A dynamic model of conflict and appropriation

This paper presents an extension of a static model of economic conflict analyzed by Hirshleifer, 1991 and Hirshleifer, 1995 and Skaperdas (1992) to an infinite horizon differential game. Our aim is to highlight the strategic role of appropriation among a smaller group of agents in an intertemporal context. The model yields the conclusion that there exists a unique linear/nonlinear Markov perfect equilibrium strategy, even when strategies are defined over the entire state space. We demonstrate that “partial cooperation” can be seen as a long-run response to conflict. Moreover, a decrease in the effectiveness of appropriation, the depreciation rate of a common-pool stock, the rate of time preferences or an increase in the “degree of noise” improves the degree of “partial cooperation” and thus welfare in an anarchic society.

Research Highlights
► This paper conducts the analysis of conflict and appropriation by extending the static contest models such as Hirshleifer, 1991 and Hirshleifer, 1995 and Skaperdas (1992) to a differential game setting.
► There is a unique Markov perfect equilibrium strategy, which may be linear or nonlinear depending on the structural parameters of the model.
► “Partial cooperation” can be seen as a long-run response to conflict.
► A decrease in the effectiveness of appropriation, the depreciation rate of a common-pool stock or the rate of time preferences or an increase in the ‘degree of noise’ improves the degree of “partial cooperation”.