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5
votes
2answers
510 views

Gandhi's quote formalized [closed]

Hello, I hope this question is appropriate for Mathoverflow. Gandhi said, "Be the change that you wish to see in the world". I don't understand anything in Game/optimization theory (I don't know ...
1
vote
5answers
862 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 ...
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 ...
1
vote
0answers
182 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 ...
3
votes
1answer
223 views

Indeterminacy of long games

Hello, all, Several months ago I sat in on a seminar on AD+, which was incredibly wonderful even though I could barely follow it at all. AD+ is a technical variant of AD, the axiom of determinacy, ...
4
votes
1answer
969 views

Finding the Nash Equilibrium of $0-1$ poker with one betting round

While working on a hobby project I encountered a difficult math problem. Or at least, difficult for me. Here is the problem: Given an $a > 0$, find all pairs of a value $λ \in [0,1]$ and a ...
5
votes
1answer
356 views

Resources-Aware Combinatorial Game Theory

First of all, I preemptively apologize if my question happens to be naive, I am no expert of CGT (or general game theory, for that matter). Now the question: **is there such a thing as the study of ...
9
votes
3answers
437 views

Representing a real number as the value of a countably infinite game

Is it true that for any real number $p$ between 0 and 1, there exist finite or infinite sequences $x_m$ and $y_n$ of positive real numbers, and a finite or infinite matrix of numbers $\varphi_{mn}$ ...
13
votes
0answers
430 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 $xy\in W$. ...
6
votes
1answer
410 views

Cake-cutting and amenable groups

I recently heard Alan Taylor speak about envy-free fair division and started wondering if questions like these make sense if we replace finitely additive measures with invariant means on amenable ...
5
votes
2answers
571 views

Pursuit-Evasion on a Manifold

I know pursuit-evasion has been studied in many contexts, including on a manifold (e.g., Melikyan, "Geometry of Pursuit-Evasion Games on Two-Dimensional Manifolds"), but I have not seen this version: ...
2
votes
3answers
896 views

Motivation for the Sprague-Grundy theorem

The Sprague-Grundy theorem states that every impartial combinatorial game under the normal play convention is equivalent to a (unique) nimber. What does the equivalence relation thus defined tell us ...
3
votes
0answers
187 views

References for this game

Hello everybody, 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 ...
3
votes
2answers
315 views

Uniqueness of equilibrium from infinite strategies

I took the following game from the Peter Winkler collection (chapter "Games"): Two numbers are chosen independently at random from the uniform distribution on [0,1]. Player A then looks at the ...
1
vote
0answers
670 views

What would be nice open problem in evolutionary game theory ?

Hello, i was trained as a biologist, but have taught myself mathematics to a level that is roughly equivalent to that of a masters degree in math. I decided to try do some phd-research in ...
0
votes
2answers
2k 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 ...
2
votes
3answers
375 views

Why are Nash-Equilibria inside the Simplex S_n unique ?

Hello, i came across a remark that states that nash equilibria inside the simplex S_n are unique. Or stated differently: If there is more then one such equilibrium, then they have to lie on the ...
5
votes
1answer
509 views

Decay of Relative Growth in Conway's Game of Life

Intro The question is about Game of Life. Let us denote the set of points obtained from initial configuration $A$ after $m$ steps as $A(m)$ (we are only interested in finite initial configuration, ...
3
votes
2answers
555 views

Set Cardinality Game - Can a player with numbers in R win over a player with numbers in N as each of them in one turn has to present a new number?

Let there be 2 players, p$\mathbb{N}$ and p$\mathbb{R}$. They are playing the Set Cardinality Game where p$\mathbb{N}$ has to present some number n that has not been used in the game so far by either ...
5
votes
1answer
684 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 ...
6
votes
1answer
743 views

Drawing lines and removing squares - an Alice and Bob game

Thought about the following while in a Complex Analysis lecture: Let there be a $N \times N$ grid of squares and two players $A$ and $B$. First, $A$ needs to draw a line $l$ that needs to intersect ...
4
votes
1answer
617 views

Conditioning on one term of a sum of random variables

Let $\theta$ be normally distributed with mean $\bar \theta$ and variance $s^2$. Let $Z$ be normally distributed with mean $0$ and variance $\sigma^2$, and chosen independently of $\theta$. Define ...
4
votes
1answer
618 views

Are there any interesting connections between game theory and engineering?

