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

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Matrix multiplication in game theory doesn't add up? Min y^T*Ax

I'm studying game theory and something seems weird to me. My book says y is the probability of the row player and x is the probability of column player, both x and y are vectors. A = [a$_i$$_j$] is ...
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2answers
128 views

Puzzle with pirates

That one I'm pretty low on ideas of how to approach it. Five pirates of different ages have a treasure of 50 gold coins. On their ship, they decide to split the coins using this scheme: The oldest ...
2
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0answers
125 views

What is the optimal strategy for this 2 player game?

Let some finite array of integers is given initially. There is a number k which is initially '0'. In a move, a player will select a number from the array arr[i] and change k to gcd(k,arr[i]). Also, ...
12
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1answer
238 views

Optimal strategy for Jackpot Rock Paper Scissors

Jackpot Rock Paper Scissors is a gambling variant of Rock Paper Scissors, wherein ties result in the wager being carried forward into a jackpot. If a player plays the same hand (rock, paper or ...
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1answer
66 views

Game Theory in relation to economics and sociology [closed]

I know some algebra and calculus, and have been reading about Linear Programming/Game Theory. How are the models in this field, even the infinite calculus models, usable in macro economics. Even ...
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2answers
384 views

Game of cards and GCD

Alice and Bob play the game. The rules are as follows: Initially, there are n cards on the table, each card has a positive integer written on it. At the beginning Alice writes down the number 0 on ...
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1answer
29 views

Finding Nash Equilibriums

Nash Equilibrium for this Normal Game 1,1 2,4 1,4 0,8 1,1 1,1 3,0 0,0 7,0 I know ...
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2answers
31 views

How to calculate the mixed Nash Equilibrium in the matching pennies game?

The matching pennies game is the following: \begin{array}{|c|c|c|c|} \hline Player1\backslash Player2 & H & T \\ \hline H & (\color{red}{+1}, -1) & (-1, \color{blue}{+1}) \\ \hline T ...
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1answer
47 views

Spinner game outcomes: What has the best chance of winning with your last two coins?

We are discussing probability and odds in my elementary math class. The students came up with two scenarios. They are as follows... In a spinner wheel game based on the days of the week, students bet ...
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0answers
46 views

Is the expected utility function linear?

Given the definition of the mixed extension of a finite game as in the link below (only first 7 lines): How to find perfect equilibria in a finite game? We define the expected utility function in the ...
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1answer
46 views

Is there any dominant strategy? [closed]

Is there any dominant strategy for the below matrix? I think no... But I am not sure. please check my answer:) $$\left (\begin{array}{ccc} (0,0) & (0,1) \\ (1,0) & (-1,-1) \end{array}\right ...
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0answers
33 views

How to find perfect equilibria in a finite game?

If we define a game with $n$ persons as below: (i) for each player $i$, he has his strategy set $S_i$, $|S_i|=m_i<\infty$, and denote $S=\Pi_iS_i$; (ii) $u_i:S\rightarrow\mathbb{R}$ is a payoff ...
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1answer
43 views

Show a simple strategy.

Imagine that we have 49 cards with the values written on their faces, (they are all visible ) as follows; $$25, 24, 23, 22, ........3, 2, 1, 2, 3, .........23, 24, 25$$ suppose Paola and Victor are ...
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1answer
35 views

Help me writing Payoff matrix.

I guess, in order to answer this question, I need to write Payoff matrix. But I cannot write it. And then, I Will able to answer this question by myself. Thank you for helping. (These are just ...
2
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1answer
48 views

Check my answers: Dominant strategy.

I saw another question on Game theory. My answer for part a the nash equlibria (T, L) and (B,R). for part-b, Player-1's action T is strictly diominated. So Player1 never choose T. For part ...
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1answer
72 views

A question on Game theory

I'm studying Game theory, I saw the question: Consider two players; player A and player B playing the following estimation game. Each player chooses a number from {1, 2, 3}. If the difference ...
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2answers
298 views

The Last Man Standing

This is my second question following this post. Three players are playing a game. They all have small amounts of money, let say: player 1 has $\$a$, player 2 has $\$b$, and player 3 has $\$c$, ...
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0answers
28 views

state graph and MEx position

I am in a bit trouble. My midterm exam is coming and I do not understand state graphs and MEx positions. I am confused about this concept. Here is an example I give you. Please can you explain to me ...
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0answers
32 views

Game theory:Baye's rule for tournament

I'm having challenge with the following computations from the book I'm using. How are the steps obtain from the preceding step? In the expressions below, $E_i$ and $E_j$ are independent, random ...
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3answers
561 views

Optimal strategy for the Rope Climbing Game

Define a two-player, turn-based climbing game as follows. Each turn, players have the option to climb or tie a knot at his current position. If the player chooses to climb, there is a 50% chance ...
0
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1answer
55 views

Game Theory and Uniform Distribution question?

In an Auction , two players are bidding. Their bids will be a unknown fraction of their valuations. The valuations come from a uniform distribution $$[0,1] $$ If Player 2 bids $$ v/2 $$ and Player ...
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2answers
29 views

Joint Game Theory?

I am confused. A Game is, generally, defined by: $\mathcal{G}=(\mathcal{P}, \mathcal{A}, \mathcal{U})$ where $\mathcal{P}$ is the set of players, $\mathcal{A}$ is the set of actions $\mathcal{U}$ is ...
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2answers
53 views

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 ...
2
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1answer
50 views

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 ...
2
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1answer
95 views

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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1answer
41 views

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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3answers
183 views

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 ...
0
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1answer
34 views

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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0answers
40 views

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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39 views

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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0answers
73 views

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 use ...
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3answers
145 views

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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2answers
53 views

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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2answers
51 views

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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2answers
41 views

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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0answers
22 views

Minimum number of steps to guess an item in a database

Let's say I have a database of N*N size (N rows N columns) My friend wants me to guess the location of an item. We start by binary guess, means I ask him if it is in upper half, he says yes or no, if ...
3
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1answer
82 views

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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2answers
124 views

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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1answer
42 views

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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2answers
40 views

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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0answers
89 views

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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1answer
302 views

What is the probability of a $4$ appearing in the game $2048$? [closed]

I'm not sure if this is the appropriate SE, so please suggest a more appropriate website if not. I'm making a facsimile of $2048$, and I've just one question I've been unable to work out: what is the ...
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0answers
26 views

n-player zero-sum rating

I am trying to make a rating system like Elo-rating for n-players in SET with rules here. In each game 1 player plays against n-1 other players. The player collects a number of SETs, $s$. Based on ...
4
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1answer
67 views

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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0answers
46 views

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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249 views

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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202 views

The Right Triangle Game

I am looking for a deeper understanding, particularly the optimum strategy and the maximum score as a function of grid size, of the following (single-player) game played with an $n$ by $m$ grid: ($6 ...
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1answer
70 views

What is the definition of “Winning Strategy” in an Ehrenfeucht-Fraïssé game?

I've read many descriptions and applications of a Winning Strategy, as much as many for a Strategy tout court, but when a formal, algebraic definition is called upon, I've found close to no input. I ...
5
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1answer
148 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
3
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1answer
171 views

Game Theory - A joint project problem

I'm new to this forum and as such not sure if this is the correct place to ask for help on Game Theory. As such I am currently working out of the Introduction to Game theory book by Martin J Osborne ...