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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Repeated games with random time horizon (?# of turns per repeated game)
Searching for a subfield of game theory related to repeated games and games with random time horizons.
Specifically:
Multiple, repeated games
Each game of some finite, yet unknown length to 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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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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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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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:
$$\begin{cases}
x_{k+1} = x_{k} - \eta \nabla_{x} g(x_{k}, y_{k}) \\
y_{k+1} = y_{k} + \eta \nabla_{y} g(x_{k+1}, y_{k})
\end{...
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Upper and Lower Games in Zero-Sum Games
I am working on some theory related to controls in the context of stochastic games, and I am a bit confused on some terminologies for zero-sum games.
Suppose we have a zero-sum game with two players.
...
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1
answer
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Do hybrid games exist?
I'm new to game theory. So far, I know that we have games with finite strategy sets and games with continuous strategy sets. I was wondering if there are any games in which some players have finite ...
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Lion and Rabbit in a Cage — references
I am looking for references to a problem with the following approximate statement:
There is a lion and a rabbit in cage $C$. At the initial time they are at locations $I_l$ and $I_r$, they have ...
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Can one solve a mean field game numerically with a finite number of players?
I am analyzing the following problem: given a set of players $x^i_t$
for $i=1,\dots,N$ satisfying the SDE
$$
dx^i_t = \alpha^i_t dt + \sigma dW^i_t
$$
where $W^i_t$ are independent Brownian Motions, ...
- 107
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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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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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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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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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