| Research Projects on Dynamic Games Supported by the Russian Fundamental Research Foundation |
Main results (year 1997):
The research connected with the construction of the optimality
principles that determines a unique outcome of n-person extensive
game was continued. The solution named
"type-equilibrium" is based on the concept of players'
types (which characterise a system of players' preferences) and
on the level of players' knowledge about their opponents' types.
In general case type-equilibrium (TE) does not coincide with
Nash equilibrium (NE) but it is one of the NE generalisations as
soon as the TE strategy of player i maximises the mathematical
expectation of her payoff with respect to her level of knowledge.
For the extensive games with perfect information the uniqueness
(in payoff sense), the time consistency and some others desirable
properties of TE were proved, and the appropriate backwards
induction procedure for the TE construction was offered.
To investigate the dynamic model of air pollution we have used
the multistage "supergame" construction that accounts
the possibility of players to change their behaviour from
cooperative to non-cooperative one (and inversely) during the
dynamic game evolution. The dynamic payoffs distribution
procedures (PDP) that lead to the cooperative interaction which
is better for all players than some non-cooperative NE were
offered. If we consider PDP as the strategy in supergame, the
offered PDP is proved to be NE in the supergame. Such type of
players' behaviour in dynamic game has some advantages of
cooperative and non-cooperative approaches.
In a case of time inconsistency of agreeable solutions in
n-person differential games we have used new regularization
approach based on some expansion of Pareto optimal set. The
existence of time consistent agreeable solutions was also proved.
The NE refinements and some new selectors of the core that
satisfy the properties of time consistency, coalition stability
and consistency (in reduced games) were offered. In addition the
NE in mixed strategies was constructed for the game-theoretic
model of multistage auction.
Main publications:
Project leader:
Petrosjan Leon Aganesovich Title:
Equilibrium solutions in dynamic games Project number:
96-01-00398 (1996-1998) Organization:
Saint-Petersburg State University
Petrosjan L.A., Zakharov V.V.
Petrosjan L.A., Kuzutin D.V.
Petrosjan L.A., Savishenko N.I.
Design by Usenko V.
Usenko.ru
© 1997-2012 ISDGRus.