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Four different types of equilibrium are possible within a two-player model of society where only armed self-enforcement of property rights is possible. The main underlying parameters are the total resource endowment and the initial distribution of this endowment between the players. The parameter space is partitioned into regions in which the respective types of equilibrium occur The equilibrium types involve positive arms expenditure by, respectively, neither player the richer player, and both players; the latter case involves a sub-type in which the poorer player's entire endowment is expended on arms. (JEL D30, D72, D74)