SUPERVISOR'S REPORT

ON THE MASTER’S THESIS

Game-theoretic analysis of the Restricted Play principle

by

Gulyaev Nikita Alekseevich

Program: Games theory and operations research 

The research work of Nikita Gulyaev is devoted to the application of game theory methods to solving practical game design problems for computer games. An approach to game structure design and optimization based on the use of the "Restricted Play" principle was investigated. Using the game in normal form as a mathematical basis, Nikita formulated a number of formal criteria for certain conditions imposed on the set of rational strategies of the players, and gave a detailed analysis of both the criteria themselves and the relations between them. 
In order to formalize the requirements imposed on the player's experience of the game, the notion of aspects of the game was introduced. An aspect is defined as a subset of a player's strategies that satisfy certain requirements. A player's game experience is characterized by which set of aspects is (or can be) realized in the course of the game.
The obtained results were applied to a continuous version of the game "Colonel Blotto" in several versions. It was shown that the game had to be modified in a certain way in order for the game process to include the realization of the given aspects. The obtained results were transferred into an algorithmic form, which allows to constructively solving the problem of realization or impossibility of realization of some given aspect. Special software procedure was designed and written in Python 3.9 to corroborate obtained theoretical results and proofs. All results are proofed and presented correctly.
Results of master’s dissertation have been presented at the international conference «Game Theory and Applications». A publication is being prepared on the results of the work.  List of references contains 26 items; the total number of pages is 41 including Appendix. Due to these reasons I suppose that the research work earns an excellent mark (A in ECTS system).

Supervisor								PhD, associated prof.
									Gubar E.A.

24.05.2023