A DynamicModel of Conflict and Appropriation

Abstract

This paper conducts the analysis of conflict and appropriation by extending the static contest models such as Hirshleifer (1991, 1995) and Skaperdas (1992) to a continuoustime, differential game setting. This paper shows that there is a unique Markov perfect equilibrium (MPE) strategy, which may be linear or nonlinear depending on the structural parameters of the model, when strategies are defined over the entire state space. We show that 'partial cooperation' can be seen as a long-run response to conflict. In particular, we find that a decrease in the effectiveness of appropriation, the depreciation rate of a common-pool stock which is subject to appropriation or the rate of time preferences or an increase in the 'degree of noise' improves the degree of 'partial cooperation' and thus the welfare of an anarchic society in the long run.