I am doing a senior project and it must be based off game theory, but I am having trouble finding any connections to engineering, possibly structural, or architectural, maybe even civil or mechanical. ...
14
votes
5answers
2k views

Irreversible chess

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
8
votes
2answers
386 views

A competitive root finding game

Inspired by a question about bisection I wondered about the following: The are two players X and Y and a moderator Z who knows two (random,independent, uniformly chosen) hidden reals $x$ and $y$ from ...
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 ...
9
votes
2answers
967 views

The duel problem

The following duel problem is due to Ben Polak (maybe there's earlier origin, which I'll be glad to be informed about). The rule is as follows: Two players 1 and 2 start a duel $N$ steps away from ...
3
votes
2answers
355 views

Truel extended to n persons

n players numbered 1~n play a shooting game. Their accuracy rates p1~pn are strictly between 0 and 1, and strictly increases from p1 to pn. This is common knowledge. Before the game starts, the ...
0
votes
1answer
280 views

Zermelo's stone game in 3 dimensional space

Well, first let me make this clear: I'm actually not sure about the background of the game, whether it was really posed (and solved) by Zermelo. But I'll state the game anyway (perhaps someone can ...
10
votes
9answers
2k 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 ...
2
votes
2answers
529 views

Non-measurable sets and Determinacy…

Assume AC. Suppose $X$ is a subset of the irrationals (Baire Space) for which neither player has a winning strategy (i.e. the game $G(\omega, X)$ is not determined). Is $X$ non-measurable in the ...
0
votes
0answers
367 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 ...
3
votes
1answer
307 views

Approximating the maximin value of a zero-sum game

For square matrix $P$, define $$V(P) = \sup_x \inf_y x^T P y^T$$ where $x$ and $y$ lie on the unit $n-1$-simplex. ($P$ is a payoff matrix for a symmetric game, $x$ and $y$ are mixed strategies, ...
5
votes
0answers
747 views

A Fun Game with Coins [closed]

Assume you have a pair number of coins $2n$ with possibly different values, ordered in a line. Let us enumerate the coins as $x_1,x_2,\ldots,x_{2n}$. The coins are not ordered in any particular way. ...
2
votes
2answers
631 views

Games of imperfect information (e.g. Blackwell's games) in Set Theory?

Hello, Intro about standard two player games Gale-Stewart games are the well-known games played by two Players $I$ and $II$, which in turn play natural numbers for infinitely many ($\omega$) steps. ...
6
votes
2answers
251 views

Truthful multi-unit auctions that guarantee selling all items

Suppose an auctioneer has $k$ units for sale. There are $n$ bidders, each of whom are interested in a single good, and have value $v_i$ for it. If bidder $i$ has to pay $p_i$ and gets the good, he ...
1
vote
1answer
512 views

Simple(?) game theory

3 players are playing a game where they get to pick independently without knowing the other players picks one of 2 prizes (A,B) and the payout is (a,b) for the two prizes, divided by how many people ...
1
vote
1answer
468 views

Is there variance in chess? [closed]

Quite a simple question, but can't decide either way. Does the game of chess have mathmatical variance in it? (Like poker does?)
2
votes
1answer
776 views

Applications of Algebraic Geometry in Evolutionary Game Theory

Hello, do you know any papers or books that use algebraic geometry in evolutionary game theory ?
15
votes
3answers
964 views

Fairest way to choose gifts

Suppose that a parent brings home from a trip $2n$ gifts of roughly equal value for his/her two children. The children get to choose one at a time which gifts they want. What is the fairest way to do ...
4
votes
1answer
347 views

Is the convex combination of two potential games a potential game?

My question: is the set of potential games closed under convex combinations? An n player game with action set $A = A_1 \times \ldots \times A_n$ and payoff functions $u_i$ is called an exact ...
12
votes
6answers
1k views

Untrustworthy people picking a random number

Inspired by the party game Mafia, in particular those situations where nobody is clearly innocent or guilty and the group wants to decide on someone random to eliminate. Suppose n people each have ...
4
votes
1answer
287 views

Subsets of sequences of natural numbers vs. strategies under ZFC

This question is related to a previous question of mine: Determinacy interchanging the roles of both players Given any set A of sequences of natural numbers, every strategy (no matter for which ...
3
votes
2answers
605 views

What is the optimal strategy for participants in this situation?

Consider a simplified version of eBay where everyone bids once on an item, nobody sees each-other's bid, and the highest bid wins. This is called a "First-price sealed-bid auction". One day you find ...
3
votes
2answers
481 views

Determinacy interchanging the roles of both players

Let me refer to Jech's "Set Theory" Chap. 33 Determinacy: "With each subset A of $\omega^\omega$ we associate the following game $G_A$, played by two players I and II. First I chooses a natural ...
13
votes
5answers
1k views

Finding the largest integer describable with a string of symbols of predefined length

(This question is motivated by the reading of the article Large numbers and unprovable theorems by Joel Spencer, which can be found at ...
11
votes
5answers
3k views

Guess a number with at most one wrong answer

Consider a game where one player picks an integer number between 1 and 1000 and other has to guess it asking yes/no questions. If the second player always gives correct answers than it's clear that ...
7
votes
4answers
1k views

Infinite games: are they well defined?

It is just my curiosity about this question where we have an infinite game and (according to the answers) winning strategies for both players. I am familiar with terminating games only, and I am ...
11
votes
1answer
706 views

The Worst Possible Winner

First a little background. In racing it is possible for a player to win a tournament without winning a single race, however, how bad can a tournament winner actually be? Can a player win a tournament ...
4
votes
1answer
741 views

Responses from mathematicians concerning Flash trading [closed]

Have there been any responses from the mathematics community regarding flash trading, for example from a game theory or system dynamics point of view? Please answer with personal comments or ...