Games with distorted information and self-verification of beliefs with applications to financial markets

In the paper we examine discrete time dynamic games in which theglobal state variable changes in response to a certain function of the profile ofplayers’ decisions, called statistic, while the players form some expectations aboutits future values based on the history. Besides, there are also players’ private statevariables.A general model is built, encompassing both games with finitely many players aswell as games with infinitely many players. This model extends the class of gameswith distorted information considered by the author in [20], in which there wereno private state variables and there were much stronger assumptions about thestatistic of players’ decisions considered. The notions of pre-belief distorted Nashequilibrium (pre-BDNE), self-verification and belief distorted Nash equilibrium(BDNE), defined already in [20], are applied to our wider class of games. Therelations between Nash equilibria, pre-BDNE and BDNE are examined as well asthe existence and properties of pre-BDNE.A model of a financial market – a simplified stock exchange – is presented as anexample. Pre-BDNE using threshold prices are proposed. One of further resultsin this example is potential self-verification of fundamental beliefs and beliefs ininfinite speculative bubbles