The game-theory tag has no usage guidance.

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**1**answer

66 views

### Is there always a symmetric “subset equilibrium” for an equilibrium in a symmetric game?

Consider a 2-player symmetric game given by a payoff matrix $A\in [0,1]^{n,n}$ for the row player (i.e. the column player matrix is $A^t$).
Let $s=<s_1,s_2>$ be a (possibly mixed-strategies, ...

**4**

votes

**1**answer

712 views

### Did Nash prove that every game or every symmetric game has a symmetric equilibrium?

Most references seem to state that Nash showed every symmetric game has a symmetric equilibrium point, but as far as I can tell from Nash's paper, he actually showed the much more general statement ...

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vote

**0**answers

288 views

### What is known about multiplayer poker with flop?

I am interested in the following simplified version of poker.
Each player gets a card (for example, either A or B).
Then they bet knowing their own cards (for example, the pot initially has 1 euro, ...

**2**

votes

**1**answer

117 views

### How to find equilibrium of the following game?

I'm looking at the following game:
2 symmetric players $\{A,B\}$, each choose a number $x_a,x_b\in [0,1]$.
The utility of player $A$ is:
$$U_A = \
\begin{cases} p\cdot x_a &\mbox{if } x_a> ...

**16**

votes

**1**answer

797 views

### Removing pawns - the game

Here is a simple game I've invented (if the idea is not fresh, then please let me know):
The game is played on a board.
The board has some (finite) number of lines drawn on it.
A pawn is placed on ...

**10**

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**1**answer

301 views

### Game on the tree [closed]

There's a problem from programming competition which already finished:
http://codeforces.com/contest/458/problem/F
Two weeks already passed but still nobody solved it yet - in fact you can see here ...

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**2**answers

195 views

### Are sums of 0-1 Pareto efficient vectors Pareto efficient?

Does there exist $m,n\ge1$, an $m \times n$ matrix $A$, and a vector $x \in \mathbb{R}^n$ such that:
The entries of $A$ are $\in \{0, 1\}$.
For all pairs of columns $u, v$ of $A$ the entries of $u - ...

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**1**answer

384 views

### Guessing the larger integer: A game-theoretic twist

The starting point for this question is the old chestnut, already discussed on MO, about a game show on which the host has chosen two distinct integers and the contestant gets to reveal one of them at ...

**7**

votes

**1**answer

506 views

### Explicit examples of undetermined games

Suppose we have a game between two players in which they take alternating turns. The game can have finite length, length $\omega$ or any transfinite number of steps (however, I'm not concerning games ...

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**1**answer

124 views

### What is the (mixed strategies) equilibrium of this game?

Given a weight vector $w\in [0,1]^d$ such that $\sum w_i=1$, the game goes as follows:
Two players, $X,Y$ choose strategies $x,y\in [0,1]^d$ such that $\sum x_i = \sum y_i = 1$.
The utility (profit) ...

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**3**answers

325 views

### Limiting probabilities for two-player game drawing random uniform numbers

Consider this simple 2-person game I just made up:
Player A goes gets to draw a uniform U[0,1] number up to X times. At any time, he may either keep his number, or draw a brand new uniform number. ...

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votes

**1**answer

416 views

### Stromquist's 3 knives procedure

(copied from math.SE)
BACKGROUND: A cake has to be divided among 3 people with possibly different tastes, such that each person receives a single connected piece, and no person prefers another person'...

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votes

**1**answer

866 views

### Maximal score for the 2048 game [duplicate]

t's been weeks (months?) since the 2048 game--by Gabriele Cirulli--took Internet by storm. I have an explicit integer $X$ which is greater or equal than any score of this game. Possibly my $X$ is the ...

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votes

**5**answers

3k views

### Escape the zombie apocalypse

Consider zombies placed uniformly at random over $\mathbb{R}^2$ with asymptotic density $\mu$ zombies/area. You are placed at a random point and can move with speed $1$. Zombies move with speed $v\leq ...

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votes

**0**answers

98 views

### Mean Capture time for the Rabbit-Hunter paper by Peres et al [closed]

I am a non-math student. I am trying to read the paper "Hunter, Cauchy Rabbit, and Optimal Kakeya Sets" by Yuval Peres et al.
Link - http://arxiv.org/abs/1207.6389
In his video based on the paper - ...

