Some problems in discounted stochastic games

This thesis addresses three problems in the theory of iscounted stochastic games, all motivated by the effects of time-dependent dis-counting. First, it investigates the Nash equilibrium of finite stochastic games with generalised discounting. By employing the framework of gener-alised continuous games, it is shown that every finite stochastic game with generalised discounting admits a Nash equilibrium. Moreover, an example is provided to illustrate that a stationary Nash equilibrium does not necessarily exist in these stochastic games. Second, the thesis examines zero-sum stochastic games with sepa-rable discounting. Using the concept of supergames, it is demonstrated that every zero-sum finite stochastic game with separable discounting admits a value. Furthermore, it is established that, under certain conditions, this result can be extended to zero-sum countable stochas-tic games with separable discounting. In addition, three models of zero-sum infinite stochastic games with separable discounting - Borel, Suslin, and Nowak - are considered, and the existence of a value is established for each case. Finally, the thesis investigates finitely additive Markov decision processes under separable and ripple discounting. In the case of sep-arable discounting, it is shown that the player always possesses an optimal Markov strategy. In contrast, under ripple discounting, only the existence of an optimal behavioural strategy can be guaranteed.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

Budapesti Corvinus Egyetem

Year dc:date.issued

2026

Author dc:creator

• Balog, Imre

• Közgazdasági elméletek

Language dc:language

en, hu