All Questions
Tagged with game-theory stochastic-processes
11 questions
8
votes
1
answer
585
views
One flip coin game
Nate has $n \geq 2$ coins $\{C_i\}_{0 \leq i \leq n-1}$ that each turn up heads with probability $\frac{i}{n-1}$ each, but he is not sure which ones are which.
He has \$1 with which to bet with. On ...
- 6,205
9
votes
1
answer
257
views
Higher or lower? (#2)
$N \geq 2$ players play a game - at the start of the game, they are each given independently and uniformly a number from $[0, 1]$. On each round, they are to guess whether their number is higher or ...
- 6,205
19
votes
2
answers
2k
views
Higher or lower?
Consider the following game - I draw a number from $[0, 1]$ uniformly, and show it to you. I tell you I am going to draw another $1000$ numbers in sequence, independently and uniformly. Your task is ...
- 6,205
8
votes
1
answer
522
views
One step forward, one step back
$N \geq 2$ players play a cooperative game on the integers $\mathbb Z$. All of them start from $0$. At each turn, they are simultanously given the same yes or no question to answer.
The questions ...
- 6,205
8
votes
2
answers
572
views
Optimally betting a beta-biased coin
This question is inspired by How to optimally bet on a biased coin? by Nate River but generalized slightly. I decided the generalization might be interesting enough to be its own question.
A number $p$...
- 148k
1
vote
1
answer
285
views
Is there an equilibrium for this non-zero-sum game?
The game $G(N,M)$ is played:
$N$ ($N\geq 2$) is the number of players, labeled $1$~$N$. In the beginning they have a pot with some chips in it. Players move alternatively in the order from $1$ to $N$....
- 2,619
3
votes
0
answers
72
views
Random Two-Player Asymmetric Game
About half a year ago I asked a question on MSE about a random two player game. At the time, the question received some attention and some progress was made, but was not resolved completely. I have ...
- 181
1
vote
0
answers
80
views
What is the Bruss-Yor concept of no information?
A few years ago, a question related to a paper of Thomas Bruss and Marc Yor on the so-called last arrival problem received some attention on this forum.
What I'd like to know now is:
What are the ...
- 5,492
1
vote
0
answers
159
views
How to find the equilibrium of the following stochastic game (numerically)
I build up a stochastic game with two groups of players (Group A and Group B) and within each group, the players can have two labels as H and L (label of each player may change from period to period). ...
- 191
4
votes
1
answer
427
views
What's the best betting strategy to double money if we have $\delta$ advantage?
Suppose that I am very skilled in a gambling game, and any day that I bet $x$, I get back $2x$ with probability $\frac 12+\delta$ (and nothing with probability $\frac 12-\delta$). My goal is to double ...
- 18.9k
56
votes
6
answers
5k
views
Escape the zombie apocalypse
Consider zombies placed uniformly at random over $\mathbb{R}^2$ with asymptotic density $\mu$ zombies/area. You are placed at a random point and can move with speed $1$. Zombies move with speed $v\leq ...
- 720