In game theory, a Perfect Bayesian Equilibrium (PBE) is a solution with Bayesian probability to a turn-based game with incomplete information. More specifically, it is an equilibrium concept that uses Bayesian updating to describe player behavior in dynamic games with incomplete information.
Perfect Bayesian equilibrium (PBE) strengthens subgame perfection by requiring two elements: (P i(v | h) for all information sets h of player i) In our entry example, firm 1 has only one information set, containing one node. His belief just puts probability 1 on this node.
We define perfect Bayesian Nash equilibrium, and apply it in a sequential bargain-ing model with incomplete information. As in the games with complete information, now we will use a stronger notion of rationality – sequential rationality.
ini-tion of perfect Bayesian equilibrium that meets several goals. First, it constrains only how individual players update beliefs on consecutive information sets—that is, from one informa-tion set to the next one that arises for the same player—thus lending itself
A weak perfect Bayesian equilibrium for this game is that Player 1 chooses L, Player 2 believes that Player 1 chooses L with probability 1, and Player 2 chooses L .
In this chapter, we follow a similar problem and solution but applied to an incomplete information context, that is, some BNEs predict sequentially irrational behavior, so we introduce a solution concept, Perfect Bayesian Equilibrium (PBE), which ensures sequentially rational behavior given players’ beliefs at that point of the game tree.
The concept of Per-fect Bayesian Equilibrium (PBE) addresses this problem. A PBE combines a strategy profile and conditional beliefs that players have about the other players’ types at every information set.