Stabilizing Power Sharing

Power sharing is modeled as a duel over some prize. Each of two players may either share the prize in some ratio or fire at the other player - either in sequence or simultaneously - and eliminate it with a specified probability. If one player eliminates the other without being eliminated itself, it captures the entire prize, but the prize is damaged over time when there is shooting. Simultaneous shooting, which is more damaging than sequential shooting, tends to induce the players to share the prize and expand their opportunities for sharing it.