The Instability of Power Sharing

27 Pages Posted: 28 Nov 2007

See all articles by Steven J. Brams

Steven J. Brams

New York University (NYU) - Wilf Family Department of Politics

D. Marc Kilgour

Wilfrid Laurier University - Department of Mathematics

Date Written: January 2007

Abstract

Three models are presented in which two players agree to share power in a particular ratio, but either player may subsequently "fire" at the other, as in a duel, to try to eliminate it. The players have positive probabilities of eliminating each other by firing. If neither is successful, the agreement stays in place; if one is successful, that player obtains all the power; if each eliminates the other, both players get nothing. In Model I, the game is played once, and in Model II it is repeated, with discounting of future payoffs. Although there are conditions under which each player would prefer not to shoot, satisfying these conditions for one player precludes satisfying them for the other, so at least one player will always have an incentive to shoot. In anticipation, its rival would prefer to shoot, too, so there will be a race to preempt. In Model III, a damage factor caused by shooting, whether successful or not, is introduced into Model II. This mitigates the incentive to shoot but does not eliminate it entirely. The application of the models to conflicts, especially civil wars, is discussed.

Keywords: power sharing, duel, repeated game, civil war

JEL Classification: C72, D74

Suggested Citation

Brams, Steven and Kilgour, D. Marc, The Instability of Power Sharing (January 2007). Available at SSRN: https://ssrn.com/abstract=1030021 or http://dx.doi.org/10.2139/ssrn.1030021

Steven Brams (Contact Author)

New York University (NYU) - Wilf Family Department of Politics ( email )

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HOME PAGE: http://politics.as.nyu.edu/object/stevenbrams.html

D. Marc Kilgour

Wilfrid Laurier University - Department of Mathematics ( email )

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