# 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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### Big Balloon Game

The problem In this game, you are given empty balloons one by one, and for each balloon you are to inflate it with air until you are satisfied. If it does not burst, you gain happiness points ...
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### Nash equilibrium: Can I delete weakly dominated strategies in this case?

As far as I know, an equilibrium can involve a weakly dominated strategy, but cannot involve a strictly dominated strategy. Is there a general rule for when/if you can safely delete a weakly dominated ...
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### On a possibility/impossibility of a certain twisted situation in a tournament

Recently I encountered the following puzzle: Consider a game for two players which can only result in a win of one of the players (no ties). Now $n$ players decided to play this game each with ...
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### Prisoners' Dilema

I started to learn about game theory just now. I am confused about the prisoners' dilema, when 2 prisoners are given a choice whether to keep silent or rat out the other guy. From what I read, if one ...
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### Number Game: 31 - Winning Strategy?

My Maths teacher taught us how to play a game called 31 on Friday. Not once did my Maths teacher lose. I want to know why. I'll explain the game... 31 is a game between two people. Let's say you've ...
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### What is a good introductory book on Rational Choice Theory for a mathematician?

I'm interested in Rational Choice Theory as an approach to political science. Amongst other, related subjects, I'd like to know a thing or two about Arrow's impossibility theorem (and other aspects of ...
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### Does introducing penalties for getting true/false questions incorrect result in higher skill penetration (less luck/variance)?

A student is asked to answer 50 true/false questions and he would get 35 right and 15 incorrect if he had to put his best guesses for each question down. Now, for each question he has a certain ...
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### Generalized First Price Auction or Generalized Second Price?

Sorry if I ask the same question again but in the other post I'm not able to edit my question because I wasn't using an account. By the way, the question: I'm running some tests to decide which type ...
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### Game Theory: (basic) minmax linear function help

Background I am looking for some help with the reasoning here for a few things in my game theory book (my math expertise is quite weak - below is from the text): From Text Book \begin{eqnarray} min ...
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### (Infinite hat)-guessing problem

$2$ men are playing a game: they are wearing countably infinitely many hats on their heads. The hats are either black or white with probability $\frac 12$. They see the other's man hats but cannot see ...
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### simplex method tableau

If I have the matrix: x1 x2 s1 s2 s3 z 1 4 1 0 0 0 | 12 2 5 0 1 0 0 | 2 1 3 0 0 0 1 | 4 ---------------- -2 -1 0 0 0 1 | 0 Then, where x1 is the row of 1, 2, 1....x2 is the row of 4, 5, 4.......
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### How to create a fair dynamic scoring system? [closed]

I am currently in the process of creating a game consisting of a fixed set of tasks of varying difficulty. Each player gets the same set of tasks to choose from and is awarded a certain number of ...
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### The Notion Of Degenerate Two Player Game

I try to get the intuitive understanding of the notion "degenerate two player game". Definition. A two-player game is called non degenerate if no mixed strategy of support size $k$ has more than $k$ ...
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### what is the fairest ratio of k to n for this game

Here is a description of a two player game with players plr1 and plr2 that is played on a n by n grid. Players take turns filling cells in the grid. plr1 goes first and wins by completing a straight (...
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### I can't find the Nash equilibrium of this 3x2 game.

Sorry for my English, I am French but i couldn't find help on the French website (so I am here). I have a question about this two-player game:  \begin{array}{c|cc} & y_1 & y_2 \\ \hline ...
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### Reduce the payoff matrix using (weakly) dominated strategies

Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? ...
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### Expected value and variance of a random variable, defined as the largest of $6$ randomly drawn numbers

Let each of the numbers from $1$ up to $49$ be written on a ball, and let all these balls be contained in a box. From this box, we randomly draw exactly $6$ numbers (without putting them back, so we ...
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### Compute the set of subgame perfect equilibria for this game (mixed strategies help)

In the above game there are 2 proper subgames (not including the whole game itself). I know there's 9 sub-game perfect equilibrium i have to figure out. I've managed to work out 4 of those, the ...
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### How exactly is the St Petersburg Paradox giving bounded payoff in average-of-N-trials?

I understand why the expected value of the St Petersburg Paradox is algebraically infinite, but intuition tells me that in practice any given round of the game will not go on multiplying the pot for ...
The question I have is in some ways a variation on the stable marriage problem adapted to the situation of dating. Suppose there are $n$ boys and $n$ girls, where every boy ranks the girls from $1$ ...