# Questions tagged [game-theory]

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### The multiplication game on the free group

Fix $W\subseteq\mathbb F_2$ and consider the following two-person game: Player 1 and Player 2 simultaneously choose $x$ and $y$ in $\mathbb F_2$. The first player wins, say one dollar, iff $xy\in W$. ...
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### Finding an optimal strategy for a combinatorial sequential game

We are given a set $\{p_1, p_2, \ldots, p_n\}$ of players and a set of $\{\ell_1, \ell_2, \ldots, \ell_n\}$ of locations, where $n\in\mathbb{N}$. Each location can be either free or occupied, and each ...
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### Extension of Standard English Peg Solitaire

An entire analysis of standard English Peg Solitaire has been given. See Berlekamp, E. R.; Conway, J. H.; Guy, R. K. (2001) [1981], Winning Ways for your Mathematical Plays (paperback) (2nd ed.), A ...
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### What is the Bruss-Yor concept of no information?

A few years ago, a question related to a paper of Thomas Bruss and Marc Yor on the so-called last arrival problem received some attention on this forum. What I'd like to know now is: What are the ...
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### Zero-sum games where getting information helps the opponent more

You may know of the paper on the "Memory" game - sometimes the best strategy is turning known cards (here: https://www.math.kth.se/xComb/x1.pdf). Here is a simpler toy example: You and your opponent ...
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### How does one reconcile a formula for the Shapley value for a coalition with the one given in a relatively old paper?

This is a cross-post from this question on MSE. In the Wikipedia article on the Shapley value (here), a formula is given that generalises the notion of the Shapley value from an individual player to ...
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### rank-choice shared-resource fair-division

I'm looking for an algorithm or a paper that solves a problem with a particular set of properties. Imagine you have some number of rooms and some greater number of people. Each person should be ...
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### A universal framework for Game Theory?

Ever since the seminal work of Von Neumann and Morgestern Game Theory has grown into a formidable sector of pure and applied mathematics. There are all sorts of games: perfect information, ...
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### How to find the equilibrium of the following stochastic game (numerically)

I build up a stochastic game with two groups of players (Group A and Group B) and within each group, the players can have two labels as H and L (label of each player may change from period to period). ...
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### Projecting on a convex compact polytope with special form

Let $E$ be a large sparse $l$-by-$n$ matrix ($l$ and $n$ can be in the billions...) with coefficients in $\{-1, 0, 1\}$: the first row of $E$ is the vector $(1,0,0,\ldots,0) \in \mathbb R^n$, and ...
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### On the Theory of Infinite Step Processes of Sequential Decision Making

On the border of Set Theory and Game Theory there is a broad class of Infinite Step Processes of Sequential Decision Making that can be characterized by the main following property: a Future ...
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### Convergence proof for fictitious play!

In "Fictitious play property for games with identical interests" by D. Monderer and L.S. Shapley, the convergence of fictitious play to a Nash equilibrium is proved for a potential game with players ...
I am currently trying to solve a maximization problem given by $\max_{f(x)} \int_0^1 \int_\mathbb{R} (c-y\cdot f(x)-d\cdot (x+f(x)-b)^2) \ h(x) \ dx \ dy$. Or in other words, I have a utility ...