**17**

votes

**1**answer

671 views

### A Ramsey avoidance game

Consider the following game: Given $K_n$ the complete graph on $n$ vertices, two players take turns coloring its edges. Initially no edges are colored. At his turn a player can color a prevoiusly not ...

**2**

votes

**1**answer

163 views

### QBF of exponential length?

We consider a slightly extended version of a nondeterministic finite automaton, call it a "propositional nondeterministic finite automaton". It is defined as follows. Consider a fixed propositional ...

**42**

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**5**answers

12k views

### Why was John Nash's 1950 Game Theory paper such a big deal?

I'm trying to understand why John Nash's 1950 2-page paper that was published in PNAS was such a big deal. Unless I'm mistaken, the 1928 paper by John von Neumann demonstrated that all n-player non-...

**0**

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**0**answers

211 views

### Game Theory - need references on analysis of particular game

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I was sure that such game has well-known name. But my question on math.stackexchange, where I ...

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**0**answers

432 views

### Proof of Upper bound of price of anarchy in local connection game

I am looking at the work by Fabrikant "On a Network Connection Game" (http://webcourse.cs.technion.ac.il/236620/Spring2005/ho/WCFiles/FLMPS_netDesign.pdf). This work presents a game-theoretic ...

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votes

**1**answer

401 views

### Nash Equilibrium in general graphical game

Any one has any ideas about how to compute the Nash Equilibrium in general graphical game? Especially, when the graph structure is not a tree.

**16**

votes

**5**answers

2k views

### Is a fair lottery possible?

I'm trying to come up with a scheme for a lottery where each individual has roughly the same chance of becoming the winner, regardless of the number of tickets one holds. So no individual should have ...

**1**

vote

**1**answer

143 views

### Optimum control of a probabilistic automaton

Suppose we have a probabilistic automaton and we assign a weight to each state. An "interaction strategy" would be a fixed map from states to inputs. Any interaction strategy could be used to ...

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votes

**2**answers

623 views

### Generalized Sprague-Grundy Theorem

Hey,
I know what is Sprague-Grundy theorem, but I want to know about generalized Sprague-Grundy (GSG) theorem ( which is used for games with cycles ). Apparently there seems to be very less ...

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**9**answers

4k views

### a mathematically rigorous introduction to game theory

I am looking for the best book that contains a mathematically rigorous introduction to game theory. I am a group theorist who has taken a recent interest in game theory, but I'm not sure of the best ...

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votes

**0**answers

568 views

### Coin Toss Probabilities like Penney's Game

Generate a binary number, using coin toss. Until you receive a predefined sequence. What is the probability that the number is a multiple of some k.
For example, the terminating sequence could be '11'...

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votes

**1**answer

167 views

### To what equal constant in the Gibbs lemma

The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is:
Lemma (Gibbs). $f_1,f_2,\ldots,f_n$ be ...

**5**

votes

**1**answer

579 views

### What can be done with computability logic that previous logic systems can't?

I've been reading a lot about computability logic lately and I'm superficially aware that it unifies classical, intuitionistic and linear logics.
What I'm seeking to know is:
Can computability logic ...

**5**

votes

**1**answer

1k views

### Algorithm on winning strategy of Winner (Simplified card game)

Here's an introduction to the ordinary Winner (card game):
http://en.wikipedia.org/wiki/Winner_(card_game)
I'm thinking about a simplification of the game.
** I've copied this problem to cstheory **...

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**0**answers

253 views

### Identification of a curious function

The following question was asked on math.stackexchange, but there were no replies.
During computation of some Shapley values (details below), I encountered the following function:
$$
f\left(\sum_{k \...

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votes

**3**answers

265 views

### Simulating Mixed Nash Equilibria

I have a $N$ person game where each person has a set of $M$ discrete strategies. I know from the theory that at least one mixed strategy Nash Equilibrium exists.
Can someone please tell me how do I ...

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votes

**1**answer

176 views

### How many different states of Nash equilibrium?

So there is this quite well known Prisoner's dilemma where two parties can both defect and cooperate (and get points based on their decisions). In my presently used example I take it that cooperating ...

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votes

**1**answer

327 views

### Optimal auction for risk-averse seller

Consider an auction of a single unit of indivisible good. There are $n$ buyers whose values of the object is drawn independently from the uniform distribution on $[0,1]$. The buyers have interim ...

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**2**answers

786 views

### Is quantum game theory reducible to classical game theory?

Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:
Superposed initial states,
Quantum ...

