Two Ph.D dissertations were made on Game Theory at the Faculty of Applied Mathematics in Saint Petersburg State University.

Traditional game theory describes a negotiation by means of arbitrage scheme for normal form games. Further development of this direction is connected also with works of Prof.S.Brams [Brams, 1984; 1988; 1994], and others. This approach is concentrating on modeling of negotiation as a dynamic process and final agreement is considered as a final position of this process. Dynamic process occurs according fixed system of negotiation rules or a negotiation procedure. At this work we discuss another formalization of this idea which allows to analyze n-person games with arbitrary strategy sets.

Let us consider a conflict between several participants which they are solving by negotiation and are establishing an agreement as a result of this negotiation.

Suppose that every participant has some set of possible propositions (strategies) about it's behavior under discussed agreement. Then, a final agreement is a composition of all participants' offers.

Construct a formal as a non zero-sum game G= [I, {Xi}, {Ri}], where I - set of participants (agents), Xi - strategy set of agent i, X - set of possible agreements (profiles in game G) and Ri: - strict preference ordering of profiles for agent i. Assume that every agent is capable to choose its worst profile xi: Ri(xi)>Ri(xi), and the best: xi: Ri(xi)>Ri(xi) for all xi.

Negotiation process is described as follows. Agents are declaring sequentially their offers (strategies). Choosing strategies by all agents defines an agreement which can be fixed. Switch of agent's current strategy (offer) to a new strategy is its strategic move in the party of game. Moving process is defined by corresponding rules of a negotiation scheme.

Negotiation scheme B is a correspondence which for a given game G and profile x0 is setting the only strategic profile. The correspondence is defined by a system of rules.

At this work finite games and games with compact profile sets are considered and three alternative negotiation schemes for such games are constructed. Theorems about negotiation result establishing were proved.

The work is devoted to construction of stable solutions for the game-theoretic models of auctions. A sealed-bid multy-object auctions are modelled as n-person non-zero sum games. Unique mixed Nash equilibrium for two-person (bimatrix and infinite)games has been obtained in certain classes of mixed strategies.

Incomplete information (Bayesian) games of the auctions are considered. Properties of two-players Bayesian game with infinite number of types are investigated. A unique Bayesian equilibrium has been found for the game with finite number of player types.

A model of dynamic auction is proposed. A subgame-perfect equilibrium for the dynamic auction model is constructed.

Design by Usenko V.
Usenko.ru
© 1997-2012 ISDGRus.