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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 ...
-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 ...
14
votes
0answers
438 views

The multiplication game on the free group

Fix $W\subseteq\mathbb F_2$ and consider the following two-person game: Player 1 and Player 2 simultaneously choose $x$ and $y$ in $\mathbb F_2$. The first player wins, say one dollar, iff $xy\in W$. ...
8
votes
0answers
2k views

Group Theory, Game Theory, a bit of Philosophy and a post in Tao's blog

I've decided to write this post after reading the incredibly beautiful and highly recomended post by Terence Tao ...
5
votes
0answers
158 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 ...
5
votes
0answers
211 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 ...
4
votes
0answers
349 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 ...
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 ...
4
votes
0answers
238 views

References for this game

I would like to know how the following game is known in the literature and, possibly, to have references for related papers. Description of the game: Fix a space $X$ and two Borel probability ...
3
votes
0answers
101 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 ...
2
votes
0answers
51 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
33 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 ...
1
vote
0answers
252 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, ...
1
vote
0answers
205 views

Allocation game optimal strategy

There are two players, Alice and Bob. There is an initial pool of 100 dollars. Alice proposes an allocation of the dollars (real numbers, not necessarily integers), and Bob can either accept or ...
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 ...
0
votes
0answers
487 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 ...
0
votes
0answers
70 views

Computing maximum point for minimal function of a family of linear functions

Let $x \in S^n $ where $S^n = ${$ [x_1,x_2,...,x_{n+1}]\in \mathbb{R}^{n+1} \mid x \ge 0 , \sum x_i = 1 $} and let $f_i : I^n \to \mathbb{R}$ be a finite $m$-sized family of LINEAR functions such ...
0
votes
0answers
393 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 ...