Is there any solution for the extension of the Bellman optimality Equation for Markov decision problem while the state and action spaces both are uncountable and bounded and compact?
Do you mean a single-agent decision problem or a game?
For a single-agent DP, the Bellman equation with continuous state spaces and continuous action spaces can be easily solved. The key reference is the book by Stokey and Lucas.
I do not know whether solutions for a game (Markov Perfect Equilibria) exist. I have not seen that but I do not have a sufficient knowledge of that field.
your help was great! Thank you very very much. I don't know how I can say that referencing to this book was a GREAT help.
Good luck with your research project! As you know, dynamic programming is difficult. You may need to use numerical solution methods to solve your DP problem. In that case you may want to look at the book by Judd or the book by Miranda & Fackler.
Thank you so much. I will work on it and try to solve my problem. Thank you for your kindness.
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