منابع مشابه
Nontransitive Dice With Equal Means∗
We analyze a game in which two players choose in turn and roll an n-sided die, each player having his choice of numbering of the faces, subject to certain constraints. The player who rolls the larger number wins. We say die B “dominates” die A if P [B > A] > P [A > B]. The nontransitivity of this dominance relation for dice has been studied by several authors. We analyze the case of n-sided dic...
متن کاملNontransitive Dice Paradox in Networking ∗
Here is a simple trick that you can use to try to dupe a friend out of his money with high probability. Bet with him on the outcome of three specially numbered dice labelled X , Y , and Z each with six faces marked as: X (3 3 5 5 7 7), Y (2 2 4 4 9 9), Z (1 1 6 6 8 8). Each person chooses a different die. The larger number wins when the dice are rolled. Strangely, whichever die your friend has ...
متن کاملA Game of Nontransitive Dice
We consider a two player simultaneous-move game where the two players each select any permissible n-sided die for a fixed integer n. A player wins if the outcome of his roll is greater than that of his opponent. Remarkably, for n > 3, there is a unique Nash Equilibrium in pure strategies. The unique Nash Equilibrium is for each player to throw the Standard n-sided die, where each side has a dif...
متن کاملBalanced Non-Transitive Dice
We study triples of labeled dice in which the relation “is a better die than” is non-transitive. Focusing on such triples with an additional symmetry we call “balanced,” we prove that such triples of n-sided dice exist for all n ≥ 3. We then examine the sums of the labels of such dice, and use these results to construct an O(n) algorithm for verifying whether or not a triple of n-sided dice is ...
متن کاملThe Concave Nontransitive Consumer
The preference of a concave nontransitive consumer is represented by a skew-symmetric and concave-convex bifunction on the set of all commodity bundles. This paper characterizes finite sets of demand observations that are consistent with the demand behavior of such kind of consumer by a generalized monotonicity property.
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ژورنال
عنوان ژورنال: The College Mathematics Journal
سال: 2017
ISSN: 0746-8342,1931-1346
DOI: 10.4169/college.math.j.48.1.10