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votes

**2**answers

7k views

### Lowest Unique Bid

Each of n players simultaneously choose a positive integer, and one of the players who chose [the least number of [the numbers chosen the fewest times of [the numbers chosen at least once]]] is ...

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**3**answers

314 views

### Can we efficiently compute a third Nash Equilibrium, given two?

A finite, two-player, nondegenerate, symmetric game is defined by a nondegenerate $n \times n$ payoff matrix $A$. If player 1 plays strategy $i$ and player 2 plays strategy $j$, then player 1's ...

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**5**answers

612 views

### $n$-in-a-row game on $\mathbb{R}^2$

For integers $n$ such that $\:3< n\:$,$\:$ what is known about the following 2-player game:
Player_1 and Player_2 take turn choosing points on $\mathbb{R}^2$ that were not previously chosen, with ...

**24**

votes

**6**answers

3k views

### I know that you know…

A bit unsure if the following vague question has enough mathematical content to be suitable upon here. In the case, please feel free to close it.
In several circumstances of competition, a particular ...

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**2**answers

1k views

### Is there an equivalent of Heisenberg's uncertainty principle in the decision sciences ?

From memories of a quantum mechanics class and Wikipedia:
In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the ...

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votes

**5**answers

1k views

### Nash Equilibrium of simple betting game [closed]

I'm trying to find the Nash Equilibrium of a simple betting game, and have come up with a very surprising result which I'd like to solicit comment on.
The game is simple: Two players each receive a ...

**2**

votes

**1**answer

188 views

### Non-Constant-Sum Blotto Game for Only 2 Players and 2 Battlefields

In the simplest asymmetric Colonel Blotto game with 2 players, dividing their given Ni soldiers (i=1,2) over 2 battlefields, what are their expected utilities, Ui (i.e., expected number of battlefield ...

**0**

votes

**2**answers

3k views

### Game Theory: Is there a Mixed Strategy Nash Equilibrium?

The game looks like this:
a b
A [(-12, 1) (8, 8)]
B [(15, 1), (8,-1)]
(15, 1) and (8,8) are Nash Equlibria. However, could you still mix ...

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votes

**1**answer

554 views

### M-matrix plus S-matrix is P-matrix?

I am trying to prove that a mapping has a unique fixed-point by showing that its Jacobian is a P-matrix. In this particular case the Jacobian can be decomposed as the sum of two matrices and I would ...

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**3**answers

1k views

### Nim game for odd number of stones

Consider the classical Nim game with total number of stones being odd. Then the first players wins, of course, what follows from the general description of winning positions. But is there some shorter ...

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**2**answers

784 views

### An unfair game involving an odd number of pieces of chocolate

Two greedy chocolate eaters play the following game involving $n$ pieces of chocolate
and an additional parameter $\alpha$ with initial value $1$: Each player eats either $\alpha$
pieces of chocolate ...

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votes

**0**answers

166 views

### Examples of functions from matrices to real numbers with certain properties

Let $M(\mathbb{R})$ be the set of all matrices (of any size) over $\mathbb{R}$. Let $v : M(\mathbb{R}) \rightarrow \mathbb{R}$ be a function which satisfies the following 5 properties:
If $\mathbf{...

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**1**answer

580 views

### The Chow & Robbins game ≈ 0.79295350640: improvements could come from simple statistics, or from a continuous version of the game

This question seeks help with improving a numerical estimate of the value of the Chow and Robbins game. Much about this game is unknown, such as whether its value is rational, but there are two routes ...

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**2**answers

5k views

### Simple proof of the existence of Nash equilibria for 2-person games?

Is there a nice elementary proof of the existence of Nash equilibria for 2-person games?
Here's the theorem I have in mind. Suppose $A$ and $B$ are $m \times n$ matrices of real numbers. Say a ...

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votes

**5**answers

2k views

### Algorithm to solve Sokoban-like game on graphs - move chips from one set of vertices to another

The question is close to the Sokoban game (thanks to Dima Pasechnik !), but a little different in details.
Consider a directed graph (multi-graph). Consider some set of marked chips (chip1, chipe2,......

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**12**answers

5k views

### Are there any interesting connections between Game Theory and Algebraic Topology?

I've been learning game theory on my own and was just curious how it connected with previous things I've learned. So are there any interesting connections between Game Theory and Algebraic Topology? ...