# Tagged Questions

The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under [tag:combinatorial-game-theory], and algorithmic aspects (e.g. auctions) are under [tag:algorithmic-game-theory].

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### While finding an optimal strategy for a mixed nash equilibrium, why do we not consider strategies which are never a best response?

"A strategy cannot be plausibly chosen by a rational player if and only if it is never a best response." I understand the logic behind neglecting the strategies that are strictly dominated. But why ...
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### A variation of Nim game

There are two players X and Y . They write N integers on paper ( A_1 , A_2 , A_3 , .... A_N ). They have also p integers (b_1 , b_2 , b_3 , .... b_p ) . Now , Player X always takes turn first . He ...
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### Mathematical game with numbers

We invented a mathematical game, which i am going to explain here. The first player choose a natural number, lets call it $n$ (if you play it for real, you must choose a sufficiently big number so ...
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### Alice and Bob make all numbers to zero game

Alice and Bob are playing a number game in which they write $N$ positive integers. Then the players take turns, Alice took first turn. In a turn : A player selects one of the integers, divides it ...
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### Three games of two-players each being played by three players simultaneously

Has the game theory literature considered situations wherein there are three two-player games being played by three players concurrently with each other; and the outcomes of those games may impact the ...
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### How can the policeman catch the gangster?

I try to solve the following problem (Moscow Mathematical Olympiad, 1978) There is a town with six streets: four sides of a square and two its middle lines. Policeman tries to catch a gangster. If ...
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### Looking for info on game theory for a scenario where participants earn points, and the top K earners receive a reward determined by rank

Say there's some competition that lasts for a week and takes place in a community. Participants receive points for collecting littered cans in the streets. Each can collected is a point. At the end ...
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### Strategy optimisation

This is a question from the Singapore Invitational Mathematics Challenge 2016. The question paper can be found here. (Part C:Question 2) http://www.nushigh.edu.sg/qql/slot/u90/file/simc/...
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### Dice role: What is the probability to observe 2 times 1 and 2 times 5 with the outcome of a fifth die role being unknown?

I tried to solve the following exercise: Given a dice with $P(X=2) = P(X=4) = P(X=5) = \frac{2}{15}$ and $P(X=1) = P(X=6) = P(X=3) = \frac{2}{10}$. What is the probability to observe 2 times 1 and 2 ...
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### A bin-assignment infinite 2-player zero-sum game

What is known about the following infinite 2-player zero-sum game? There are $k$ bins. Each player has 1 unit of mass and, simultaneously, divides it arbitrarily among the $k$ bins. The player wins ...
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### Enunciating utility maximization problem using set theory

I need to enunciate a problem using set theory and I am not sure how to start. The problem goes like this: You are a car manufacturer and need to decide how many colours to use in your next bash of ...
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### Variation of Nim, where one has to divide a pile into any number of piles.

I am learning the basics of combinatorial game theory (impartial games). After learning about decompose a game into the sum of games, I feel comfortable with games that can divided into the sum of 1 ...
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### He who has the largest real number in $[0,1]$ wins

Let's play a game: Let $X,Y \sim U (0,1)$ be random variables uniformly distributed over $[0,1]$. The game is as follows: I obtain a realization of $X$. You obtain a realization of ...
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### Stackelberg problem?

Suppose that two firms have different production costs: Player I's cost of producing x is x+2, while Player II's cost to produce y is 3y+1. Suppose that the price function is p(x,y)=17−x−y, where x ...
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### Game is winnable if and only if $n \neq k$

Integers $n$ and $k$ are given, with $n \ge k \ge 2$. You play the following game against an evil wizard. The wizard has $2n$ cards; for each $i = 1, \ldots, n$, there are two cards labelled $i$. ...