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 the global state variable changes in response to a certain function of the pro_le of layers' decisions, called statistic, while the players form some expectations about its future values based on the history. Besides, there are also players' private state variables. A general model is built, encompassing both games with _nitely many players as well as games with in_nitely many players. This model extends the class of games with distorted information considered by the author in [20], in which there were no private state variables and there were much stronger assumptions about the statistic of players' decisions considered. The notions of pre-belief distorted Nash equilibrium (pre-BDNE), self-veri_cation and belief distorted Nash equilibrium (BDNE), de_ned already in [20], are applied to our wider class of games. The relations between Nash equilibria, pre-BDNE and BDNE are examined as well as the existence and properties of pre-BDNE. A model of a _nancial market { a simpli_ed stock exchange { is presented as an example. Pre-BDNE using threshold prices are proposed. One of further results in this example is potential self-veri_cation of fundamental beliefs and beliefs in in_nite speculative bubbles.