Rational Instability in the Natural Coalition Forming

We are investigating a paradigm of instability in coalition forming among countries, which indeed is intrinsic to any collection of individual groups or other social aggregations. Coalitions among countries are formed by the respective attraction or repulsion caused by the historical bond propensities between the countries, which produced an intricate circuit of bilateral bonds. Contradictory associations into coalitions occur due to the independent evolution of the bonds. Those coalitions tend to be unstable and break down frequently. The model extends some features of the physical theory of Spin Glasses. Within the frame of this model, the instability is viewed as a consequence of decentralized maximization processes searching for the best coalition allocations. In contrast to the existing literature, a rational instability is found to result from forecast rationality of countries. Using a general theoretical framework allowing to analyze the countries’ decision making in coalition forming, we feature a system where stability can eventually be achieved as a result of the maximization processes. We provide a formal implementation of the maximization principles and illustrate it in the multi-thread simulation of the coalition forming. The results shed a new light on the prospect of searches for the best coalition allocations in the networks of social, political or economical entities.

💡 Research Summary

The paper presents a novel theoretical framework for understanding instability in the formation of international coalitions, drawing an explicit analogy to the physics of spin glasses. It begins by distinguishing two sources of coalition volatility: structural instability, which arises from the inherent heterogeneity and evolution of bilateral “bond propensities” (historical affinities or antagonisms) among states, and rational instability, which emerges when each state acts as a forward‑looking, utility‑maximizing agent. While much of the existing literature attributes coalition turnover to exogenous shocks, institutional constraints, or power asymmetries, this work places the decision‑making process of sovereign actors at the core of the analysis.

The authors formalize the international system as a complete graph of N countries. For every ordered pair (i, j) a real‑valued bond strength (B_{ij}) is assigned; positive values denote attraction, negative values denote repulsion. A binary variable (x_i \in {-1,+1}) encodes the coalition choice of country i (e.g., alignment with one of two rival blocs). The utility of a state i is defined as
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