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

Gupta, Abhishek; Başar, Tamer; Schwartz, Galina

doi:10.1007/978-3-319-12601-2_12

Cited by 18 publications

(19 citation statements)

References 6 publications

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“…In particular, [17] introduced a two-vs-one model, and identified when a (public) unilateral transfer of resources between coalitional players is beneficial. Subsequent work in [24], [25] considers similar settings where the two players can decide to add battlefields in addition to transferring resources amongst each other. Counter-intuitively, they showed that the players in the coalition achieve better performance if the transfers are made public to their adversary.…”

Section: Related Literaturementioning

confidence: 99%

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Strategically revealing intentions in General Lotto games

Paarporn¹,

Chandan²,

Kovenock³

et al. 2021

Preprint

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In this paper, we highlight scenarios in General Lotto games where there exist incentives to reveal one's intentions to an opponent. The General Lotto game is a popular model of competitive resource allocation. We study a multi-step extension where one player has the option to publicly pre-commit resources to battlefields before play begins. In response, the opponent decides which of these battlefields to secure by matching the pre-commitment with its own resources, and which of them to withdraw from entirely. They then engage in a General Lotto game over the remaining set of battlefields. We show that the weaker-resource player never has an incentive to precommit, while a stronger player can have incentives to precommit. However, this is not necessarily true in settings where the battlefield valuations are asymmetric across players. This setting is known to admit a richer set of outcomes, where multiple payoff-distinct equilibria can arise in simultaneous play. We show that pre-committing in this environment can guarantee a payoff that exceeds the second-highest equilibrium payoff from simultaneous play. Our work highlights the strategic role that revealing information plays can have in a variety of adversarial contexts.

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Section: Related Literaturementioning

confidence: 99%

“…It takes its maximal value at p * . To prove u B (p * ) < π nom B , it suffices to show that player B has an incentive to pre-commit only if player A matches a precommitment p > p * , which is impossible due to (25). Indeed,…”

Section: B Guaranteed Payoffs Through Pre-commitmentsmentioning

confidence: 99%

Strategically revealing intentions in General Lotto games

Paarporn¹,

Chandan²,

Kovenock³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In recent years, simpler variants of Blotto games have been considered to study team settings. For instance, [13], [14] study coalitional scenarios where two players opposing a common enemy can decide to unilaterally transfer resources among themselves before play begins. The model in [15] considers a similar setup, where a team's players instead decide to pre-commit resources onto battlefields.…”

Section: Equal Divisionmentioning

confidence: 99%

The Division of Assets in Multiagent Systems: A Case Study in Team Blotto Games

Paarporn¹,

Chandan²,

Alizadeh³

et al. 2021

Preprint

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Multi-agent systems are designed to concurrently accomplish a diverse set of tasks at unprecedented scale. Here, the central problems faced by a system operator are to decide (i) how to divide available resources amongst the agents assigned to tasks and (ii) how to coordinate the behavior of the agents to optimize the efficiency of the resulting collective behavior. The focus of this paper is on problem (i), where we seek to characterize the impact of the division of resources on the bestcase efficiency of the resulting collective behavior. Specifically, we focus on a team Colonel Blotto game where there are two sub-colonels competing against a common adversary in a two battlefield environment. Here, each sub-colonel is assigned a given resource budget and is required to allocate these resources independent of the other sub-colonel. However, their success is dependent on the allocation strategy of both sub-colonels. The central focus of this manuscript is on how to divide a common pool of resources among the two sub-colonels to optimize the resulting best-case efficiency guarantees. Intuitively, one would imagine that the more balanced the division of resources, the worse the performance, as such divisions restrict the subcolonels' ability to employ joint randomized strategies that tend to be necessary for optimizing performance guarantees. However, the main result of this paper demonstrates that this intuition is actually incorrect. A more balanced division of resources can offer better performance guarantees than a more centralized division. Hence, this paper demonstrates that the resource division problem is highly non-trivial in such enmeshed environments and worthy of significant future research efforts.

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“…We consider a modified version of the three-player coalitional General Lotto game studied in, e.g., [11], [12], [4], [13]. In the game, a player A competes against two players, 1 and 2, on two disjoint sets of battlefields, B 1 and B 2 , with battlefield values v j = (v j,1 , .…”

Section: A Coalitional General Lotto Games With Pre-commitmentmentioning

confidence: 99%

“…Previous work has considered similar three-stage, threeplayer setups, in which the team players have the option of transferring resources among each other, or of adding battlefields to their respective one-shot games [11], [12], [4], [13]. The problem we pose here differs in regard to the non-possibility of forming alliances even when there is a common enemy.…”

Section: Introductionmentioning

confidence: 99%

When showing your hand pays off: Announcing strategic intentions in Colonel Blotto games

Chandan¹,

Paarporn²,

Marden³

2020

Preprint

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In competitive adversarial environments, it is often advantageous to obfuscate one's strategies or capabilities. However, revealing one's strategic intentions may shift the dynamics of the competition in complex ways. Can it ever be advantageous to reveal strategic intentions to an opponent? In this paper, we consider three-stage Colonel Blotto games in which one player can choose whether or not to pre-commit resources to a single battlefield before play begins. This pre-commitment is public knowledge. In response, the opponent can either secure the battlefield by matching the pre-commitment with its own forces, or withdraw. In a two-player setting, we show that a weaker player never has an incentive to pre-commit any amount of resources to a battlefield regardless of how valuable it is. We then consider a three-player setting in which two players fight against a common adversary on separate fronts. Only one of the two players facing the adversary has the option of pre-committing. We find there are instances where this player benefits from pre-committing. The analysis indicates that under non-cooperative team settings and no possibility of forming alliances, there can be incentives to publicly announce one's strategic intentions to an adversary.

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

Cited by 18 publications

References 6 publications

Strategically revealing intentions in General Lotto games

Strategically revealing intentions in General Lotto games

The Division of Assets in Multiagent Systems: A Case Study in Team Blotto Games

When showing your hand pays off: Announcing strategic intentions in Colonel Blotto games

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