The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under (combinatorial-game-theory), and algorithmic aspects (e.g. auctions) are under (algorithmic-game-theory).
12
votes
4answers
773 views
Probability of dice sum just greater than 100
Can someone please guide me to a way by which I can solve the following problem.
There is a die and 2 players. Rolling stops as soon as some exceeds 100(not including 100 itself). Hence you have the ...
12
votes
5answers
803 views
A lady and a monster
A famous problem: a lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of ...
2
votes
2answers
592 views
Winning strategy for a matchstick game
There are $N$ matchsticks at the table. Two players play the game.
Rules:
(i) A player in his or her turn can pick $a$ or $b$ match sticks.
(ii) The player who picks the last matchstick loses the ...
1
vote
0answers
79 views
Shifted Young tableaux & Hook numbers & Bulgarian Solitaire
I would like to find articles or documentation regarding this process:
Starting from what ever integer partition, e.g. 5,2 for the number 7. Construct his Young tableaux and then fill it with Hook ...
5
votes
6answers
3k views
Deal or no deal: does one switch (to avoid a goat)?/ Should deal or no deal be 10 minutes shorter?
Okay so this question reminded me of one my brother asked me a while back about the hit day-time novelty-worn-off-now snoozathon Deal or no deal.
For the uninitiated:
In playing deal or no deal, the ...
3
votes
1answer
58 views
Why the set of outcomes generated by a fixed strategy of one player in Gale-Stewart game is a perfect set?
In the proof that there is a payoff set $X$ such that the Gale-Stewart game is not determined(see here, Proposition 3.1.).
I don't know why $X$, the set of all outcomes generated by a fixed strategy ...
3
votes
1answer
170 views
Game Theory Matching a Deck of Cards
Moderator Note: This question is from a contest which ended 1 Dec 2012.
Suppose we have a deck of cards labeled from $1$ to $52$. Let them be shuffled in a random configuration, then made ...
3
votes
1answer
377 views
Set of rationalizable strategies
Consider a guessing game with ten players, numbered 1 through 10. Simultaneously and independently, the players select integers between 0 and 10. Thus player i's strategy space is $\mathbf{S}_i$ $=$ ...
2
votes
1answer
197 views
Saddle points in zero sum game
We only had one lecture about the subject and already have quite difficult questions, could someone please help me?
The matrix looks something like this:
\begin{matrix}
3 & 2 & 1 & 4 ...
2
votes
1answer
73 views
Name for a certain “product game”
Let $G,H$ be two (combinatorial impartial) games. Consider the following new game $P$: The positions are the pairs of positions of $G$ and $H$. A move in $P$ is a move in $G$, or a move in $H$, or a ...
17
votes
1answer
726 views
Number of moves to solve a flood-it/sock-dye game
[ Question based on the sock dye game ]
[ Update: It appears that this game is better known as "Flood it" and is NP-hard. Also, "the number of moves required to flood the whole board is $\Omega(n)$ ...
16
votes
6answers
1k views
Game theory - self study
I want to self study game theory. Which math-related qualifications should I have? And can you recommend any books? Where do I have to begin?
13
votes
7answers
572 views
Game theory textbooks/lectures/etc
I looking for good books/lecture notes/etc to learn game theory. I do not fear the math, so I'm not looking for a "non-mathematical intro" or something like that. Any suggestions are welcome. Just put ...
6
votes
4answers
239 views
Good non-mathematician book on Game Theory
I'm looking for a good book on Game Theory. I run a software company and from the little I've heard about Game Theory, it seems interesting and potentially useful.
I've looked on Amazon.com but ...
12
votes
3answers
426 views
Best Strategy for a die game
You are allowed to roll a die up to six times. Anytime you stop, you get the dollar amount of the face value of your last roll.
Question: What is the best strategy?
According to my calculation, for ...
9
votes
5answers
231 views
How can the observed strategies* in this actual auction be explained?
This is a "real world" question.
Recently I witnessed the separate auctions of about 30 houses. The place where I went uses the following rules. The following describes the procedure for the ...
7
votes
1answer
264 views
Optimal strategy for slice weighing game
I watched an interesting contest on a Swedish game show the other night. I have tried to find an english name of the contest but haven't found any. Two contestants were each given one large sausage ...
6
votes
1answer
58 views
Invariance of strategy-proof social choice function when peaks are made close from solution
A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428.
The setting is as follows:
A finite set ...
6
votes
1answer
425 views
Number Game: 31 - Winning Strategy?
My Maths teacher taught us how to play a game called 31 on Friday. Not once did my Maths teacher lose. I want to know why.
