Related papers: The Monty Hall Problem in the Game Theory Class

Game versions of the Monty Hall Problem are discussed. The focus is on the principle of eliminating the dominated strategies, both in the zero-sum and noncooperative formulations.

Elementary decision-theoretic analysis of the Monty Hall dilemma shows that the problem has dominance. This makes possible to discard nonswitching strategies, without making any assumptions on the prior distribution of factors out of…

We propose a new approach to solve the classical Monty Hall problem in its general form. The solution is based on basic tools of probability theory, by defining three elementary events which decompose the sample space into a partition. The…

The Monty Hall problem is notorious for its deceptive simplicity. Although today it is widely used as a provocative thought experiment to introduce Bayesian thinking to students of probability, in the not so distant past it was rejected by…

This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

In this tutorial, the basics of game theory are introduced along with an overview of its most recent and emerging applications in signal processing. One of the main features of this contribution is to gather in a single paper some…

We emphasize the dominance in the Monty Hall problem, both in the classical scenario and its multi-door generalization. This is used to show optimality of the class of always-switching strategies for nonuniform allocation of the prize and…

Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…

These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…

This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD…

Selection of input features such as relevant pieces of text has become a common technique of highlighting how complex neural predictors operate. The selection can be optimized post-hoc for trained models or incorporated directly into the…

We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which…

We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we…

In this work, we present a logic based on first-order CTL, namely Game Analysis Logic (GAL), in order to reason about games. We relate models and solution concepts of Game Theory as models and formulas of GAL, respectively. Precisely, we…

I argue that we must distinguish between: (0) the Three-Doors-Problem Problem [sic], which is to make sense of some real world question of a real person. (1) a large number of solutions to this meta-problem, i.e., many specific…

We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.

The Monty Hall puzzle has been solved and dissected in many ways, but always using probabilistic arguments, so it is considered a probability puzzle. In this paper the puzzle is set up as an orthodox statistical problem involving an unknown…