Sequential, nonzero-sum “Blotto”: Allocating defensive resources prior to attack

Powell, Robert

doi:10.1016/j.geb.2009.03.011

Cited by 90 publications

(25 citation statements)

References 15 publications

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“…The agents' choices and utilities are the same in sequential and simultaneous games. This stands in contrast to Powell's (2009) finding where the second mover can be deterred. With variable resources we show that the second mover is deterred (exerts no effort) when disadvantaged with a unit effort cost more than twice that of the first mover.…”

Section: Resultscontrasting

confidence: 82%

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On the Impossibility of Deterrence in Sequential Colonel Blotto Games

Hausken

2012

Int. Game Theory Rev.

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A sequential Colonel Blotto and rent seeking game with fixed and variable resources is analyzed. With fixed resources, which is the assumption in Colonel Blotto games, we show for the common ratio form contest success function that the second mover is never deterred. This stands in contrast to Powell's (Games and Economic Behavior 67(2), 611-615) finding where the second mover can be deterred. With variable resources both players exert efforts in both sequential and simultaneous games, whereas fixed resources cause characteristics of all battlefields or rents to impact efforts for each battlefield. With variable resources only characteristics of a given battlefield impact efforts are to win that battlefield because of independence across battlefields. Fixed resources impact efforts and hence differences in unit effort costs are less important. In contrast, variable resources cause differences in unit effort costs to be important. The societal implication is that resource constrained opponents can be expected to engage in warfare, whereas an advantaged player with no resource constraints can prevent warfare.

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Section: Resultscontrasting

confidence: 82%

“…One rare exception to the assumption of simultaneous moves is Powell (2009). He analyzes a sequential Colonel Blotto game, where the defender moves first and the attacker moves second.…”

Section: Introductionmentioning

confidence: 99%

On the Impossibility of Deterrence in Sequential Colonel Blotto Games

Hausken

2012

Int. Game Theory Rev.

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“…In further related research, Powell analyzes defense allocation across multiple sites before an attacker chooses where to attack; Patterson and Apostolakis rank geographic regions to allow decisionmakers to determine critical locations susceptible to terrorist attacks; Bier et al . allocate resources for defense of targets based on differing measures of attractiveness; Paté‐Cornell and Guikema determine priorities among countermeasures against terrorist threats; Michaud and Apostolakis rank the elements of water‐supply networks; Levitin considers defense against intentional attacks; Brown et al .…”

Section: Introductionmentioning

confidence: 99%

On the Effectiveness of Security Countermeasures for Critical Infrastructures

Hausken

2014

Risk Analysis

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A game-theoretic model is developed where an infrastructure of N targets is protected against terrorism threats. An original threat score is determined by the terrorist's threat against each target and the government's inherent protection level and original protection. The final threat score is impacted by the government's additional protection. We investigate and verify the effectiveness of countermeasures using empirical data and two methods. The first is to estimate the model's parameter values to minimize the sum of the squared differences between the government's additional resource investment predicted by the model and the empirical data. The second is to develop a multivariate regression model where the final threat score varies approximately linearly relative to the original threat score, sectors, and threat scenarios, and depends nonlinearly on the additional resource investment. The model and method are offered as tools, and as a way of thinking, to determine optimal resource investments across vulnerable targets subject to terrorism threats.

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“…In a recent work [12], motivated by critical infrastructure protection scenarios, Powell posed a sequential defensive Colonel Blotto game in which the defensive player allocates its assets to protect multiple targets. The attacking player then receives perfect information regarding the exact distribution of those resources.…”

Section: Introductionmentioning

confidence: 99%

A sequential Colonel Blotto game with a sensor network

Fuchs

Khargonekar

2012

2012 American Control Conference (ACC)

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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.

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Sequential, nonzero-sum “Blotto”: Allocating defensive resources prior to attack

Cited by 90 publications

References 15 publications

On the Impossibility of Deterrence in Sequential Colonel Blotto Games

On the Impossibility of Deterrence in Sequential Colonel Blotto Games

On the Effectiveness of Security Countermeasures for Critical Infrastructures

A sequential Colonel Blotto game with a sensor network

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