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6
votes
1answer
406 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
567 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
856 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
186 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
311 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
641 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
372 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
504 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
543 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
662 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
736 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
557 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
574 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
380 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
916 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
348 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
276 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
526 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
365 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
305 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
733 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
612 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
497 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
458 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
758 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 ?
14
votes
3answers
944 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
342 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
604 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
477 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
696 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 ...
5
votes
2answers
686 views

Is perfect play possible in continuous rock-paper-scissors? game “step size” vs. “acceleration”

The first part of my question is simple: Is every game continuous in time and strategy-space also a game of perfect information with a good equilibrium? For example, consider rock-paper-scissors. The ...
16
votes
2answers
6k 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 ...
1
vote
2answers
243 views

How to assign a score to items based on a set of partial rankings

I have the following setup: There is a collection of items I and a collection of partial rankings V. That is, an element of V is a total ordering on a subset of I. There is no expectation of ...
62
votes
50answers
17k views

Which popular games are the most mathematical?

I consider a game to be mathematical if there is interesting mathematics (to a mathematician) involved in the game's structure, optimal strategies, practical strategies, analysis of the game ...
8
votes
3answers
946 views

Weighted Regular Graphs

The following graph theoretic notion appeared in an economics paper entitled: "Prize competition under limited comparability, by Michele Piccione and Ran Spiegler which studies models of economics ...
2
votes
1answer
826 views

About the Shannon Switching Game

I was playing around with the Shannon Switching Game for some planar graphs, trying to get some intuition for the strategy, when I noticed a pattern. Since I only played on planar graphs, I'll ...
0
votes
1answer
2k views

Baccarat and the way to win it [closed]

Recently, A friend of mine tell me something about "Baccarat"--a hot game of gambling.and he want to know some way to play it that can win more money. and he guess that math can help to do this. But I ...
46
votes
9answers
7k views

Does War have infinite expected length?

My question concerns the (completely deterministic) card game known as War, played by seven-year-olds everywhere, such as my son Horatio, and sometimes also by others, such as their fathers. The ...
22
votes
2answers
1k views

Five Front Battle

Two generals are fighting a five front battle. Each general has 1 unit of army, which he divides into five separate armies that he sends to the five fronts. If one general sends more army to a front ...