The role of noise in alliance formation and collusion in conflicts

Many real-world conflicts are to some extent determined randomly by noise, and many also depend critically on the formation of alliances or long-run cooperative relationships. In this paper, we emphasize that the specific manner by which noise is modeled in contest success functions (CSFs) has implications for both the possibility of forming cooperative relationships and the features of such relationships. The key issue is that there are two distinct approaches to modeling noise in CSFs, each with their own merits and each leading to different results depending on which type of alliance formation is under consideration. In a one-shot conflict, we find that when noise is modeled as an exponential parameter in the CSF, there is a range of values for which an alliance between two parties can be beneficial; that is not the case for models with an additive noise parameter. In an infinitely repeated conflict setting, we again find discrepant results: with additive noise, sustaining collusion via Nash reversion strategies is easier the more noise there is and more difficult the larger the contest's prize value, while an increase in the contest's number of players can make sustaining collusion either more or less difficult. This is all in marked contrast to the case of an exponential noise parameter, when noise plays no impact on the sustainability of collusion. Given that alliances do occur in both scenarios in the real world, this contrast could be seen as supporting the importance of both specifications.