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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Correlated Equilibrium - Transforming a non-linear objective function into a linear one

I am trying to transform a non-linear objective function into a linear one, in order to create a LP. How might I go about to do this (I have never taken a course in linear programming). I have that I ...
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1answer
312 views

subgame perfect nash equilibrium for war of attrition

the question is as follow: suppose that two players are playing war of attrition, that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
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2answers
5k views

cournot competition with N-firms

The question is as follow: Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
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2k views

cournot equilibrium and stackelberg equilibrium question

Question is as follow: there are 2 firms that want to enter the apple juice market in country A. There are no existing firms in the market or potential entrants. They need to decide on yearly ...
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178 views

Always win without a winning strategy

On Page 141, Axiom of Choice, Herrlich(2006) Show that if in a game of the form $G(1, X_1, Y_1, A)$, the first player has no winning strategy, then the second player can always win, even ...
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471 views

Simple game with coins - strategy

Let's play a game: There are $n$ stacks of coins in a row. $i$-th stack consists of $d_i$ coins. Two players: $\text{Player1},\text{Player2}$ make moves alternately. Player in his turn can only take ...
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114 views

Card game-ordering a deck [duplicate]

Possible Duplicate: Game Theory Matching a Deck of Cards Suppose we take a blank deck of $52$ cards, write the number $1$ on the first card, $2$ on the second card, and so on until we write ...
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1answer
170 views

Cournot-game problem

I'm so stuck with an exercise about Cournot game and was hoping if someone could help me out here. Would appreciate all the help. This is the exercise: Consider the market for Blue Turtle (a new ...
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2answers
160 views

Poker, number of three of a kind, multiple formulaes

I wanted to calculate some poker hands, for a three of a kind I infered, 1) every card rank can form a 'three of a kind' and there are 13 card ranks, 2) there are $\binom{4}{3}$ ways to choose three ...
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380 views

Determine market price and quantities produced; non-cooperative cournot game

$P(Q)$ represents a market where demand $Q$ is related to price $P$ by $$P(Q) = Q^{-\frac{1}{2}}$$ In this market there are $m$ identical producers, say firm 1, 2, up to $m$ which can produce any ...
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130 views

Tree search on game of Imperfect Information

Ok... I have a game of imperfect information and I want to compute its Minimax Value.From the lectures I know that in order to find the value for a Perfect information game I can use tree search ...
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305 views

A game played on a rectangle

Suppose two players play the following game on a $m$ by $n$ rectangle. Alternatingly they have to make a cross in some empty $1\times 1$ square. They are not allowed to make a cross next to another ...
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728 views

Game Theory - Centipede Game

I am working on a game theory question. The question is as follows: Characterize the unique subgame-perfect equilibrium in the following game. Can you find any Nash equilibrium which is not ...
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2answers
149 views

Why does menace work?

Consider the repeated Prisoner's Dilemma. Every day, for many days, two players play this game: $\left(\begin{array}{ccc} \left(3,3\right) & \left(0,10\right) & (-2,-2)\\ (10,0) & (1,1) ...
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0answers
139 views

Optimal strategy in a VCG auction with partial collusion?

Suppose you control the bid prices in a multiple-item VCG auction for a partial coalition of bidders. Each bidder is only allowed to win one item out of the set of multiple items, which are all ...
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2answers
306 views

Determine Nash equilibrium

How can I determine the nash equilibria in the following matrix? $$\begin{pmatrix}-\pi,-\pi & e,0 \\ 0,e & -\pi,-\pi \end{pmatrix}$$ I know the definition of a Nash equilibrium, but because ...
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1k views

Value of a zero sum game

I've been looking some around on the net for some info on zero-sum games, But I don't think I fully understand the principle; If we consider the (simple) matrix: $$\begin{pmatrix}\pi&0 \\ 0&e ...
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2answers
189 views

The name of the game (Hawk-Dove variant?)

I stumbled upon the following symmetric two-person game. We have two objects $X,Y$ with positive value $x$ and $y$, and two persons that have to pick independently form each other simultaneous one of ...
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1answer
235 views

mixed strategy nash equilibrium question!

Suppose the game consists of only $2$ players, player $1$ and player $2$, and each of them has only $2$ strategies to choose between. This gives a $2$ by $2$ payoff matrix. Player $2$ has no ...
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287 views

Question on mixed nash equilibrium!

The question is as follows: Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows: ...
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0answers
229 views

On a zero-sum game betting market

I'm trying to come up with the rules for a betting game. My problem is to figure out under what constraints that game has zero-sum game properties: in other words, I want to make sure that no money is ...
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1answer
2k views

Is War necessarily finite?

War is an cardgame played by children and drunk college students which involves no strategic choices on either side. The outcome is determined by the dealing of the cards. These are the rules. A ...
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160 views

Game Theory - Extensive Zero-Sum Game Property Proof

How I might I go about to prove (or disprove, but I believe that this is true) the following: We call a 2-player extensive game $\Gamma$ a zero-sum game if the sum of the 2 payoffs for an terminal ...
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393 views

Game Theory Matching a Deck of Cards

Moderator Note: This question is from a contest which ended 1 Dec 2012. Suppose we have a deck of cards labeled from $1$ to $52$. Let them be shuffled in a random configuration, then made ...
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1answer
655 views

Saddle points in zero sum game

We only had one lecture about the subject and already have quite difficult questions, could someone please help me? The matrix looks something like this: \begin{matrix} 3 & 2 & 1 & 4 ...
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1answer
431 views

Which side has winning strategy in Go?

