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## A colonel blotto gladiator game

Venue: | Mathematics of Operations Research |

Citations: | 2 - 0 self |

### Citations

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2553 | A Course in Game Theory
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- 1994
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Citation Context ...m,cA) min b∈B(n,cB) Hm,n(a, b) = min b∈B(n,cB) max a∈A (m,cA) Hm,n(a, b) = Hm,n(a ∗, b∗). 6 Since we are dealing with a finite zero-sum game, Nash equilibria and minmax solutions coincide (see, e.g., =-=Osborne and Rubinstein, 1994-=-, Proposition 22.2). The quantity Hm,n(a ∗, b∗) is called the value of the game G . The next theorem characterizes the structure of Nash equilibria of the game G (m,n, cA, cB). Theorem 3.1. Consider t... |

1020 |
Probabilistic model for some intelligence and attainment tests
- Rasch
- 1980
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Citation Context ...score wins a dollar. The model described below for the probability that gladiator i defeats j, is equivalent, with different parametrization, to the well-known Rasch model in educational statistics, (=-=Rasch, 1980-=-), in which the probability of correct response of subject i to item j is eαi−βj /(1 + eαi−βj) (see Lauritzen, 2008, for a recent mathematical study of Rasch models). A similar model has been used als... |

415 | E¢ cient rent seeking - Tullock - 1980 |

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170 |
Contest success functions
- Skaperdas
- 1996
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Citation Context ...ullock (1980) with the purpose of studying efficient rent seeking: hγ(a, b) = aγ aγ + bγ , γ > 0. (7.1) These functions have been studied, axiomatized, and widely used in different fields (see, e.g., =-=Skaperdas, 1996-=-, Szymanski, 2003, Corchón and Dahm, 2010, and many others). The reader is referred to Corchón (2007), Garfinkel and Skaperdas (2007), Konrad (2009) for surveys on this topic. In (7.1), when γ →∞, t... |

101 |
The economic design of sporting contests
- Szymanski
- 2003
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Citation Context ...h the purpose of studying efficient rent seeking: hγ(a, b) = aγ aγ + bγ , γ > 0. (7.1) These functions have been studied, axiomatized, and widely used in different fields (see, e.g., Skaperdas, 1996, =-=Szymanski, 2003-=-, Corchón and Dahm, 2010, and many others). The reader is referred to Corchón (2007), Garfinkel and Skaperdas (2007), Konrad (2009) for surveys on this topic. In (7.1), when γ →∞, then hγ(a, b)→ h∞(... |

100 | Strategy and Dynamics in Contests - Konrad - 2009 |

41 |
Total Positivity Vol. I
- KARLIN
- 1968
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Citation Context ...tly larger than any mode of fλ0(x). Proof. This result is similar to Székely and Bakirov (2003, Lemma 1). We provide a quick proof using variation diminishing properties of sign regular kernels (see =-=Karlin, 1968-=-). First, since the density of λY is log-concave (a.k.a. strongly unimodal) its convolution with the unimodal f(x) is also unimodal, that is, the pdf of X + λY is unimodal (see Ibragimov, 1956, Karlin... |

39 | The colonel blotto game - Roberson |

38 | Campaign Spending Regulation in a Model of Redistributive Politics - Sahuguet, Persico - 2006 |

34 | Discrete colonel blotto and general lotto games - Hart - 2008 |

31 | Economics of conflict: An overview - Garfinkel, Skaperdas - 2006 |

30 | Game-theory models in the allocation of advertising expenditures - Friedman - 1958 |

26 | Contests with limited resources - Kvasov - 2007 |

21 | Rent seeking and rent dissipation: A neutrality result - Alcalde, Dahm - 2010 |

21 | An experimental investigation of Colonel Blotto games - Chowdhury, Kovenock, et al. - 2013 |

21 |
On the composition of unimodal distributions. Theory Prob
- Ibragimov
- 1956
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Citation Context ...rnels (see Karlin, 1968). First, since the density of λY is log-concave (a.k.a. strongly unimodal) its convolution with the unimodal f(x) is also unimodal, that is, the pdf of X + λY is unimodal (see =-=Ibragimov, 1956-=-, Karlin, 1968). Differentiating (justified by (i)) yields f ′λ(x) = ∫ ∞ 0 f ′(x− z) 1 λ e−z/λ dz = ∫ x −∞ f ′(z) 1 λ e(z−x)/λ dz = e−x/λ λ ∫ 1(−∞,x)(z)f ′(z) ez/λ dz. Suppose f ′λ(x0) = 0. Since f ′(... |

