Differential Game Theory studies conflict in dynamical systems described by differential equations.
Questions tagged [differential-games]
36 questions
30
votes
4 answers
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 diameter of the circle (you are on opposite sides of…
Sasha
- 403
23
votes
4 answers
Does Tom catch Jerry?
Tom has Jerry backed against a wall. Tom is distance 1 away (perpendicularly). At time t=0, Jerry runs along the wall. Tom runs directly towards Jerry. Tom always runs directly towards Jerry. Tom and Jerry both run at the same speed.
Does Tom catch…
Colonel Panic
- 1,212
22
votes
8 answers
A lady and a monster
A famous problem:
A lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of the lady is to come to the ground without…
SBF
- 36,568
21
votes
2 answers
Escaping from a circle of fat lions.
You are surrounded, by X fat lions equally spaced around a circle of radius 200 meters in an open field. While making your escape plan you note several things: they are slow, they can only travel at one tenth of your speed, they are stupid,
they…
mtheorylord
- 4,340
17
votes
3 answers
Chased by a lion and other pursuit-evasion problems
I am looking for a reference (book or article) that poses a problem that seems to be a classic, in that I've heard it posed many times, but that I've never seen written anywhere: that of the possibility of a man in a circular pen with a lion, each…
Jamie Banks
- 13,410
14
votes
2 answers
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 other's positions. Wolf speed is $1$ and sheep…
Eric
- 1,919
9
votes
1 answer
Meaningful connections between game theory and differential geometry
I'm a 3rd year undergrad in mathematics who has recently developed a burgeoning interest in differential geometry. I'm also quite interested in dynamical systems and game theory, both of which are heavily employed in my research.
Are there any…
Argent
- 141
8
votes
1 answer
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 which is determined to eat you. The lions start at a…
Ovi
- 24,817
6
votes
0 answers
Pursuit-evasion game with n pursuers and one evader
Assume $n$ pursuers ($P_i$) at the vertices of an $n$ sided regular polygon with
the evader ($E$) at the centre. For what all $n$ can be the evader be caught?
Pursuers and evader have same speed
For $n≥3$, pursuers win. Consider the case with…
ghosts_in_the_code
- 2,062
4
votes
0 answers
System of quadratic autonomous ODEs - convexity of the solution curve
Crossposted on MathOverflow
Problem:
For a given parameter $a>0$, consider the following autonomous system of ODEs for $(x,y,z): \mathbb R_+\to [0,1)^3$:
\begin{align*}
\dot{x}_t &= (1-x_t) (z_t-x_ty_t)
&=:F^x(x_t,y_t,z_t) \\
\dot{y}_t &= \tfrac 1…
Pavel Kocourek
- 1,648
4
votes
1 answer
Game Theory Reccomendation, Mean Field Theory
I'm about to do a sort of reading course with a mathematics professor wherein I read and teach him about Game Theory. He claims not to know Game Theory. After that, we aim to read about Mean Field Game Theory - and other crossovers of Game Theory…
msm
- 2,876
4
votes
2 answers
Four-Dogs Pursuit
Four dogs start at the corners of square $ABCD$ (labelled anti-clockwise). Running anti-clockwise, the dog starting at $A$ pursues the dog starting at $B$, which pursues the dog starting at $C$, which pursues the dog starting at $D$, which pursues…
D.Master
- 49
3
votes
1 answer
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 to the pollutions $u_i$. Thus, the strategy of a…
Yang
- 74
3
votes
0 answers
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 lower $\underline V(x)$ and upper $\overline V(x)$…
clueless
- 811
2
votes
1 answer
Clarification of Battles of Extinction
I am working through chapter 3 of Rufus Isaacs's work on differential games which is devoted to discrete games. I am stuck trying to understand his section 3.3 Battles of Extinction game where there are 2 players E and P (E tries to maximize, P to…
user35202
- 479