On the Impossibility of Deterrence in Sequential Colonel Blotto Games

Abstract

A sequential Colonel Blotto and rent seeking game with fixed and variable resources is analyzed. With fixed resources, which is the assumption in Colonel Blotto games, we show for the common ratio form contest success function that the second mover is never deterred. This stands in contrast to Powell's (Games and Economic Behavior 67(2), 611-615) finding where the second mover can be deterred. With variable resources both players exert efforts in both sequential and simultaneous games, whereas fixed resources cause characteristics of all battlefields or rents to impact efforts for each battlefield. With variable resources only characteristics of a given battlefield impact efforts are to win that battlefield because of independence across battlefields. Fixed resources impact efforts and hence differences in unit effort costs are less important. In contrast, variable resources cause differences in unit effort costs to be important. The societal implication is that resource constrained opponents can be expected to engage in warfare, whereas an advantaged player with no resource constraints can prevent warfare.

Additive Security Games: Structure and Optimization

“…The allocation of limited resources by interacting agents has long been a fundamental object of study in game theory. Classical examples include Colonel Blotto games (Gross and Wagner (1950); Hausken(2012); Bhurjee(2016)), Gale's games of finite resources (Ferguson and Melolidakis (2000)) such as inspection games or goofspiel, and fair division problems (Brams et al (1996)). Two-player noncooperative resource allocation games have been the subject of extensive study.…”