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"This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a 'guerilla warfare' strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a 'stochastic complete coverage' strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields." (author's abstract)

The Colonel Blotto game is a two-player constant-sum game in which each player simultaneously distributes her fixed level of resources across a set of contests. In the traditional formulation of the Colonel Blotto game, the players' resources are use it or lose it" in the sense that any resources which are not allocated to one of the contests are forfeited. This paper examines a non-constant-sum version of the Colonel Blotto game which relaxes this use it or lose it feature. We find that if the level of asymmetry between the players' budgets is below a threshold, then the unique set of equilibrium univariate marginal distributions of the non-constant-sum game is equivalent up to an affine transformation to the unique set of equilibrium univariate marginal distributions of the constant-sum game. Once the asymmetry of the players' budgets exceeds the threshold we construct a new equilibrium.

In this paper, we generalize the General Lotto game and the Colonel Blotto game to allow for battlefield valuations that are heterogeneous across battlefields and asymmetric across players, and for the players to have asymmetric resource constraints. We completely characterize Nash equilibrium in the generalized version of the General Lotto game and then show how this characterization can be applied to identify equilibria in the Colonel Blotto version of the game. In both games, we find that there exist sets of non-pathological parameter configurations of positive Lebesgue measure with multiple payoff nonequivalent equilibria.

"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 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." (author's 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 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. ; Diese Arbeit analysiert Colonel Blotto-Spiele mit mehr als zwei Spielern, die an mindestens zwei Fronten miteinander kämpfen. Spieler A kämpft gleichzeitig in zwei Colonel Blotto-Spielen mit zwei verschiedenen Kontrahenten, B1 und B2. Die Kontrahenten können vor der eigentlichen Konfliktphase eine Allianz eingehen. Das erlaubt es ihnen ihre Mengen an einer homogenen Konfliktressource (Truppen, Waffen, Geld) untereinander zu transferieren. Das Papier untersucht dabei "nicht-kooperative" Allianzen. Darunter wird verstanden, dass der Einsatz der transferierten Ressourcen auf den jeweiligen Konfliktschauplätzen von dem jeweiligen Spieler B1 bzw. B2 in seinem eigenen Interesse eingesetzt wird und Seitenzahlungen im Anschluss an die Konfliktphase ausgeschlossen sind. Es zeigt sich, dass es dennoch zu einseitigen und freiwilligen Ressourcentransfers der Spieler B1 und B2 im Vorfeld des Konflikts kommen kann, dass also beispielsweise B1 an B2 z.B. Waffen liefert, B2 diese als Geschenk akzeptiert und sich beide, B1 und B2 besser stellen. Ursache für die Besserstellung ist der strategische Effekt solcher Transfers auf das Kampfverhalten von A, der seine Kampfkraft vom Kampfgeschehen mit B1 zum Kampfgeschehen mit B2 verlagert. Das Ergebnis widerspricht den früheren Ergebnissen zu Allianzen (vgl. Sandler und Hartley, 2001), das im Kontext der privaten Bereitstellung öffentlicher Güter erzielt wurde.