Nonzero-sum Risk-sensitive Stochastic Games on a Countable State Space
نویسندگان
چکیده
The infinite horizon risk-sensitive discounted-cost and ergodic-cost nonzero-sum stochastic games for controlled Markov chains with countably many states are analyzed. For the discounted-cost game, we prove the existence of Nash equilibrium strategies in the class of Markov strategies under fairly general conditions. Under an additional geometric ergodicity condition and a small cost criterion, the existence of Nash equilibrium strategies in the class of stationary Markov strategies is proved for the ergodic-cost game.
منابع مشابه
On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points
A new class of nonzero-sum Borel state space discounted stochastic games having stationary Nash equilibria is presented. Some applications to economic theory are also included.
متن کاملWeighted Discounted Stochastic Games with Perfect Information
We consider a two-person zero-sum stochastic game with an innnite time horizon. The payoo is a linear combination of expected total discounted rewards with diierent discount factors. For a model with a countable state space and compact action sets, we characterize the set of persistently optimal (sub-game perfect) policies. For a model with nite state and action sets and with perfect informatio...
متن کاملN–person Stochastic Games: Extensions of the Finite State Space Case and Correlation
In this chapter, we present a framework for m-person stochastic games with an infinite state space. Our main purpose is to present a correlated equilibrium theorem proved by Nowak and Raghavan [42] for discounted stochastic games with a measurable state space, where the correlation of the different players’ strategies employs only “public signals” [16]. We will also provide a detailed survey of...
متن کاملA reinforcement learning approach to stochastic business games
The Internet revolution has resulted in increased competition among providers of goods and services to lure customers by tearing down the barriers of time and distance. For example, a home buyer shopping for a mortgage loan through the Internet is now a potential customer for a large number of lending institutions throughout the world. The lenders (players, in generic game theory nomenclature) ...
متن کاملStochastic Differential Games and Intricacy of Information Structures
This paper discusses, in both continuous time and discrete time, the issue of certainty equivalence in two-player zero-sum stochastic differential/dynamic games when the players have access to state information through a common noisy measurement channel. For the discrete-time case, the channel is also allowed to fail sporadically according to an independent Bernoulli process, leading to intermi...
متن کامل