A Three-Stage Colonel Blotto Game: When to Provide More Information to an Adversary

In this paper, we formulate a three-player three-stage Colonel Blotto game, in which two players fight against a common adversary. We assume that the game is one of complete information, that is, the players have complete and consistent information on the underlying model of the game; further, each player observes the actions taken by all players up to the previous stage. The setting under consideration is similar to the one considered in our recent work [1], but with a different information structure during the second stage of the game; this leads to a significantly different solution.

[1]  Pushmeet Kohli,et al.  Colonel Blotto on Facebook: the effect of social relations on strategic interaction , 2012, WebSci '12.

[2]  Émile Borel,et al.  Applications sux jeux de hasard , 1938 .

[3]  B. Roberson.  The Colonel Blotto game , 2006 .

[4]  Ariel Rubinstein,et al.  Colonel Blotto's Top Secret Files: Multi-Dimensional Iterative Reasoning in Action , 2011 .

[5]  Drew Fudenberg,et al.  Game theory (3. pr.) , 1991 .

[6]  Dan Kovenock,et al.  Coalitional Colonel Blotto Games with Application to the Economics of Alliances , 2012 .

[7]  Sajal K. Das,et al.  Decision and Game Theory for Security , 2013, Lecture Notes in Computer Science.

[8]  John S. Baras,et al.  Decision and Game Theory for Security , 2010, Lecture Notes in Computer Science.

[9]  Émile Borel,et al.  Théorie mathématique du bridge : à la portée de tous , 1940 .

[10]  Pern Hui Chia,et al.  Colonel Blotto in the Phishing War , 2011, GameSec.

[11]  Oliver Alfred Gross,et al.  A Continuous Colonel Blotto Game , 1950 .

[12]  Dmitriy Kvasov,et al.  Contests with limited resources , 2007, J. Econ. Theory.

[13]  S. Shankar Sastry,et al.  A three-stage Colonel Blotto game with applications to cyberphysical security , 2014, 2014 American Control Conference.

[14]  Michael J. Mauboussin,et al.  Asymmetric Conflicts with Endogenous Dimensionality , 2010 .

[15]  Y. Ho,et al.  Informational properties of the Nash solutions of two stochastic nonzero-sum games , 1974 .

[16]  Ariel Rubinstein,et al.  Colonel Blotto’s Top Secret Files , 2010 .