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0
votes
1answer
289 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 ...
11
votes
9answers
3k 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 ...
3
votes
2answers
552 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
420 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
320 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
819 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
683 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
255 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
551 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 ...
2
votes
1answer
887 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
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3answers
1k 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
372 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
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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
292 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
614 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
486 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
7answers
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 ...
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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
727 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
748 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
702 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
273 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 ...
70
votes
52answers
22k 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
983 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
921 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
3k 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 ...
49
votes
9answers
8k 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 ...
23
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 ...
21
votes
1answer
627 views

The density hex

Gale famously showed that the determinacy of n-player, n-dimensional Hex is equivalent to the Brouwer fixed point theorem in n dimensions. We can (and Gale does) view this as saying that if you ...
10
votes
12answers
4k 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? ...