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- All Subjects: Markov Decision Processes
- Creators: Shakkottai, Srinivas
- Resource Type: Text
Description
The seminal work of Lasry and Lion showed the existence of Nash equilibria in thecontinuum limit of agents who try to optimize their own utility functions. However,
a lot of work in this region is predicated on strong assumptions on the asymptotic
independence of the agents and their homogeneity. This work explores the existence
of Equilibria under the limit for Markov Decision Processes for density dependent
continuous time Markov chains. Under suitable conditions it is possible to show
that the empirical measure of the agents converges in finite time to a time invariant
distribution which makes the solution of the MDP tractable. This key step allows
one to show not only the existence of equilibria for these MDPs without asymptotic
independence but also a tractable means to find said equilibria. Finally, this work
shows that a fixed point does exist in the in finite state limit. However, to show that
such a limit is indeed a Nash equilibrium remains an open problem.
ContributorsNarasimha, Dheeraj (Author) / Ying, Lei (Thesis advisor) / Dasarathy, Gautam (Thesis advisor) / Liu, Yongmin (Committee member) / Shakkottai, Srinivas (Committee member) / Arizona State University (Publisher)
Created2021