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:

• Mathematical Models in Ecology. St-Petersburg Univ. Publ., 1997, 256p.
  Petrosjan L.A., Zakharov V.V.
• Games in Extensive Form: Optimality and Consistency. St-Petersburg Univ. Publ., 1998, 317p.
  Petrosjan L.A., Kuzutin D.V.
• Game-theoretical Model of Air Pollution. St-Petersburg Univ. Publ., 1997, 92p.
  Petrosjan L.A., Savishenko N.I.

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