Titans that clash and a state that buffers

We present a game-theoretic approach to the analysis of the emergence or survival of buffer states. We analyze a two-stage game with three players orderly located on a linear territory, where the player in the middle is passive, and the players on the two ends are aggressive with options to declare war against the others. We conduct an equilibrium analysis and characterize the conditions under which the passive player acts as a buffer state between the aggressive players. We find various equilibrium outcomes, which can be grouped into the following categories: (i) peace with buffer, (ii) peace without buffer, and (iii) the last man standing. Our comparative static analyses reveal valuable insights regarding the factors affecting the existence of buffer states.