Related papers: On infinite versions of the prisoner problem

We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…

We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the…

This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational…

Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum…

So far, the theory of equilibrium selection in the infinitely repeated prisoner's dilemma is insensitive to communication possibilities. To address this issue, we incorporate the assumption that communication reduces -- but does not…

In this paper I present a mathematically novel approach to the Prisoner's Dilemma. I do so by first defining recursively a distinct action type, what I call 'universalizing', that I add to the original prisoner's dilemma. Such a modified…

100 prisoners and a light bulb is a long standing mathematical puzzle. The problem was studied mostly in 2002 [5], 2003 [1], and 2004 [3]. Solutions in published articles had average number of visits above 3850, but best solutions on forums…

The Pandora's Box problem models the search for the best alternative when evaluation is costly. In the simplest variant, a decision maker is presented with $n$ boxes, each associated with a cost of inspection and a hidden random reward. The…

Prisoner's dilemma has been heavily studied. In classical model, each player chooses to either "Cooperate" or "Defect". In this paper, we generalize the prisoner's dilemma with a new alternative which is neither defect or cooperation. The…

Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…

The standard iterated prisoner's dilemma is an unrealistic model of social behaviour because it forces individuals to participate in the interaction. We analyse a model in which players have the option of ending their association. If the…

This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in samples from populations with…

For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.

We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…

The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…

A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…

In this short note, we provide the necessary and sufficient condition for an infinite collection of axis-parallel boxes in $\mathbb{R}^{d}$ to be pierceable by finitely many axis-parallel $k$-flats, where $0 \leq k < d$. We also consider…

We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.

We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his $n$ prisoners in and out of $r$ rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large…