Final answer:
The Bayesian-Nash Equilibrium incorporates private information and expected utility given beliefs, whereas the Nash Equilibrium assumes common knowledge with no strategies changing unilaterally. Firms can affect market equilibriums and cause market failures by creating positive or negative externalities.
Step-by-step explanation:
The difference between a Bayesian-Nash Equilibrium and a standard Nash Equilibrium lies in the incorporation of private information and beliefs about other players' types in a game. A Nash Equilibrium is a concept within game theory where no player can benefit by unilaterally changing their strategy, given that other players' strategies remain unchanged. It assumes that the players have common knowledge of the game structure and payoffs.
In contrast, a Bayesian-Nash Equilibrium deals with strategic games where players have incomplete information about other players' types, which could be their preferences, utility functions, or available strategies. Each player holds beliefs about the types of the other players, reflected by a probability distribution. Players then maximize their expected utility given their beliefs and the strategies of other players. A player's strategy is a function of their own type and the beliefs about other players' types.
For example, consider an auction where bidders have valuations of an item that are not publicly known (private information). Each bidder makes a bid based on their valuation and their belief about others' valuations. The Nash Equilibrium of this auction would have each bidder placing a bid that reflects their valuation without strategies changing if others' bids are known. However, a Bayesian-Nash Equilibrium takes into account their beliefs about others' valuations and adjusts their bids to maximize their expected utility under uncertainty.
Another clear illustration of these concepts can be seen in the market. The equilibrium price and quantity occur where the market demand meets market supply. Firms can contribute to market failure by creating externalities which are costs or benefits affecting third parties, not directly involved in a transaction. Positive externalities, like vaccines, benefit others, while negative externalities, such as pollution, impose costs on non-participating individuals.