All Questions
Tagged with differential-games optimization
7
questions
14
votes
2
answers
642
views
How will the wolf catch the sheep in minimum time?
In $\mathbb{R}^2$, a wolf is trying to catch two sheep. At time $0$ the wolf's at $(0,0)$ and the sheep are at $(1,0)$. The animals are moving continuously and react instantaneously according to each ...
- 1,919
3
votes
1
answer
128
views
How can I solve following cooperative differential game?
Consider a game-theoretic model of pollution control. There are 2 players join in the game, N = {1, 2}. Each player has an industrial production site. It is assumed
that the production is proportional ...
- 74
1
vote
1
answer
131
views
ODE equivalent to a system of Difference Equations (Discrete to Continuous time)
Consider the following gradient-descent ascent system of equations:
$$\begin{cases}
x_{k+1} = x_{k} - \eta \nabla_{x} g(x_{k}, y_{k}) \\
y_{k+1} = y_{k} + \eta \nabla_{y} g(x_{k+1}, y_{k})
\end{...
- 313
0
votes
0
answers
95
views
Lion and Rabbit in a Cage — references
I am looking for references to a problem with the following approximate statement:
There is a lion and a rabbit in cage $C$. At the initial time they are at locations $I_l$ and $I_r$, they have ...
- 3,702
3
votes
0
answers
116
views
Zero-sum differential game
We consider a zero sum differnetial game.
Let $x \in (0, M] \subset \mathbb R_{++}$ denote the state and $(u,v) \in [0,x]$ the control of player 1 and 2 respectively with $u + v \leq x$.
Denote the ...
- 771
8
votes
1
answer
344
views
Which way should you run from the lions?
This is a fun problem that I saw somewhere on the internet a long time ago:
Suppose you are at the center of an equilateral triangle with side length $s$. At each of its vertices, there is a lion ...
- 23.8k
30
votes
4
answers
2k
views
Run away from lions in a cage
I came across an interesting problem:
There is a round cage and you are in it. Also two lions are in this cage
too. The start position is that the distance between you and both lions is
the ...
- 403