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Questions tagged [differential-games]

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

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58 views

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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1answer
24 views

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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1answer
38 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.
2
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1answer
64 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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0answers
49 views

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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1answer
40 views

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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0answers
29 views

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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0answers
36 views

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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1answer
91 views

Reference request - 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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1answer
223 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 ...
14
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2answers
472 views

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
549 views

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 ...
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3answers
840 views

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 ...