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3
votes
2answers
609 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
483 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
6answers
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
715 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
744 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
693 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
261 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 ...
65
votes
50answers
19k 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
964 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
883 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 ...
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 ...
21
votes
1answer
616 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? ...