# Questions tagged [game-theory]

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### Variant of Parthasarathy's minimax theorem

Does there exist a variant of Parthasarathy's minimax theorem  that relaxes the assumption that the spaces $X$ and $Y$ are $[0,1]$?  https://en.wikipedia.org/wiki/Parthasarathy%27s_theorem
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### Can the fugitive escape?

A fugitive is surrounded by $N$ police officers, with the nearest one at distance $1$ away. The fugitive and the officers move alternatively. In a fugitive move, the fugitive can travel no more than ...
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### Dubious matrix monotonicity

Coming from a problem in game theory, I arose at some dubious monotonicity like property for matrices of the following art. Let $H=\lbrace h\in\mathbb{R}^{n}\colon h_{1}+\dots+h_{n}=0\rbrace$. I'm ...
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### Nash equilibria for “presidential election” game

Suppose, in a country there are $m$ different social issues, positions on which are being indexed with numbers $[-1; 1]$, with radicals on the opposing ends and moderates in the center. In this ...
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### Suggestions for two-choice game played in ladder graph

I was just working on counting all the possible Nash Equilibrium solutions for a two-choice game played on a ladder graph (I got my results and all that for a generic number of players). And I was ...
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### Pursuit-evasion with many slow pursuers

Question: Suppose that intelligent pursuers with speed $v<1$ are randomly scattered on the plane with area density $1/r$  ($r>0$ is distance from the origin). If you start at the origin ...
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### What is the fairest order for stage-striking (and is it the Thue-Morse sequence)?

Here's a fair-sequencing problem that doesn't quite match the usual fair-division problems. I think that, like those, the answer should also be the Thue-Morse sequence ("balanced alternation"), ...
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### Optimal Strategies for a “Blind” Graph Coloring Game

By the "blind" graph coloring game I denote the following problem, which is played by two players: player A has $k<n$ colors at hand to color the $n$ vertices of a graph $G$, but that ...
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### A community effort: equilibrium in quitting games [closed]

This thread is in the spirit of the polymath project: a combined effort of the community to solve a difficult open problem. It is an activity of the European Network for Game Theory whose goal is to ...
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### Matrix tic tac toe

So we have a 3x3 matrix and two players, a player that only puts in ones and a player that only puts in zeros. A coin flip is used to decide which player goes first. The first move is always to fill ...
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### Strong Nash Equilibria in repeated games

Suppose we have a simultaneous game, that has a strong Nash equilibrium (SNA), i.e. a weak Pareto efficient Nash equilibrium (no deviation of any subset of player brings a benefit to them). Now ...
The standard Penney's game is played by two players. Player $A$ chooses a sequence of $k>2$ bits and $B$ (seeing $A$'s selection) chooses a different sequence of $k$ bits. A fair coin is flipped ...