Questions tagged [differential-games]
Differential Game Theory studies conflict in dynamical systems described by differential equations.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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
...
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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) (...
- 1,590
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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 ...
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Four-Dogs Pursuit [closed]
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 ...
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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 ...
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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 ...
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Clarification of notation used in differential games
I'm working through Rufus Isaacs's work on differential games and I need clarification on the notation used. Some context: The Value of the game is to be the minmax of the payoff which symbolically is ...
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