I'll explain the game...
31 is a game between two people.
Let's say you've ...
3
votes
1answer
239 views
Which side has winning strategy in Go?
Go is actually a finite two-person game of perfect information and cannot end in a draw. Then by Zermelo's theorem, it is exactly one of the two has winning strategy, either Black or White.
So my ...
2
votes
0answers
79 views
What is the (expected) outcome of this hybrid auction?
A certain hybrid auction can be accurately modelled as follows.
There are $n$ risk-neutral, rational participants $i=1,2,\ldots,n$, and a guy called Zerro: $i=0$.
Each, except Zerro, has a private ...
1
vote
1answer
121 views
Understanding common knowledge in logic and game theory
For $k = 2$, it is merely "first-order" knowledge. Each
blue-eyed person knows that there is someone with blue eyes, but each
blue eyed person does ''not'' know that the other blue-eyed person ...
4
votes
2answers
197 views
Game theory Computing pure Nash equilibrium probability
We have a $2$-player game and each player has $n$ strategies. The payoffs for each player are in range $\left[0,1\right]$ and are selected at random.
Show that the probability that this random game ...
3
votes
1answer
324 views
Game about placing pennies on table
This problem is from The Art and Craft of problem solving book:
Consider the following two player game. Each player takes turns placing a penny on the surface of a rectangular table. No penny can ...
3
votes
2answers
293 views
Finding best response function with probabilities (BR) given a normal-matrix representation of the game
We are given players 1, 2 and their respective strategies (U, M, D for player 1, L, C, R for player 2) and the corresponding pay-offs through the following table:
$\begin{matrix}
1|2 & L & C ...
2
votes
2answers
38 views
$n$-player version of Zermelo's Theorem
Zermelo's Theorem states that "Every finite zero-sum 2-player game is determined (one of the two players has a winning strategy)." I was wondering if anyone has investigated the generalization of this ...
2
votes
1answer
181 views
Nim Variant (reducing by divisors)
Alice and Bob play the following game. They choose a number $N$ to play with. The rules are as follows:
Alice plays first, and the two players alternate.
In his/her turn, a player can subtract from ...
1
vote
0answers
113 views
Determine market price and quantities produced; non-cooperative cournot game
$P(Q)$ represents a market where demand $Q$ is related to price $P$ by
$$P(Q) = Q^{-\frac{1}{2}}$$
In this market there are $m$ identical producers, say firm 1, 2, up to $m$ which can
produce any ...
0
votes
2answers
103 views
Nash Equilibrium for the prisoners dilemma when using mixed strategies
Consider the following game matrix
$$
\begin{array}{l|c|c}
& \textbf{S} & \textbf{G} \\ \hline
\textbf{S} & (-2,-2) & (-6, -1) \\ \hline
\textbf{G} & (-1,-6) ...
0
votes
2answers
144 views
GameTheory, Solve for optimal strategies by solving a system of linear equations
In a book on game theory I saw the following example of a game, a modified version of Roshambo (or Rock-paper-scissors), which is described by the following payoff-matrix:
$$
\begin{array}{c|c|c}
...
0
votes
0answers
68 views
Finding all number combination which XOR results to 0
Let's say I have a fixed list of numbers:
$2, 3, 1, 2$
and I can reduce every number from $n$ to $0$, for instance: $1,3,1,2$ or $0,3,0,1$ etc.
I am looking for all combinations of this sort, where ...
0
votes
1answer
118 views
Nim Variant (Restricted removal)
Alice and Bob play the following game : There are $N$ piles of stones with $S_i$ stones in the $i$th pile. Piles are numbered from 1 to $N$. Alice and Bob play alternately, with Alice starting. In a ...
0
votes
1answer
152 views
Given a victory condition and a set strategy, what are the chances of winning on a given turn in a game of Magic: The Gathering?
Tl;DR: You have winning cards. To win, you must be able to play those cards, and have them in your hand. Your hand is randomly drawn. When might you win? How could find the answer to this (very ...
0
votes
0answers
117 views
Extension of lady and monster
A famous problem: a lady is in the center of the circle lake, the monster is on the boundary of the lake. The speed of the monster is $v_m$, of swimming lady - $v_l$. The goal of the lady is to come ...
-4
votes
1answer
232 views
Nash equilibria and best response functions
a) Let $G=(A,u)$ be a strategic game such that, for each $i \in N$
$A_i$ is a nonempty, convex, compact subset of $R^{m_i}$
$u_i$ is continuous
For each $a_{-i}$, $u_i(a_{-i}, . )$ is quasi-concave ...
