Coalitional Colonel Blotto Games with Application to the Economics of Alliances

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may Coalitional Colonel Blotto Games with Application to the Economics of Alliancesby Dan Kovenock and Brian Roberson * This paper examines a multi-player and multi-front Colonel Blotto game in which one player, A, simultaneously competes in two disjoint Colonel Blotto games, against two separate opponents, 1 and 2. Prior to competing in the games, players 1 and 2 have the opportunity to form an alliance to share their endowments of a one-dimensional resource (e.g., troops, military hardware, money). This paper examines "non-cooperative" alliances in which only individually rational ex ante transfers of the resource are allowed. Once these transfers take place, each alliance member maximizes his payoff in his respective Colonel Blotto game, given his resource constraint and player A's allocation of its endowment across the two games. No ex post transfers are enforceable. Remarkably, there are several ranges of parameters in which endogenous unilateral transfers take place within the alliance. That is, one player gives away resources to his ally, who happily accepts the gift. Unilateral transfers arise because they lead to a strategic shift in the common opponent's force allocation away from the set of battlefields of the player making the transfer, towards the set of battlefields of the player receiving the transfer. Our result demonstrates that there exist unilateral transfers for which the combination of direct and strategic effects benefits both allies. This stands in stark contrast to the previous literature on alliances (see Sandler and Hartley, 2001), which relies on the assumption of pure or impure public goods. Abstract This paper examines a multi-player and multi-front Colonel Blotto game in which one player, A, simultaneously competes in two disjoint Colonel Blotto games, against two separate opponents, 1 and 2. Prior to competing in the games, players 1 and 2 have the opportunity to form an alliance to share their endowments of a one-dimensional resource (e.g., troops, military hardware, money). This paper examines "non-cooperative" alliances in which only individually rational ex ante transfers of the resource are allowed. Once these transfers take place, each alliance member maximizes his payoff in his respective Colonel Blotto game, given his resource constraint and player A's allocation of its endowment across the two games. No ex post transfers are enforceable. Remarkably, there are several ranges of p...

A Three-Stage Colonel Blotto Game with Applications to Cyber-Physical Security

“…Following the fundamental work of [3] and [4], many interesting theoretical extensions followed, and numerous papers targeting specific domain of application are published; see for example [5], [6,7], [8], [9] among many others. There have also been experimental studies for various applications in [10], [11], [12] among many others.…”

The Neumann-Morgenstern Project – Game Theory as a Formal Language for the Social Sciences

“…Alfred North Whitehead and Bertrand Russell wrote their Principia Mathematica (Whitehead and Russell, 1910), Wittgenstein produced his Tractatus (Wittgenstein, 1921), and Albert Einstein's two papers from 1905 first remained like Bellman (Bellman, 1969), and in certain mathematical dimensions even finalized (Roberson, 2006). But as (Kovenock and Roberson, 2008) show the interpretative power of this type of conflict models has not been exhausted at all.…”

The non-constant-sum Colonel Blotto game

“…That is, given that the opponent is using the equilibrium strategy, the expected payoff to each player is independent of the aggregate level of resources that they commit across the n all-pay auctions. 8 Now suppose that we are in case (b) in which only player A uses all of her budget. Case (b) corresponds to the situation in which the total value of the n all-pay auctions nv is high enough that the weaker player optimally commits all of her resources but not so high that the stronger player must also commit all of her resources to the n all-pay auctions.…”

“…While a focal point in the early game theory literature, 1 the Colonel Blotto game has also experienced a recent resurgence of interest (see for example Golman and Page (2006), Hart (2008), Kovenock and Roberson (2007), Laslier (2002), Laslier and Picard (2002), Roberson (2008), or Weinstein (2005)). Most closely related to this paper are Roberson (2006) and Kvasov (2007).…”