The game-theory tag has no wiki summary.

**4**

votes

**1**answer

948 views

### Finding the Nash Equilibrium of $0-1$ poker with one betting round

While working on a hobby project I encountered a difficult math problem. Or at least, difficult for me. Here is the problem:
Given an $a > 0$, find all pairs of a value $λ \in [0,1]$ and a ...

**5**

votes

**1**answer

354 views

### Resources-Aware Combinatorial Game Theory

First of all, I preemptively apologize if my question happens to be naive, I am no expert of CGT (or general game theory, for that matter).
Now the question:
**is there such a thing as the study of ...

**9**

votes

**3**answers

436 views

### Representing a real number as the value of a countably infinite game

Is it true that for any real number $p$ between 0 and 1, there exist finite or infinite sequences $x_m$ and $y_n$ of positive real numbers, and a finite or infinite matrix of numbers $\varphi_{mn}$ ...

**13**

votes

**0**answers

425 views

### The multiplication game on the free group

Fix $W\subseteq\mathbb F_2$ and consider the following two-person game: Player 1 and Player 2 simultaneously choose $x$ and $y$ in $\mathbb F_2$. The first player wins, say one dollar, iff $xy\in W$. ...

**6**

votes

**1**answer

408 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

**2**answers

571 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

**3**answers

881 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

**0**answers

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

**2**answers

314 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

**0**answers

656 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

**2**answers

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

**3**answers

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

**1**answer

506 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

**2**answers

547 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

**1**answer

670 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

**1**answer

739 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

**1**answer

583 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

**1**answer

597 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

**5**answers

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

**2**answers

382 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

**0**answers

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

**2**answers

932 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

**2**answers

352 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

**1**answer

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 ...

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votes

**9**answers

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 ...

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votes

**2**answers

528 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 ...

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votes

**0**answers

367 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

**1**answer

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

**0**answers

738 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.
...

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votes

**2**answers

623 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

**2**answers

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

**1**answer

498 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

**1**answer

464 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

**1**answer

770 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**

votes

**3**answers

957 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

**1**answer

343 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

**6**answers

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

**1**answer

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

**2**answers

605 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

**2**answers

478 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 ...

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votes

**5**answers

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

**5**answers

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

**4**answers

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

**1**answer

701 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

**1**answer

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

**2**answers

687 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 ...

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votes

**2**answers

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 ...

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vote

**2**answers

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 ...

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votes

**50**answers

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 ...

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votes

**3**answers

949 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 ...