Tpic 6 Key Concepts Flashcards
A game with incomplete (or private) information
Game with private or incomplete information: Some pieces of relevant information are known by some players (private information) but not by others before the game is played. That is, some players do not know the true payoffs or motivation of their opponents.
(A player (uninformed) does not have perfect information about something relevant from the other player (informed). The uninformed player knows that the informed player is going to be of a specific type, but he doesn’t know which type. The uninformed player knows the proportion of different types in the population (distribution of types), but not who belongs to each type.)
Bayesian Games. Types of a player with private information
Bayesian game (Harsanyi): players, sets of strategies, sets of types, a probability distribution on the set of types and the payoff functions of the players (which will depend on actions and types).
A player (uninformed) does not have perfect information about something relevant from the other player (informed).
The uninformed player knows that the informed player is going to be of a specific type, but he doesn’t know which type. The uninformed player knows the proportion of different types in the population (distribution of types), but not who belongs to each type.
Beliefs in sequential games with private information
A BELIEF is a probability distribution over the set of types after observing an action of the player with private information.
Perfect Bayesian Equilibrium (PBE)
A Perfect Bayesian Equilibrium (PBE) is a combination of strategies and beliefs such that:
1. Each player’s strategy is sequentially optimal given the other player’s strategy and given the beliefs (this is the perfect equilibrium requirement).
2. Beliefs are consistent with strategies. The belief function is derived from the informed player’s strategy using Bayes’ rule where possible (that is, after actions that have positive probability in the strategy).
Separating PBE
2 different types of equilibria that might arise: separating equilibria and pooling equilibria.
SEPARATING EQUILIBRIA: Each type of the informed player chooses a different action in the equilibrium strategy.
Therefore, after any of these actions, beliefs would assign probability one to the type who is supposed to choose that particular action –> private information completely disappears.
(So for a separating equilibrium to exist, each type prefers to choose his action, revealing his true type, instead of imitating the action of the other type)
Pooling PBE
2 different types of equilibria that might arise: separating equilibria and pooling equilibria.
POOLING EQUILIBRIA: All types choose the same action in equilibrium. (Therefore, there is no learning at all: after that action, beliefs coincide with the a priori probability distribution)
Adverse selection
Adverse selection occurs when there is asymmetric information between parties leading to inefficient market outcomes. Example: used cars -> high-quality cars sellers are adversely affected by the existence of incomplete information. This is an example of the problem of adverse selection in markets where a product whose quality is private information of one side of the market is exchanged at a unique price. (there are other adverse selection problems caused by assymetric information)
Signalling
When a informed player has “good” information (for himself), the player with private information will try to take actions (signals) that credibly transmit this information: Signalling.
Signalling is about informed good types wanting to reduce the information asymmetry: they want the uninformed part to know they are good
This signal is only credible if it is so costly for the “bad” type that he will never use it even if by doing so convinces the uninformed player that he is the “good” type.
Screening
The uninformed player can use strategies that reduce his informational disadvantage in some situations (for instance, proposing a contract).
Sometimes, it’s the uninformed part the one that can reduce the information asymmetries by providing incentives to the informed player to reveal his type.
