# 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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### Probability Theory $\Rightarrow$ Game Theory?

It is a very simple question. I would like to learn Game Theory but I am not that good at Probability Theory. I would like to know it is necessary to be good at probability theory in order to learn ...
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### puzzle on [13,10,3] perfect Hamming code over $\mathbb F_{3}$

The soccer betting form contains a list of 13 games. There are three possible outcomes for each game: “the first team won”, “the second team won” and “draw”. Each betting form allows to chose one ...
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### Unbalanced game: probability of winning over an infinite number of possible match sequences

We have 2 players, A and B, competing. The probability that A wins a match is p, making the probability that B wins a match (1-p) = q. The game is won by player A as soon as he gets one more win than ...
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### How to solve this problem? Distributed Game theory?

I have this problem: We dispose of some resources, say $\{f_1, f_2, \dotsc, f_m\}$; We have some agents or players, say $\{\mathrm{p}_1, \mathrm{p}_2, \dotsc, \mathrm{p}_n\}$; Every player has some ...
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### How practically relevant is game theory?

I usually don't care too much about the practical relevance of nice mathematics :-) But this time, as I am looking to find some areas where I can apply maths and possibly collaborate with ...
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### Why all games are not Potential?

A definition given in wikipedia of an exact potential game as follow: A game $G=(N,A=A_{1}\times\ldots\times A_{N}, u: A \rightarrow \mathbb{R}^N)$ is: an exact potential game if there is a ...
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### Game Theory - Voting

In this setup there are 4 candidates running. For a candidate to be eliminated, the candidate needs to receive less than 1/3 of the votes when paired up with another candidate. This process ...
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### Is it possible to represent any arbitrary game as a 2 player game?

[I'm sorry that I wasn't more specific. Please bare with me I'm a curious novice and a new comer here to stack exchange.] original question: "Is it possible to represent any arbitrary game as a 2 ...
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### Proof that $12$ in a row tic-tac-toe is a tie game?

How can be it proved that tic-tac-toe on an infinite grid (winning with $12$ in a row, a column or a diagonal) can always end in a tie (with optimal strategies of both players)? There is a hint: to ...
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### Precise definition of a “game of incomplete information” (Game Theory)

Question: In game theory, what is the precise definition of a "game of incomplete information"? What I've found so far: In the standard first year graduate economics textbook on microeconomics ...
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### The Fundamental Theorem of Matrix Games, and the “indifference” method of solving games

In the following we will consider two-person zero-sum games. Let $A = (a_{ij})$ be the payoff-matrix of such a game. In this book the fundamental theorem of such games is states as: Theorem: Given ...
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### A little question about payoff functions being continuous.

In the mixed extension of a finite game $G$, why are the payoff functions of players continuous? Does it has something to do with being von Neumann and Morgenstern utility functions? Is there other ...
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### Game theory: inheritance distribution

An old man is dying and wishes to split his $2^n$-dollar fortune between his two sons. It shall be distributed this way: (1) The older brother should propose a way to split the money. If the younger ...
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### Minimum number of steps to guess an item in a database given a liar

Let's say I have a database of $N\times N$ size ($N$ rows and $N$ columns). My friend wants me to guess the location of an item. We start by binary guess, meaning I ask him if it is in upper half and ...
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### Best strategy for rolling 20-sided and 10-sided dices

There are a 20-sided (face value of 1-20) dice and a 10-sided (face value of 1-10) dice. A and B respectively roll the 20 and 10-sided dices. Both of them can roll the dice twice. They may choose ...
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### Pure vs mixed strategy Nash Equilibria

Just learning about Nash Equilibria. The pure strategy one is explained as an outcome where both/all players feel like they couldn't have done better given what the others were doing. Mixed strategy ...
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### Overview of game theory

I have a good high school math background, and I am interested in game theory, so I wanted to know something more about it, but I found very technical things or wikipedia. I am looking for something ...
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### Committee Voting Choice

