Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

Abstract

In this paper, a new concept of equilibrium in dynamic games with incomplete or distorted information is introduced. In the games considered, players have incomplete information about crucial aspects of the game and formulate beliefs about the probabilities of various future scenarios. The concept of belief distorted Nash equilibrium combines optimization based on given beliefs and self-verification of those beliefs. Existence and equivalence theorems are proven, and this concept is compared to existing ones. Theoretical results are illustrated using several examples: extracting a common renewable resource, a large minority game, and a repeated Prisoner's Dilemma.Keywords Distorted information · Dynamic games · Nash equilibrium · Belief distorted Nash equilibrium (BDNE ) · Self-verification of beliefs

Dynamic Stackelberg duopoly with sticky prices and a myopic follower

“…This encompasses, among many other cases, the asymmetry between a fashion firm and a counterfeiter or, in a slightly different approach, a company with fishing rights and a poacher. The other obvious explanation assumes that the leader is the one who dictates prices and the follower just does not know the pricing rules of the leaderso there is partly a problem with distorted information as in Wiszniewska-Matyszkiel (2016) and Wiszniewska-Matyszkiel (2017).…”

Subjective Equilibria under Beliefs of Exogenous Uncertainty for Dynamic Games

“…Other relevant references include Adlakha et al (2015), Weintraub et al (2011), Wiszniewska-Matyszkiel (2017, Shamma (2012, 2014), Kalai and Lehrer (1995). The notion of equilibrium introduced in Adlakha et al (2015), called stationary equilibrium, is based on the assumption that the players view the population states (which play the role of the environment variables in this paper) as deterministic and constant.…”