16
votes
1answer
466 views

A Ramsey avoidance game

Consider the following game: Given $K_n$ the complete graph on $n$ vertices, two players take turns coloring its edges. Initially no edges are colored. At his turn a player can color a prevoiusly not ...
12
votes
2answers
667 views

An unfair game involving an odd number of pieces of chocolate

Two greedy chocolate eaters play the following game involving $n$ pieces of chocolate and an additional parameter $\alpha$ with initial value $1$: Each player eats either $\alpha$ pieces of chocolate ...
2
votes
5answers
858 views

Algorithm to solve Sokoban-like game on graphs - move chips from one set of vertices to another

The question is close to the Sokoban game (thanks to Dima Pasechnik !), but a little different in details. Consider a directed graph (multi-graph). Consider some set of marked chips (chip1, ...
0
votes
0answers
396 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 ...
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 ...
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 ...
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
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 ...
11
votes
1answer
695 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 ...
8
votes
3answers
945 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
822 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 ...
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 ...
21
votes
1answer
612 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 ...