[Turkmath:2579] İAS - 20 October 2017 - Naci Saldı, Özyeğin University

[Nihat Gokhan Gogus]

Dear all,

The details of the seminar talk for this week is below. Hope to see you in
İAS.
Gökhan Göğüş

* İAS is supported by Sabancı University

*Speaker: Naci Saldı, Özyeğin University*
*Title: Approximate Nash Equilibria in Mean-Field Games with Discounted
Cost*
*Date: 20 October 2017*
*Time: 15.40*
*Place: Sabancı University, Karaköy Communication Center, Bankalar Caddesi
2, Karaköy 34420, İstanbul*


In this talk, I will present a general theory for discrete-time mean-field
games with discounted infinite-horizon cost. I will cover both perfect
state and partial state information structures. The state space of each
player is a Polish space, and at each time, the players are coupled through
the empirical distribution of their states, which affects both the players
individual costs as well as their state transition probabilities. I will
first discuss the difficulties to be encountered in any attempt to obtain
the exact Nash equilibrium in such dynamic games with decentralized
information, with a finite number of players. The mean-field approach
offers a way out of this difficulty. First focusing on the perfect state
information, and using the solution concept of Markov-Nash equilibrium, I
will show under some mild conditions the existence of a mean-field
equilibrium in the infinite population limit. I will then show that the
policy obtained from the mean-field equilibrium is approximately
Markov-Nash when the number of players is sufficiently large. Following
this, I will turn to the class of discrete-time partially observed
mean-field games. Using the technique of converting the original partially
observed stochastic control problem to a fully observed one on the belief
space and the dynamic programming principle, I will establish the existence
of Nash equilibria under mild technical conditions. I will again show, as
in the perfect state information case, that the mean-field equilibrium
policy, when adopted by each player, forms an approximate Nash equilibrium
for games with sufficiently many players.
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