Related papers: Penney's game between many players
In this work we present a detailed analysis using the Markov chain theory of some versions of the truel game in which three players try to eliminate each other in a series of one-to-one competitions, using the rules of the game. Besides…
Consider a system of \(n\) players in which each initially starts on a different team. At each time step, we select an individual winner and an individual loser randomly and the loser joins the winner's team. The resulting Markov chain and…
Based on NFL game data we try to predict the outcome of a play in multiple different ways. An application of this is the following: by plugging in various play options one could determine the best play for a given situation in real time.…
In this paper we present a matricial result that generalizes Hironaka's game and Perron transforms simultaneously. We also show how one can deduce the various forms in which the algorithm of Perron appears in proofs of local uniformization…
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…
We extend the classical coupon collector's problem to one in which two collectors are simultaneously and independently seeking collections of $d$ coupons. We find, in finite terms, the probability that the two collectors finish at the same…
We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system.…
This thesis will be discussing scoring play combinatorial games and looking at the general structure of these games under different operators. I will also be looking at the Sprague-Grundy values for scoring play impartial games, and…
We introduce a natural variant of weighted voting games, which we refer to as k-Prize Weighted Voting Games. Such games consist of n players with weights, and k prizes, of possibly differing values. The players form coalitions, and the i-th…
We study the following game. Three players start with initial capitals of $s_{1},s_{2},s_{3}$ dollars; in each round player $P_{m}$ is selected with probability $\frac{1}{3}$; then \emph{he} selects player $P_{n}$ and they play a game in…
This paper studies Ebert's hat problem for three and four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning…
It is known that a player in a noncooperative game can benefit by publicly restricting his possible moves before play begins. We show that, more generally, a player may benefit by publicly committing to pay an external party an amount that…
We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the…
We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they…
This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with…
In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…
A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…