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 profile of players' 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 finitely many players as well as games with infinitely many players. This model extends the class of games with distorted information considered by the author in , 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-verification and belief distorted Nash equilibrium (BDNE), defined already in , 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 financial market - a simplified stock exchange - is presented as an example. Pre-BDNE using threshold prices are proposed. One of further results in this example is potential self-verification of fundamental beliefs and beliefs in infinite speculative bubbles. (original abstract)
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