Go is actually a finite two-person game of perfect information and cannot end in a draw. Then by Zermelo's theorem, it is exactly one of the two has winning strategy, either Black or White. So my ...
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87 views

graph-theory combinatorics

Here is a combinatorics problem having to do with graph-theory Ten players participate at a chess tournament. Eleven games have already been played. Prove that there is a player who has played at ...
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1answer
409 views

Relevant Topics for Presentations

I have to make an presentation as a part of our math course. We are provided relavent topics but I am looking for somethat that is challenging, related to economics something like game theory or ...
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266 views

Carrier of a mixed strategy in a 3x3 bimatrix game

We are given a bimatrix game (A,B) = $\begin{bmatrix}0,4 & 4,0 & 5,3\\4,0 & 0,4 & 5,3\\ 3,5 & 3,5 & 6,6 \end{bmatrix}$. Suppose (p, q) is a Nash equilibrium in (A,B). Prove ...
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1answer
57 views

Game theory multiple cooperative adversaries

Are there any papers talking about games with multiple cooperative adversaries? I do research in computer science, and I am interested in this type of game. I am really not that knowledgeable in game ...
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4answers
557 views

Cutting the cake problem if the value measures are not finitely additive

Background I have (rather recently) dabbled in game theory. I need it to design an algorithm to share chores. Obviously this is a kind of cake-cutting problem. So far, I have fought my way through An ...
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2answers
539 views

Mathematical Analysis of the Electoral College

Let us consider the electoral college voting system used to elect the American president. I have a few questions from the point of view of decision-making/gaming theory. My ultimate goal is to vote in ...
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1answer
139 views

Economics: two rival firms in two countries

I am currently working on a paper in macroeconomics, where I found a result that I cannot manage to understand. Since we don't have a macroeconomic site yet, and this is mostly game theory, I will ...
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1answer
82 views

Rough mixed strategy approximation in large zero-sum game

I have a pretty large two-player zero-sum game in which each agent must choose between many actions. I am seeking an algorithm to approximate a mixed strategy for each player. Algorithmic simplicity ...
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1answer
149 views

Nash equilibria in games with infinitely many strategies

As a simple example, suppose two players A and B play a game wherein each picks a positive integer, and if they both pick the same integer $N$ then B pays $f(N)$ dollars to A, for some given payoff ...
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1answer
79 views

Where can I find Game Theory-inspired games?

I like the idea of simple games that give players a lot of flexibility in strategy, like Prisoner's Dilemma, but something people would actually play for fun. So far, I've managed to find Pass the ...
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4answers
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Second Price Auction (Generalized Second Price)

I am trying to find out why we pay second price, but can not understand it. All that I found it is an explanation that it is a real market price, but why it is ? May be some example helps me. For ...
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1answer
131 views

Applications of mathematics to some kinds of sporting strategies

I am a rather newbie maths person. Haven't studied maths in a while and so not sure what things are called was hoping to get some information to push me in the right direction so I know what it is I ...
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149 views

Is there a totally asymmetric 2P $0$-sum game with all payoffs $\pm1$, with a unique Nash eq. which assigns positive probability to each strategy?

Is there a totally asymmetric 2-player zero-sum game with all payoffs $\pm1$, with a unique Nash equilibrium which assigns positive probability to each strategy? By totally asymmetric, I mean that ...
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1answer
516 views

Calculating the Shapley value in a weighted voting game.

Given a special case of WVG (Weighted Voting Game) of $a$ 1s and $b$ 2s and a quota q, $ [q:1,1,1,1..1,2,2,..2] $. I need help with calculating the Shapley value of a player with a weight of $2$ and a ...
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389 views

Nim Variant (Restricted removal)

Alice and Bob play the following game : There are $N$ piles of stones with $S_i$ stones in the $i$th pile. Piles are numbered from 1 to $N$. Alice and Bob play alternately, with Alice starting. In a ...
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1answer
461 views

Nim Variant (reducing by divisors)

Alice and Bob play the following game. They choose a number $N$ to play with. The rules are as follows: Alice plays first, and the two players alternate. In his/her turn, a player can subtract from ...
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2answers
91 views

Is equilibrium selection in zero sum game trivial?

Does a zero sum game always has a unique payoff, whatever the nash equilibrium selected is ? even with mixed strategies ? If so, what is the proof ?
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Do Symmetric Games with Nash Equilibria always have a symmetric Equilbrium?

Define a game with S players to be Symmetric if all players have the same set of options and the payoff of a player depends only on the player's choice and the set of choices of all players. ...
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102 views

How do we prove that e = RPC, in game theory?

Here e is the expected value of the game for the row player, P is the payoff matrix from the perspective of the row player, R is the row matrix containing the probabilities for each of the row ...
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1answer
122 views

proof using (fixed point theorem)

I am seeking to solve for a Nash equilibrium in pure strategies $(d_2,d_2)$ involving two players, $1$ and $2$. Given that $h'(.)$ is s strictly decreasing and continuous function, $\Phi(d_1-d_2)$ ...
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192 views

Two players and two coins

Two players are playing a game. The first player has unlimited gold coins of 2 types, $C_1=2\$$ and $C_2=5\$$. Each turn he chooses one of these coins and hides it in his hand. If the second player ...
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151 views

Seemingly similar but different probability games

Burger King is currently running its "family food" game in which each piece can be modeled as a scratch off game where exactly one of three slots is a winner and you may only scratch one slot as your ...
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1answer
885 views

Finding subgame-perfect Nash equilibrium in the Trust game

I am facing a game theory problem which is as follows: An experiment was designed to study individuals' propensity to be trusting and to be trustworthy in a task called the investment game. In this ...
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2answers
148 views

Question regarding technicalities in the paper Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent

For people on this board I have a probably pretty modest question, but since I'm not a mathematician (just an economist), I'm having trouble. The full pdf can be found here: ...