From memories of a quantum mechanics class and Wikipedia: In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundament …

In the simplest asymmetric Colonel Blotto game with 2 players, dividing their given Ni soldiers (i=1,2) over 2 battlefields, what are their expected utilities, Ui (i.e., expected n …

The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is: Lemma (Gibbs). $f_1,f_ …

I am trying to prove that a mapping has a unique fixed-point by showing that its Jacobian is a P-matrix. In this particular case the Jacobian can be decomposed as the sum of two ma …

For integers $n$ such that $\:3< n\:$,$\:$ what is known about the following 2-player game: Player_1 and Player_2 take turn choosing points on $\mathbb{R}^2$ that were not prev …

Two greedy chocolate eaters play the following game involving $n$ pieces of chocolate and an additional parameter $\alpha$ with initial value $1$: Each player eats either $\alpha$ …

Let $M(\mathbb{R})$ be the set of all matrices (of any size) over $\mathbb{R}$. Let $v : M(\mathbb{R}) \rightarrow \mathbb{R}$ be a function which satisfies the following 5 proper …

This question seeks help with improving a numerical estimate of the value of the Chow and Robbins game. Much about this game is unknown, such as whether its value is rational, but …

I consider a game to be mathematical if there is interesting mathematics (to a mathematician) involved in the game's structure, optimal strategies, practical strategies, anal …

Hey, I know what is Sprague-Grundy theorem, but I want to know about generalized Sprague-Grundy (GSG) theorem ( which is used for games with cycles ). Apparently there seems to b …

Is there a nice elementary proof of the existence of Nash equilibria for 2-person games? Here's the theorem I have in mind. Suppose $A$ and $B$ are $m \times n$ matrices of rea …

Consider the classical Nim game with total number of stones being odd. Then the first players wins, of course, what follows from the general description of winning positions. But i …

The question is close to the Sokoban game (thanks to Dima Pasechnik !), but a little different in details. Consider a directed graph (multi-graph). Consider some set of marked chi …

A bit unsure if the following vague question has enough mathematical content to be suitable upon here. In the case, please feel free to close it. In several circumstances of compe …

Hi, How to find, or at least express, the equilibrium of a zero-sum game with an $n*n$ payoff matrix (each player has $n$ strategies) and the payoff of the entry $(i,j)$ is $u(i, …