What is a perfect Bayesian Nash equilibrium?

In game theory, a Perfect Bayesian Equilibrium (PBE) is an equilibrium concept relevant for dynamic games with incomplete information (sequential Bayesian games). Formally, a belief system is an assignment of probabilities to every node in the game such that the sum of probabilities in any information set is 1.

What is sequential rationality in game theory?

Given a player’s beliefs, we can define sequential rationality: Definition 1 A player is said to be sequentially rational iff, at each information set he. is to move, he maximizes his expected utility given his beliefs at the information set (and.

What is the difference between incomplete and imperfect information?

Incomplete Information means there are things you simply don’t know, such as the opponent’s strategies or payoffs. Imperfect Information means you won’t know when or if an opponent makes a move.

What is weak sequential equilibrium?

Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. Whereas Weak Sequential Equilibria (sometimes referred to as Weak Perfect Bayesian) also necessitates sequential rationality, but has a weaker consistency requirement,which is my main source of confusion.

What is a weak sequential equilibrium?

What is an equilibrium path of play?

A perfect Bayesian equilibrium (PBE) is a specification of players’ strategies and beliefs about which node in the information set has been reached by the play of the game. A belief about a decision node is the probability that a particular player thinks that node is or will be in play (on the equilibrium path).

What are the difference between perfect information and imperfect information?

Perfect information refers to the fact that each player has the same information that would be available at the end of the game. Imperfect information appears when decisions have to be made simultaneously, and players need to balance all possible outcomes when making a decision.

What is the difference between complete and perfect information?

Games with complete information generally require one player to outwit the other by forcing them to make risky assumptions. Games with perfect information generally require one player to outwit the other by making them misinterpret one’s decisions.