperation, presents another simplification of complex political decision-making processes.