Bilevel Stochastic Games

Rezsa Gholami
In his thesis Reza Azad Gholami provides the members of a supply channel with an analytic tool to use the uncertain demand data when devising long-term optimal (multi-period) pricing and supply strategies. Photo:
PhD Defense

26 February 2018 10:14

Bilevel Stochastic Games

On Monday 12 March 2018 Reza Azad Gholami will hold a trial lecture on a prescribed topic and defend his thesis for the PhD degree at NHH.

Reza Azad Gholami
Reza Azad Gholami, PhD Candidate at the Department of Business and Management Science, NHH.

Prescribed topic for the trial lecture:

The newsvendor model: State of the art

Trial lecture:

10:15 in Karl Borch, NHH

Title of the thesis:

Essays on Equilibria in Non-autonomous Bilevel Stochastic Games


The main objective of the research presented in the dissertation is to provide the members of a supply channel with an analytic tool to use the uncertain demand data when devising long-term (multi-period) optimal pricing and supply strategies.

The four articles gathered in this dissertation propose general solutions for several variants of the equilibrium problems in a decentralized price-setting supply channel. The channel is to address stochastic and time-dependent demand for a specific commodity. The commodity has a limited lifespan and has to be sold within that limited time.

Economically, the scenarios addressed by these articles are ubiquitous as almost every commodity has a limited lifespan, and, demand for almost every commodity is uncertain.

Market-penetration scenarios in which entrant suppliers try to manipulate demand by offering lower prices in the beginning are among such scenarios. Incurring initial losses that may manipulate the demand and cause higher profits in the future are prescribed by solutions that consider future effects of pricing on demand and profit in a multi-period time scope.

For each scenario addressed within the papers, in a series of constructive theorems, we prove the existence of equilibrium state and provide solution algorithms outlining the procedure to obtain numerical results that constitute the equilibria.
In the first two articles, we consider scenarios in which the channel members are risk-neutral and have to maximize their expected profits through addressing the uncertain demand in a multi-period (possibly infinite) time horizon. Memory properties are embedded within the structure of the uncertain demand such that they carry the effects of pricing history onto the future demand. The resulting equilibria problems, therefore, become highly nested.

We then propose memory-based solution algorithms that decouple the nested equilibria problems and obtain numerical results. We also prove that these equilibria are subgame perfect.

In the third and fourth articles, we make our proposed bi-level optimization algorithms more robust by allowing the downstream member to postpone her decision on price and supply quantity until after observing the uncertain demand signal. In the fourth article, we provide a complete solution to the channel equilibrium problem when the channel members are bound to a buy-back contract.


12:15 in Karl Borch Aud., NHH

Members of the evaluation committee:

Professor Jonas Andersson (leader of the committee), Department of Business and Management Science, NHH

Associate Professor Zhan Pang, City University of Hong Kong

Professor Stein-Erik Fleten, NTNU


Professor Leif K. Sandal (main supervisor), Department of Business and Management Science, NHH

Professor Jan Ubøe, Department of Business and Management Science, NHH


The trial lecture and thesis defence will be open to the public. Copies of the thesis will be available from