Simultaneous battles and sequential battles in bargaining models of war

A war consists of multiple battles, yet the theoretical literature of International Relations has given little attention to how battles relate within a war. By integrating two ultimatum games with private information played by an Aggressor and a Defender, we develop bargaining models of war with two structures: (i) parallel war, where battles occur simultaneously in two domains, as the Aggressor can access both directly; and (ii) series war, where a battle in one domain (e.g., sea) precedes a battle in another (e.g., land), as the Aggressor must first control the former domain to instigate conflict in the latter. In a theoretical comparison between parallel and series wars, we demonstrate that although series war imposes structural disadvantages on the Aggressor, series war is more likely to break out than parallel war under broad circumstances. If prewar bargaining of series war fails, the Aggressor may infer that future bargaining is also likely to fail, leading him to take a greater risk of war when issuing an ultimatum. Such dynamics are absent in parallel war. We also discuss further developments in theories of war (182 words).