Questions tagged [differential-games]

Differential Game Theory studies conflict in dynamical systems described by differential equations.

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simultaneous maximization functions for differential games with superlinearity assumption

I'm trying to prove, one of the lemma for the existence of Nash equilibrium, in the notes of Bressan (bressan-non-cooperative differential games). Suppose: 1)for i=1,2 , $U_i\subset\mathbb{R}^m$ ...
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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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How to decouple/ decompose Couple Riccati Differential Equation (CRDE) in LQ differential game?

I have read some papers about differential games. We need to solve coupled Riccati differential equation in continuous-time (Jacob Engwerda, 2005) or discrete-time (Jank and Abou Kandil). In the ...
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1answer
51 views

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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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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63 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 ...
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53 views

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, ...
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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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1answer
244 views

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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1answer
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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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122 views

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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Unit of time and normalization of time preference rates

Consider an infinite horizon cake eating differential game described by \begin{align} &\max_{u_1(t)} \int_0^\infty{e^{-r_1 t}\ln(u_1(t))dt}\\ &\max_{u_2(t)} \int_0^\infty{e^{-r_2 t}\ln(u_2(t))...
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108 views

Bayesian Stackelberg game

Can anybody provide me a little example of bayesian stackelberg game with the solution. I know how to solve Stackelberg game using backward induction but have no idea about bayesian.
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157 views

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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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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Caracterization of optimal strategy in zero-sum 2 players differential stochastic game

Let a $(\Omega,\Sigma,(\mathcal{F_t})_{0\leq t\leq 1},P)$ a probability space where $\Omega$ is the space of continuous functions $f:[0, 1]\rightarrow \mathbb{R}^n$, $(\mathcal{F_t})_{0\leq t\leq 1}$ ...
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Nash Equilibrium in Normal game as a result of learning in Stochastic game

Lets have a Cournot oligopoly model. With two competitors, there is one Nash equilibrium. The thought experiment that can lead us to this result is for example the Tatonnement process, where there are ...
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Question about viscosity solutions to Hamilton-Jacobi-Isaacs equation。

Recently,I am studying differential game, especially two person zero sum differential game. And I am quite confused that why only the value functions defined in terms of non-anticipating strategies(...
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160 views

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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553 views

Fields of Interest in Game Theory for a Mathematics Dissertation

So In my final year of my Undergraduate Degree (Studying Mathematics and Economics) I have decided to focus my Undergraduate project on Game Theory. I have done quite a bit of research, and I get ...
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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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2answers
721 views

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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1answer
308 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 ...
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4answers
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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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4answers
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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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8answers
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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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3answers
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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 ...