Questions tagged [differential-games]
Differential Game Theory studies conflict in dynamical systems described by differential equations.
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Maximizing a function with binary indicators
I am an econ undergrad trying to understand how to maximize this payoff function, which includes binary components. I want to solve this equation using backwards induction, so I want to maximize 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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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) (...
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Do hybrid games exist?
I'm new to game theory. So far, I know that we have games with finite strategy sets and games with continuous strategy sets. I was wondering if there are any games in which some players have finite ...
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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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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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Playing tag with infinitely many friends
All the countably infinitely many guests of Hilbert's Hotel decide to spend the day playing tag in the park. One player is the runner, and all the others are it. The taggers can agree on a strategy ...
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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{...
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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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Upper and Lower Games in Zero-Sum Games
I am working on some theory related to controls in the context of stochastic games, and I am a bit confused on some terminologies for zero-sum games.
Suppose we have a zero-sum game with two players.
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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 Curve Modification
I've been stuck on this problem of Modified pursuit curve, in which the dog chases the cat with a constant acceleration $a$, starting from rest. The cat moves horizontally with a uniform speed of $v_0$...
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Introductory level text for differential games
I am interested in studying differential games by myself. An introductory textbook will be great. For introductory, I mean that the book shall have the definitions to concept and theorem (with proof) ...
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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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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 ...