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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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
302 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 ...
2
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1answer
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 ...
2
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2answers
188 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 ...
2
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1answer
229 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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1answer
279 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 ...
32
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1answer
1k 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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0answers
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 ...
3
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1answer
390 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 ...
2
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1answer
613 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 ...
4
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1answer
425 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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2answers
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
400 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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0answers
260 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
53 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
555 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
537 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 ...
2
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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 ...
2
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1answer
81 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 ...
2
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1answer
148 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
2k views

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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0answers
148 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 ...
4
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1answer
501 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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1answer
387 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
458 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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2answers
2k views

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. ...
0
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1answer
96 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 ...
2
votes
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, $\Phi(d_1-d_2)$ ...
4
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2answers
191 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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3answers
149 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
879 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
145 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: ...
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3answers
147 views

Consider a card game-parity

Consider a card game where the deck consists of 63 distinct cards. The deck is created in the following manner: each card consists of some number of symbols, where no two symbols are the same. There ...
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2answers
109 views

Reasonable strategy for simple game

I have a very simple probabilistic process which I have to deal with in the software project I'm involved in, yet I can't figure how to do it. I can describe the situation as a money game (in reality ...
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2answers
741 views

Subgame Perfect Nash Equilibrium

My homework question is summarized below: There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...
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0answers
131 views

Shifted Young tableaux & Hook numbers & Bulgarian Solitaire

I would like to find articles or documentation regarding this process: Starting from what ever integer partition, e.g. 5,2 for the number 7. Construct his Young tableaux and then fill it with Hook ...
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2answers
261 views

Strategy for a game of breaking sticks

Two persons have 2 uniform sticks with equal length which can be cut at any point. Each person will cut the stick into $n$ parts ($n$ is an odd number). And each person's $n$ parts will be permuted ...
3
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2answers
3k views

Winning strategy for a matchstick game

There are $N$ matchsticks at the table. Two players play the game. Rules: (i) A player in his or her turn can pick $a$ or $b$ match sticks. (ii) The player who picks the last matchstick loses the ...
5
votes
1answer
586 views

Iterated prisoners dilemma with discount rate and infinite game averages

Suppose we have two players who are perfectly rational (with their perfect rationality common knowledge) playing a game. On round one both players play in a prisoners dilemma type game. With payoffs ...
5
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1answer
329 views

Olympic Badminton, or How to Design a Tournament

Hearing the recent news about disqualified Badminton players in the ongoing 2012 London Olympics got me wondering about how best to design tournaments to avoid situations where players are ...
7
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2answers
1k views

Simple dice game: Optimal strategy?

Here's the description of a dice game which puzzles me since quite some time (the game comes from a book which offered a quite unsatisfactory solution — but then, its focus was on programming, so this ...
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1answer
1k views

Finding Nash Equilibria with Calculus

The problem is summarized as: There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
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1answer
271 views

How does this game work? (Number game: subtract prime)

Problem Alice and Bob play the following game.They choose a number N to play with.The runs are as follows : 1.Bob plays first and the two players alternate. 2.In his/her turn ,a ...
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2answers
283 views

Submodular and supermodular games

Can someone please explain to me (with concrete examples) what are submodular and supermodular games, and their related concepts of games of strategic substitutes and strategic complements. An ...
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1answer
1k views

Unable to find Nash equilibria in mixed strategies

Here is the strategic form game: Player 2 Left Middle Right Top 2,2 0,0 1,3 Player 1 Middle 1,3 3,0 1,0 ...
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2answers
949 views

Is there a winning strategy for Scrabble?

I am sure many of us are addicted to the popular Facebook app: Words with Friends, which is basically an online version of Scrabble. In Playing Games with Algorithms:Algorithmic Combinatorial Game ...