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Informational extensions in the game theory


Author: Novac Ludmila
Degree:doctor of physics and mathematics
Speciality: 01.01.09 - Mathematical cybernetics and operation research
Year:2009
Scientific adviser: Boris Hâncu
doctor, associate professor (docent), Moldova State University
Institution:
Scientific council:

Status

The thesis was presented on the 25 March, 2009
Approved by NCAA on the 18 June, 2009

Abstract

Adobe PDF document – 0.32 Mb / in romanian

Thesis

CZU 519.833

Adobe PDF document 0.62 Mb / in romanian
117 pages

Keywords

non-cooperative informational extended games, two-matrix informational extended games, game in the normal form, players (participants) of the game, set of strategies, payoff functions, payoff matrices, Nash equilibrium, Nash equilibria set, best response sets, outcome of the game, assured outcomes, point-to-set mapping, fixed point of the point-to-set mapping, make-decision problems

Summary

Using the general concept of the informational extended games (IEG) for the non-cooperative games and using some models of informational extended games, we extend the study of non-cooperative informational extended games. The informational extension concept for games has on its basis the assumptions that the participants of the game have possibility to send and to receive (or to guess) some information about the chosen strategies of other participants and about their behaviour.

We construct some types of informational extended games with two and with n players, for which we present the explicit definitions. The main problem which was formulated is to define the conditions of the Nash equilibrium existence for these types of informational extended games, as well as to define some properties which will aid to make some algorithms for determination of Nash equilibria.

We analyze the two-matrix informational extended games (2MIEG), for which we prove that the set of Nash equilibria is nonempty. We state some assertions which give the conditions for which some rows or some columns of the extended matrices of the 2MIEG do not make up Nash equilibria. We state and prove a theorem which follows from these assertions; this theorem gives the conditions of single Nash equilibrium existence for the two-matrix informational extended games. We make some algorithms which determine the Nash equilibria of the two-matrix informational extended games and these algorithms are programmed.

For the non-cooperative informational extended games we state and prove a theorem which gives the sufficient conditions of Nash equilibrium existence (for the games with two and with n players). The proof of these theorems is based on the Kakutani fixed point theorem for the point-to-set mapping and on other important theorems from the functional analysis and topology. We analyze some types of IEG and we prove a theorem which gives the property to extend the Nash equilibria sets. Thus if the amount of the information increases for all participants, then the Nash equilibria sets are larger. This treatment confirms the importance of the information' possession in all circumstances in the case of the make-decision problems and assure the best result.

The theoretical investigations in the thesis are done, in a large measure, to indicate the conditions of optimization for IEG solving. Our aim is to indicate the importance of the information' possession for all make-decision problems and for conflict problem solving. These models can be used in the several situations in various social domains, inclusively in economy, management and political theory.