The tag has no wiki summary.

learn more… | top users | synonyms

2
votes
0answers
64 views

On subset of Deterministic games

Denote strings $u,v$ from $\{0,1\}^n$. Denote concatenated pair $[uv]$. Denote $$[uv]_{1}=\{[uv]\oplus e_i\}_{i=1}^{2n}$$ collection of pairs with Hamming distance $1$ from $[uv]$ string ...
1
vote
0answers
36 views

optimal strategies for 2-player zero-sum games of perfect information

I asked essentially this on math.SE slightly more than 3 days ago, and it hasn't received any answer there. Do finite-state 2-player zero-sum games of perfect information with only win-draw-loss ...
3
votes
0answers
103 views

What mathematical models can analyze and optimize systems based on gossip?

I look for a mathematical model that can accommodate, analyze and suggest optimizations for a system that can be humanly described as people gossiping about stuff. System description: We have a ...
5
votes
0answers
160 views

Applications of a theorem of Debreu

I would like to know how the last theorem in Debreu's paper "Neighboring economic agents" (La Decision 171 (1969): 85-90; reprinted in G. Debreu, Mathematical Economics: Twenty Papers of Gerard Debreu ...
3
votes
2answers
263 views

(linear algebra) - Can a symmetric equilibrium achive higher social-welfare than some equilibrium with the same support?

EDIT: rewritting the question to linear algebra to make it more accessible. Denote by $\Delta([n])$ the set of all probability distributions over $\{1,2,\ldots,n\}$, that is: ...
2
votes
1answer
50 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, ...
1
vote
0answers
253 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
1answer
96 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> ...
15
votes
1answer
702 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 ...
3
votes
2answers
271 views

Graph game minimum vertex degree

Consider the following graph game, given a graph $G=(V,E)$ on $n$ vertices with minimum degree $ >> log(n)$. Players are BR and MA (BR moves first): BR claims an unclaimed edge from $E$, adds ...
7
votes
2answers
188 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 - ...
13
votes
4answers
821 views

Painting $n$ balls from $2n$ balls red, and guessing which ball is red, game

The game Lucy has $2n$ distinct white colored balls numbered $1$ through $2n$. Lucy picks $n$ different balls in any way Lucy likes, and paint them red. Lucy then giftwrap all the balls so that it is ...
9
votes
1answer
285 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 ...
6
votes
1answer
339 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 ...
10
votes
3answers
256 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. ...
5
votes
1answer
112 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) ...
13
votes
1answer
337 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 ...
10
votes
1answer
266 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 ...
-1
votes
1answer
641 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 ...
44
votes
5answers
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 ...
1
vote
0answers
89 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 - ...
2
votes
1answer
192 views

All solutions to a set of integral equations

I would like a better understanding of the set of pairs $(f_1,f_2)$ of functions $[0,1] \times [0,1] \to [0,1]$ which satisfy the following conditions: For all $y \in [0,1]$, $f_1(x,y) \geq ...
2
votes
1answer
112 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 ...
4
votes
1answer
424 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 ...
40
votes
5answers
7k 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 ...
0
votes
0answers
185 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 ...
16
votes
1answer
628 views

Paul Erdős: Determine or estimate the number of maximal triangle-free graphs on n vertices

Among the collections of the open problems of Paul Erdős on the website of Professor Fan Chung, there is one called "number of triangle-free graphs". ...
4
votes
1answer
200 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.
15
votes
6answers
1k 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
1answer
138 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 ...
4
votes
0answers
351 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 ...
17
votes
1answer
565 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 ...
5
votes
0answers
212 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 ...
1
vote
3answers
199 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 ...
4
votes
1answer
171 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 ...
2
votes
1answer
180 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 ...
10
votes
2answers
536 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 ...
5
votes
1answer
476 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 ...
-1
votes
1answer
145 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 ...
2
votes
1answer
165 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 ...
10
votes
2answers
918 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 ...
9
votes
1answer
432 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 ...
19
votes
5answers
574 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 ...
4
votes
0answers
148 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 ...
12
votes
2answers
712 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 ...
15
votes
1answer
488 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 ...
0
votes
2answers
334 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 ...
2
votes
5answers
1k 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, ...
15
votes
2answers
3k 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 ...
0
votes
1answer
203 views

Equilibrium of random zero-sum game,

Hi, How to find, or at least express, the equilibrium of a zero-sum game with an $n*n$ payoff matrix (each player has $n$ strategies) and the payoff of the entry $(i,j)$ is $u(i,j)$. $u$ a random ...