Polarization, Hostility, and Spillover Effects in Conflict Dynamics

This study develops a simple conflict model with two players to examine how polarization and hostility evolve over time. It explores the effects of these factors on conflict intensity, possible outcomes, and the existence of stable equilibria. The findings indicate that without external influences (spillovers), the effort exerted in conflict depends on the ratio of effort productivity to initial polarization. However, when negative spillovers impact the conflict, stable equilibria may not exist. When spillovers influence outcomes, they can lead to multiple possible equilibria, including increased polarization and hostility. The analysis further examines how various factors—such as effort productivity, initial polarization, and the growth rates of polarization and hostility—affect conflict intensity and equilibrium outcomes. The results highlight the critical role of hostility, a factor often overlooked in conflict models. Finally, the study confirms that these findings remain valid even when only partial spillover effects are considered.

The Role of Polarization and Hostility on Equilibria in a Simple Class of Symmetric Conflict Models

Cavalli, F., Gilli, M. & Naimzada, A. The role of polarization and hostility on equilibria in a simple class of symmetric conflict models. Theory Decis 98, 61–83 (2025). https://doi.org/10.1007/s11238-024-09998-4