On multilateral incomplete information decision models

Abstract

This paper treats the decision problem related to theobservation of a Markov process by decision makers. The informationdelivered to the players is based on the aggregation of thehigh-frequency data by some functions. Admissible strategies arestopping moments related to the available information. The paymentsare defined by the state at the time of stopping. The players' decision to stop has various effects which depend on the decisionmakers' type. The type β player's stopping decision assignsthe state of the process with chance β, and it offers thisstate to the opponent with probability $1-\beta$. The knowledgeabout the type of the players is not public and in this way, thepayers have also different information. The details of thedescription allow to formulate the problem as a Bayesian game withsets of strategies based on the stopping times. It is an extensionof Dynkin's game related to the observation of a Markov process withthe random assignment mechanism of states to the players. Some examples related to the best choice problem (BCP) are analyzed. MSC (2000) Primary: 90D15; Secondary: 93C30.