Sequential, nonzero-sum "Blotto": Allocating defensive resources prior to attack
The strategic allocation of resources across multiple fronts has long been studied in the context of Blotto games in which two players simultaneously select their allocations. However many allocation problems are sequential. For example, a state trying to defend against a terrorist attack generally allocates some or all of its resources before the attacker decides where to strike. This paper studies the allocation problem confronting a defender who must decide how to distribute limited resources across multiple sites before an attacker chooses where to strike. Unlike many Blotto games which only have very complicated mixed-strategy equilibria, the sequential, nonzero-sum "Blotto" game always has a very simple pure-strategy subgame perfect equilibrium. Further, the defender always plays the same pure strategy in any equilibrium, and the attacker's equilibrium response is generically unique and entails no mixing. The defender minmaxes the attacker in equilibrium even though the game is nonzero-sum, and the attacker strikes the site among its best replies that minimizes the defender's expected losses.
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- Coughlin, Peter J, 1992. "Pure Strategy Equilibria in a Class of Systems Defense Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 195-210.
- Russell Golman & Scott Page, 2009. "General Blotto: games of allocative strategic mismatch," Public Choice, Springer, vol. 138(3), pages 279-299, March.
- Kats, Amoz & Thisse, Jacques-Francois, 1992.
"Unilaterally Competitive Games,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 21(3), pages 291-299.
- Kats, A. & Thisse, J.-F., "undated". "Unilaterally competitive games," CORE Discussion Papers RP 1039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
- Martin Shubik & Robert J. Weber, 1978. "Competitive Valuation of Cooperative Games," Cowles Foundation Discussion Papers 482, Cowles Foundation for Research in Economics, Yale University.
- Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
- Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics.
- Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Discussion Paper Series dp434, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Eddie Dekel & Matthew O. Jackson & Asher Wolinsky, 2008. "Vote Buying: General Elections," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 351-380, 04.
- Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
- Laslier, Jean-Francois & Picard, Nathalie, 2002. "Distributive Politics and Electoral Competition," Journal of Economic Theory, Elsevier, vol. 103(1), pages 106-130, March. Full references (including those not matched with items on IDEAS)
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