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### 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 ...

**3**

votes

**1**answer

314 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, ...

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**0**answers

780 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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**2**answers

253 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 ...

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**2**answers

661 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. ...

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**1**answer

534 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 ...

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**2**answers

611 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 ...

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**1**answer

845 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 ?

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**3**answers

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

**1**answer

359 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 ...

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**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 ...

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**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 ...

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votes

**1**answer

290 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

485 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**

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**1**answer

722 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 ...

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**1**answer

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 ...

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**2**answers

696 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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**2**answers

271 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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**3**answers

975 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 ...

**23**

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**2**answers

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 ...

**2**

votes

**1**answer

897 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 ...

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**1**answer

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 ...

**21**

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**1**answer

621 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 ...