Conflicts with Multiple Battlefields

Kovenock, Dan; Roberson, Brian

doi:10.1093/oxfordhb/9780195392777.013.0021

Cited by 72 publications

(49 citation statements)

References 61 publications

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“…After Second World War Borel's model takes the name "Colonel Blotto game" brought into the scope of game theory the field of allocation games or a 'winner-takesall' conflicts with applications in the areas such as R&D races, presidential elections, auctions, tournaments (for an overview of research works on allocation games, see [2]). Hart [3] considered a discrete version of the Blotto game, called Colonel Lotto game where the battlefields are assumed indistinguishable.…”

Section: Introductionmentioning

confidence: 99%

“…For Colonel Lotto game, in accordance with Hart [6], payoff function H L is defined as H L (D,E ) = (1/m 2 ) ¦ i ¦ j sign(D i -E j ). In [3] it was shown that Colonel Blotto game (n, m) and the Colonel Lotto game (n, m) have the same value.…”

Section: Introductionmentioning

confidence: 99%

“…In [3] was shown that Colonel Blotto game has a mixed strategy equilibrium in which the marginal distributions are uniform on [0.2n/m] along all battlefields. In this way for Colonel Blotto game (120,6) for example the support set should contain more than 10 8 strategies taken with equal probabilities each.…”

Section: Introductionmentioning

confidence: 99%

“…Up to now it was common believe that solving minimax problem for antagonistic matrix games with constant sum like colonel Blotto or colonel Lotto games are intractable because the number of pure strategies grows exponentially with games' parameters (for partition games it is total resource n and number of part m). So all previous investigation efforts was concentrated on finding marginal distributions of the available resources that are the best for equilibrium [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…In section 3 "Experimental Design: synthesis suboptimal solution for symmetric partition games" the a matrix B(KxL) is well organized if, given x ∈ R K , it is easy to identify the columns _B[x], B¯[x] of B making the maximal, resp. the minimal, inner product with x [3]. basic stages of experimental procedure to compute equilibrium solutions are presented.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Suboptimal Solution of Antagonistic Matrix Games

Goryashko¹

2017

ITM Web Conf.

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Abstract. The paper examines resource allocation games such as Colonel Blotto and Colonel Lotto games with the goal to develop tractable method for building suboptimal solution in mixed strategies of these games without solving the relevant optimization problem. The foundation of proposed method lies in the specific combinatorial properties of the partition games. It turned out that as far as distribution of resource along battlefield is concerned that pure strategies participating in H-optimal solution possessed specific structure. Numerical experiments showed that these specific structural peculiarities can be easily reproduced utilizing previously found combinatorial properties of partition. As a result, we get H-optimal solution of partition games and support set mixed strategies can be computed in polynomial time.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Suboptimal Solution of Antagonistic Matrix Games

Goryashko¹

2017

ITM Web Conf.

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Multi‐battle Contests: An Experimental Study

Mago

Sheremeta²

2017

Southern Economic Journal

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We examine behavior of subjects in simultaneous and sequential multi-battle contests, where each individual battle is modeled as an all-pay auction with complete information. In simultaneous bestof-three contests, subjects are predicted to make positive bids in all three battles, but we find that subjects often make positive bids in only two battles. In sequential contests, theory predicts sizable bids in the first battle and no bids in the subsequent battles. Contrary to this prediction, subjects significantly underbid in the first battle and overbid in subsequent battles. Consequently, instead of always ending in the second battle, contests often proceeds to the third battle. Finally, although the aggregate bid in simultaneous contests is similar to that in sequential contests, in both settings, subjects make higher aggregate bids than predicted. The observed behavior of subjects can be rationalized by a combination of multi-dimensional iterative reasoning and a non-monetary utility of winning.JEL Classifications: C72, C91, D72

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Colonel Blotto in the Phishing War

Chia¹,

Chuang

2011

Lecture Notes in Computer Science

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Abstract. Phishing exhibits characteristics of asymmetric conflict and guerrilla warfare. Phishing sites, upon detection, are subject to removal by takedown specialists. In response, phishers create large numbers of new phishing attacks to evade detection and stretch the resources of the defenders. We propose the Colonel Blotto Phishing (CBP) game, a twostage Colonel Blotto game with endogenous dimensionality and detection probability. We find that the optimal number of new phishes to create, from the attacker's perspective, is influenced by the degree of resource asymmetry, the cost of new phishes, and the probability of detection. Counter-intuitively, we find that it is the less resourceful attacker who would create more phishing attacks in equilibrium. And depending on the detection probability, an attacker will vary his strategies to either create even more phishes, or to focus on raising his resources to increase the chance he will extend the lifetime of his phishes. We discuss the implications to anti-phishing strategies and point out that the game is also applicable to web security problems more generally.

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Conflicts with Multiple Battlefields

Cited by 72 publications

References 61 publications

On Suboptimal Solution of Antagonistic Matrix Games

On Suboptimal Solution of Antagonistic Matrix Games

Multi‐battle Contests: An Experimental Study

Colonel Blotto in the Phishing War

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