The killing game: A theory of non-democratic succession

The winner of a battle for a throne can either execute or spare the loser; if the loser is spared, he contends the throne in the next period. Executing the losing contender gives the winner a chance to rule uncontested for a while, but then his life is at risk if he loses to some future contender who might be, in equilibrium, too frightened to spare him. The trade-off is analyzed within a dynamic complete information game, with, potentially, an infinite number of long-term players. In an equilibrium, decisions to execute predecessors depend on the predecessors' history of executions. With a dynastic rule in place, incentives to kill the predecessor are much higher than in non-hereditary dictatorships. The historical illustration for our analysis contains a discussion of post-World War II politics of execution of deposed leaders and detailed discussion of non-hereditary military dictatorships in Venezuela in 1830-1964, which witnessed dozens of comebacks and no single political execution.