Let's say you're in a group of 20 people, and each person has 3 votes for different people. They're all voting for a 5 member committee, and the 5 people who get the most votes win. Ties are resolved ...
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### The name of a game from the 2013 Putnam

Does the following game from the 2013 Putnam have an official name? Based on my searches, it seems to have been created just for the exam. Let $n\geq 1$ be an odd integer. Alice and Bob play the ...
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### A game problem- double or increment by 1

Its a two player game. Initially $P=1$, and there is some fixed integer $Q>1$. A valid move consists of either increasing $P$ by $1$ or doubling it iff on doing so $P$ does NOT exceed $Q$.The ...
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### Game theory Zero Sum Game Proof

Zerosum games. A coailitional game with transferable payoﬀ is zerosum if $v(S) + v(N - S) = v(N)$ for every coalition $S$; it is additive if $v(S) + v(T) = v(S \cup T)$ for all disjoint $S$ and $T$. ...
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### A modified NIM game

Let's play a game of NIM, but with a catch! We have exactly three piles of stones with sizes $a$, $b$ and $c$, all of which are different. We move in turns. In every move, we can select a pile and ...
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### Dilemma at the dining table

I created this problem while I was having my supper a few days back. So there maybe flaw in the formulation. Please point them out as you see one. Suppose, there is a circular dining table with ...
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### Existence of a winning strategy against the probability of winning

Edit: I've made the question clearer. Suppose a game is played between $A$ and $B$, in which there exists a winning strategy for $A$. Suppose $A$ and $B$ play their moves at random, do we have ...
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### Real world application of dominating set?

can anyone tell me about the application of vertex coloring problem and algorithm for vertex color problem in graph or networks.
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### What number of robbers, under the model of the prisoner's dilemma, would be optimal?

The prisoner's dilemma is defined as "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with ...
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### The Best Strategy and Highest Possible Score for the “Threes!” Game.

[There's still the strategy to go. A suitably robust argument that establishes what is statistically the best strategy will be accepted.] Here's my description of the game: There's a $4\times 4$ ...
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### Finding Nash Equilibria of a finte game of 2 players.

In a finite game, suppose player 1 has strategies $\{\alpha_1,\alpha_2\}$ and player 2 $\{\beta_1,\beta_2\}$ with payoffs as below. \begin{array}{c|c|c} &\beta_1&\beta_2\\ \hline\\ ...
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### How to 'show your work' with game theoretic notation

Everything I've read on game theory seems to describe the game in notation and solves it in natural language. How do you work with notation in game theory? Could you recommend a straight-forward ...
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### Linear Programming with Matrix Game

It seems from an easy google of "learning linear programming" that a common way of learning it is to work with Matrices that represent "games" for two players. Here is one I have stumbled across. We ...
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### Game Theory - trying to find game name by description

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I'm almost sure that such game has well-known name and tons of research already done around it. ...
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### How to denote this in game theoretic notation

I'm writing a paper that demonstrates that linguists can use the concepts in game theory to infer what interlocutors naturally infer when the literal meaning of their utterances doesn't ostensibly ...
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### Game theory, gambling odds

I'm looking for mathematics around such game: Two games: 50%, max bet: 155000, price x1.96 0.0015%, max bet: 5, price x64224.3 Let, I will place 155,000 for 50% ...
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### Topological games

I have seen in a few abstracts, as this for instance: A survey of topological games the remark that the subject Topological games has applications in other fields of mathematics. I am familiar with ...
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### Game Of Strings

There are two strings A and B. Initially, some strings A’ and B’ are written on the sheet of paper. A’ is always a substring of A and B’ is always a substring of B. A move consists of appending a ...
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### Finding optimal thresholds for “guess if number is highest” game

Consider the following game: five numbers are chosen randomly in the interval [0..1] with uniform distribution. The player is shown each number in turn and asked if it is the highest. The game ...
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### Apple game question

Player A and Player B play a game. On the middle of the table there is a pot full of $N$ apples of different weights. Player A starts first and chooses an apple and starts eating it. Losing no time ...