Recently introductory economics has had more topics related to (non-cooperative) game theory and asymmetric information (Bayesian game). It's kind of a good trend but many students might become confused about it because it is somewhat different from what is taught in price theory.
Price(Walrasian) theory and Game(Nash) theory
Needless to say, economics has two branches: price theory and game theory. We can say that game theory has recently dominated economics more than price theory. Equilibrium concept in a game theory is Nash equilibrium, whereas it is Walrasian general equilibrium in a price theory.
Although we use the same theorem of fixed point to prove mathematically the existence of the above two equilibria, these equilibria are quite different.
Some economists have said that price theory looks at the results of market clearing while game theory looks at the processes. However, I don't know the detail of this distinction at present.
Moral hazard and Adverse selection
As a remark, I let you know about the difference between "moral hazard" and "adverse selection":
These problems are very important in a real market economy and are related to asymmetric information and Bayesian game, which means kind of "market failure (or imperfect market)".
Asymmetric information is the case where sellers (the informed party) know the quality of goods and services but buyers (the uninformed party) don't know in the market economy. It leads to a serious economic problem and can be applied to many economic phenomena.
Adverse selection is the case where bad (low-quality) goods are selected as a result of the trade, whereas moral hazard is the case where bad behaviors (laziness) are selected as a result of the trade. In both situations Pareto-optimal outcomes are not realized and should be solved by some mechanisms.
The main examples are lemon model (Akerlof: 1970) , job model (Spence: 1973), and insurance model (Rothschild and Stiglitz: 1976) . These all can be read in QJE and were worth the Nobel prize in economics.
Signaling and Screening
There are two types of model(or game) : a signaling model is the game where the informed party conveys credible information, and a screening model where the uninformed party offers a menu of choices to the informed party and their choices reveal their types.
Payoffs that the players get in these games are determined by actions, messages, and types.
Let U be the uninformed party, I the informed party, and N nature. The timing of signaling is NIU, whereas the timing of screening is UNI or NUI. In a signaling model, informed party⇒uninformed party, whereas in a screening model, the other way around, uninformed party⇒informed party.
Pooling equilibrium and Separating equilibrium
There are two types of equilibrium concept (perfect Bayesian Nash equilibrium:PBNE) : in the case of signaling model, in a pooling equilibrium signaling is unsuccessful and all types choose the same message, while in a separating equilibrium signaling is successful and each type chooses a different message.
In the case of screening model, in a pooling equilibrium screening is unsuccessful and all types choose the same action, while in a separating equilibrium screening is successful and each type chooses a different action.
Principal/Agent problem & Optimal Contract
In a signaling and screening game we have asymmetric information that exists only at the time the contract is signed. The uninformed party (principal: a working mother) gets the informed party(agent: a baby sitter) to behave in a way that is in the uninformed party's interest(a mother wants a baby sitter to take good care of her baby) after signing the contract.
How should we do to get our agents to behave in a way that is in our interest? That's the problem of the Principal/Agent problem, or as known as contract theory. In this problem people make an optimal contract to induce optimal outcomes. Subject to (1) participation constraint and (2) incentive compatibility constraint people optimize their payoff.