Questions tagged [game-theory]

Question 1

How could I prove that Von Neumann solution: its non-emptiness is undecidable for graph games $v_G$ ? This claim would be strange since $v_G$ is a finite object. What about a general characteristic ...

Question 2

From Wikipedia https://en.wikipedia.org/wiki/Rationality#In_various_fields Rationality is a core assumption of game theory: it is assumed that each player chooses rationally based on what is most ...

Question 3

The game of nim is played with two players againts each other ,by removing 1 or many stones from only one pile in each turn from n piles each pile with $n_1,...,n_k$ and a player cannot skip a turn. ...

Question 4

Yesterday I enjoyed some rounds of RISK: Global Domination with a friend from university. It is a long-running in-joke that “True Random” is the cause of winning and losing certain battles. Our ...

Question 5

You have $a$ amber, $b$ bronze, and $c$ crimson colored marbles in your hand, with $a\geq b\geq c$. An exact copy of this set of marbles is in a bag. Every turn, you select a marble from your hand to ...

Question 6

SO the problem definition is: Have X clients talking to a single API and that API has some upper bound, N, on the number of requests it will handle before it shapes i.e. the traffic and takes ten ...

Question 7

I stumbled across an answer about The envelope paradox which states that: Let Player 1 write two different numbers on two slips of paper. Then player 2 draws one of the two slips each with probability ...

Question 8

In the game "Tug of Luck" $n$ coins are tossed. Player A gets the tails and B gets the heads. Thereafter they take turns rolling a die until one player has gotten rid of all their coins and ...

Question 9

We are given two matrices $R^{N \times N}$, each containing unique integers from $0$ to $N^2 - 1$ (except $0$, it does not need to be unique). The $0$ in the matrices will be called $blank$. The task ...

Question 10

Let's consider a two-player finite strategic form game. Suppose $A$ is the payoff matrix for the row player playing mixed strategy $x$, $B$ is the payoff matrix for the column player playing mixed ...

Question 11

Let $N \in \mathbb{N}$. We successively construct permutations $$A=(A_1, \dots, A_N), B = (B_1, \dots, B_N) \quad \in \text{Sym}(\{1, \dots, N\}).$$ At each time step $ 1 \leq n \leq N$, We know $\{...

Question 12

For a positive integer n, a row of n cards is laid out, each showing a random positive integer. A legal move is to remove either the leftmost or rightmost card. Two players, A and B, take turns, with ...

Question 13

In typical Sprague-Grundy, the person making the last move wins (the node with nimber 0 is losing). If we made it so the person who made the last move is losing - like in Misere Nim - what would be ...

Question 14

I have come across this problem which was apparently very famous some years ago, in which a person is placed in front of 3 doors: one of them has a stack of gold behind it, and the other two have ...

Question 15

Suppose we have $8\times8$ grid numbered from $1$ to $64$ starting with top left corner and placing numbers to the right,then going to the second row and so on.In how many ways can you divide the grid ...

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Questions tagged [game-theory]

Von Neumann solution: an undecidability of its non-emptiness [closed]

What is the mathematical definition of rationality in game theory

The Intuition behind the nim game and the XOR?

Finding an exact closed (non-recursive) form formula for the probabilities in a game of Risk

Optimal strategy for combinatorial marble-drawing game

Optimal strategy for clients calling a rate limited API?

Guessing the outcome of a coin toss with a probability greater than 0.5

Limit of mean duration of the game "Tug of Luck"

Finding solution of a Sliding Puzzle of size $N \times N$.

Are all finite games linear programs? Why is my formulation not correct?

Fixed-points-number distribution for strategically chosen permutation

Combinatoric Question on a Card Game, which number of cards does A win?

Misere Sprague-Grundy

Simulating the door-switching problem [duplicate]

Dividing numbered grid into regions with the same sum.

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