20 | On times to quasi-stationarity for birth and death processes - Diaconis, Miclo - 2009 |

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17 | The theory of contests: a survey - Corchón - 2007 |

15 | A continuous colonel blotto game - Gross, Wagner - 1950 |

14 | 2010): “Conflicts with Multiple Battlefields,” CESifo Working Paper Series 3165, CESifo Group Munich - Kovenock, Roberson |

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10 |
The theory of play and integral equations with skew symmetric kernels (La théorie du jeu et les équations intégrales à noyau symétrique). Econometrica 21
- Borel
- 1921
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Citation Context ...otal gain. The relevance of Borel precursory insight in the theory of games was discussed in an issue of Econometrica that contains three papers by Borel, including the translation of the 1921 paper (=-=Borel, 1953-=-), two notes by Fréchet (1953b,a) and one by von Neumann (1953). Borel and Ville (1938) proposed a solution to the game when the two enemies have an equal amount of resources and there are n = 3 batt... |

9 | On a Game Without Value - Sion, Wolfe - 1957 |

8 | On Colonel Blotto and Analogous Games - Bellman - 1969 |

7 | Extremal probabilities for Gaussian quadratic forms. Probab. Theory Related Fields 126 - Székely, Bakirov - 2003 |

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6 | A Blotto game with incomplete information - Adamo, Matros - 2009 |

6 |
Numerical computation of stochastic inequality probabilities
- Cook
- 2008
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Citation Context ... · = a∗pi(r) = cA/r, api(r+1) = · · · = api(m) = 0, and b ∗ 1 = · · · = b∗n = cB/n. Hence m∑ i=1 a∗iXi ∼ Gamma(r, r/cA), n∑ j=1 b∗jYj ∼ Gamma(n, n/cB). Therefore, (see, e.g, Cook and Nadarajah, 2006, =-=Cook, 2008-=-) P ( m∑ i=1 a∗iXi > n∑ j=1 b∗jYj ) = 1− I ( rcB rcB + ncA , r, n ) , (5.13) where I is the regularized incomplete beta function defined in (3.5). (b) By Theorem 3.1(b) in this case r = m. (c) By Theo... |

6 | 2009): Sequential, nonzero sum blotto-allocating defensive resources prior to attack - Powell |

5 | General blotto: games of allocative strategic mismatch - Golman, Page - 2009 |

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3 |
Exchangeable rasch matrices
- Lauritzen
- 2006
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Citation Context ...ith different parametrization, to the well-known Rasch model in educational statistics, (Rasch, 1980), in which the probability of correct response of subject i to item j is eαi−βj /(1 + eαi−βj) (see =-=Lauritzen, 2008-=-, for a recent mathematical study of Rasch models). A similar model has been used also in the theory of contests proposed by Tullock (1980), as will be described in Section 7. Finding the Nash equilib... |

2 | Foundations for contest success functions - Corchón, Dahm - 2010 |

2 | Bounds for tail probabilities of weighted sums of independent gamma random variables - Diaconis, Perlman - 1990 |

2 | Designing competitions between teams of individuals - Tang, Shoham, et al. - 2010 |

1 | La théorie des jeux et les équations intégrales à noyau symétrique - Borel - 1921 |

1 |
Stochastic inequality probabilities for adaptively randomized clinical trials
- Cook, Nadarajah
- 2006
(Show Context)
Citation Context ...n pi we have a∗pi(1) = · · · = a∗pi(r) = cA/r, api(r+1) = · · · = api(m) = 0, and b ∗ 1 = · · · = b∗n = cB/n. Hence m∑ i=1 a∗iXi ∼ Gamma(r, r/cA), n∑ j=1 b∗jYj ∼ Gamma(n, n/cB). Therefore, (see, e.g, =-=Cook and Nadarajah, 2006-=-, Cook, 2008) P ( m∑ i=1 a∗iXi > n∑ j=1 b∗jYj ) = 1− I ( rcB rcB + ncA , r, n ) , (5.13) where I is the regularized incomplete beta function defined in (3.5). (b) By Theorem 3.1(b) in this case r = m.... |

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