A sequential Colonel Blotto game with a sensor network

Abstract

In this paper, we pose a new sequential variant of the famous Colonel Blotto game in which two players, Player A and Player B, must allocate finite resources among N regions of a battlefield. A key new feature of our problem formulation is the introduction of a deterministic sensor network employed by Player B to gain an informational advantage over Player A. The existence of the sensor network and its properties are common knowledge in the game. We pose the resulting resource allocation game and obtain necessary conditions for Nash equilibrium optimal mixed strategies for the two players in terms of each player's available resources and the sensor network characteristics. These conditions apply to the marginal probability distribution functions of each player's strategy. The optimality conditions are developed using a novel case of the associated first-price all pay auctions with upper or lower bounds on the players' allocations. A numerical example is included to show the tractability of our solution.

Strategically revealing intentions in General Lotto games

“…Due to its tractability, the General Lotto game, as well as other variants, are often adopted to study more complex adversarial environments. For instance, they have been used in engineering domains such as network security [21]- [23] and the security of cyber-physical systems [12], [24].…”

Focality and Asymmetry in Multi-Battle Contests

“…2 Randomization is independent across battlefields and in the event of zero aggregate expenditure to a battlefield, the probability that each player wins is 1 2 . 3 See, for instance, Shubik and Weber (1981), Powell (2007aPowell ( ,b, 2009, Powers and Shen (2009), Kovenock et al (2010), Chia and Chuang (2011), Arce et al (2011), Fuchs and Khargonekar (2012), Nikoofal and Zhuang (2012), Arce et al (2012), Bachrach et al (2013), Gupta et al (2014a,b), Hausken (2014), Goyal and Vigier (2014). Other applications include the optimal allocation of advertising budgets across markets or marketing budgets across channels (Friedman, 1958), the allocation of political campaign funds across different primaries or state races (Snyder, 1989;Laslier, 2002;Klumpp and Polborn, 2006;Kovenock and Roberson, 2009a), redistributive politics (Myerson, 1993;Lizzeri and Persico, 2001;Roberson, 2008;Roberson, 2008, 2009b;Crutzen and Sahuguet, 2009), and the allocation R&D budgets across several potential classes of innovations or projects (Clark and Konrad, 2008).…”