# 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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### Placing circles inside of a regular polygon.

Alice and Bob play the following game: on a table there is a regular $n$-gon. On each person's turn, they are required to place a circle of radius $r$ fully in the interior of the $n$-gon such that it ...
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### Nash Equilibria of P-Beauty

I'm a little confused with the work I am currently doing in Game Theory. Here is the questions I'm working on: ...
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### Mixed Strategy Probability Distribution

Problem Two firms with equal capacity constraints k but different marginal costs $c_i$ compete in a pay-as-bid auction for a fixed demand of (balancing) energy. The information on capacity ...
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### Proving a nash equilibria does not exist

At a certain warehouse, the price of tobacco per pound in dollars, $p$, is related to the supply of tobacco in pounds, $q$, by the formula $p=10−(q/100000)$ Thus the more tobacco farmers bring to ...
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### Game-winning strategy

Player A and Player B are playing a turn-based game. At the beginning of the game there are $N(N \ge 3)$ points in a plane. In each turn one of the players chooses exactly $3$ different points and he ...
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### Check that a Nash equilibrium point is given by $\left(0,\frac {1} {2}, \frac {1} {2}\right)$ $\left(0,\frac {1} {2}, \frac {1} {2}\right)$

Given the game matrix \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 0 \\ 1 & 0 & 2 \end{bmatrix} I already see a Nash equilibrium in pure strategies, which is $a_{11}$, ...
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### Iterated Best Response to find Pure Nash Equilibria

The context of this question is Game Theory. I've been trying to apply a simplified (?) version of the Iterated Best Response (IBR) technique to find Pure Nash Equilibria (PNE) in games generated by ...
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### Game Theory - $3\times3$Matrix - Mixed Strategy

I am trying to solve the following $3\times4$ game: \begin{array}{c|rrrr} & A & B & C & D \\\hline X & -3 & 5 & 2 & -1 \\ Y & 4 & -1 & 1 & -3 \\ Z & ...
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### Card Game Probability, the 15th card

Playing a card game in which 2 52 card decks are combined to create the pile and from this pile each player is dealt 14 cards. One rule of the game is if any player is dealt 3 doubles (a double being ...
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### How to find convergence with a learning rule that depends on the outcome of a game?

my first post here and really excited about the community. In a game theory set in which agents choose from a finite set of actions with a probability distribution, how can I look for convergence ...
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### Find a Mixed-strategy Nash equilibrium in an all-pay auction

This is an all-pay auction (Highest bidder wins the object, all players pay what they bid, player 1 wins all ties): Player 1 has $300$ dollars, Player 2 has $500$ dollars, the object being auctioned ...
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### Factor Game Calculation

Game: There are two players. The game starts off with the numbers 1 - 30 and player1 chooses a number and gets that number added to their score; however, the sum of all the available factors of that ...
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### Find a Nash Equilibrium point in mixed strategies using the simplex algorithm

Here is the game matrix A. First I note that $C_4<C_1$ and $C_4 <C_3$ So I can remove $C_1$ and $C_3$ since they are dominated strategies. Then considering only $C_2,C_4$, I note that $R_3$ ...
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### Math for game theory

I have read a bunch of book on Game Theory, and I find that one of the best is the the book of Osborne and Rubinstein. Nevertheless, all books which I found are not made for mathematician, meaning ...
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### Preference relation

Let $A=\{a,b,c\}$ and $\preceq$ is quasi-linear order on $\mathcal{L}(A)$. We also know that $a\prec b\prec c$ and for every lotery $L \notin \{[a],[c]\}$ we have $L\approx [b]$. Is $\preceq$ ...
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### The core -symmetric players

We have $n$-persons ($n\ge 3$) cooperative game. And we know that player $1$ and $2$ are symmetric. So for each element $(x_1,x_2,...,x_n)$ from the core we have $x_1=x_2$ ? Is that true ? Never seen ...
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### Game Theory Projects for Undergrads

I am looking for some project ideas for beginning math students in the topic of game theory. I am not very knowledgeable in the topic so it would be great if I could get an good introductory source to ...
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### Win/Lose ratios and selection strategies

Imagine the following scenario: You're on a TCG tournament which allowed you to bring N decks with you. After each game, you might select another deck for your next game. You are allowed to keep ...
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### Security level and equilibrium payoffs in $3-$person zero sum game.

Let the security level ($p-$payoff, $M-$set of all strategies) $$B_i:=\sup_{\sigma_i \in M_i} \inf_{\sigma_{-i}\in M_{-i}}p_i(\sigma_{-i},\sigma_i)$$ Now I consider $3-$person zero sum game. The ...
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### When solving linear equations what does ${0x_n = 0}$ mean? What if the system is used to find Nash equilibrium?

When solving systems of linear equations one sometimes gets result like ${0x_n = 0}$ what does it mean for solving the system? Is it error on part of the solver or just feature of the assignment? ...
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### How are lottery winnings calculated?

I'm pretty familiar how most chance games payouts are calculated - the ratio shoul be inversely proportional to the probability of winning, minus house edge. If we bet the same amount on the same game,...
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### Switching balls among 3 piles

There are 3 piles of balls. Each hour, I take a ball from one pile and move it to another. The amount of points I earn from this move is the amount of balls in the pile I took the ball from minus the ...
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### How to solve mixed strategy Nash equilibrium.

Lets say I have following problem: Zero sum game. Payoff matrix for player one: -1 4 4 2 6 -2 I start by writing equations for each strategy. ...
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