Asymmetric Information 2:post-contract and common values

This case is which buyer and seller knows a common value( not exactly each value, but a correlation to each value). Oil field is one example because oil price is common for all.

Signaling is costly and just a waste, but desirable. For example, price, education, gifts, non-profit, freedom, wages, and so on.

Example1: price and quality signal
Player: seller and quality sensitive customers(S), and quality insensitive customers(I)
Rule: two products: high quality and low quality.
High: cost is 1, value for S is 6, value for I is 5
Low: cost is 3, value for S and I is 4
Outcomes:
1. when quality is known:>efficient???

Example2:Education
Player: productive workers(P), unproductive workers(U)
Rule: P’s productivity is 2, and Us’ is 1. the productivity is privately known and cannot be revealed costlessly. Education shows their productivities. It costs 1/p.
Perfect Bayesian equilibrium which satisfies plausible restriction on out-of-equibrium beliefs.
Outcomes:
P takes education at a cost of 1/2, U takes nothing.

Terms:
Perfect Bayesian Equilibrium:
Bayesian Equilibrium in dynamic games.

Intuitive Creterion:
This is the method to eliminate multiple PBE. If there are deviation to improve payoff, it can be removed if it is Nash Equilibrium.

Pooling Equilibrium:
an equilibrium where senders with different types all choose the same message.

Separating equilibria:
an equilibrium where senders with different types choose different messages.

Example3: Gifts

Player: A and B
Rule: A wants to befriend with B, and it values 1 or 2. B wants to befriend with A only if A’s value is 2. Only A knows his value for friends.
Outcome: A can bring a gift to B.
Even if the gift is worthless for B, A would give the gift because it represents A’s value for friend is 2.

Example4: Effective wages(completely hard to understand…)

Player: employer, worker
Rule: employer has two job; good and bad. Good job’s productivity is qh, and bad one’s is ql. Worker can invest human capital p=qe. Employment is for two periods. In period 1,
Payoff:worker gets w, offered by employer, and in period 2, worker gets βqe where β<1/2(why?)
Outcome: in the least costly separating equilibrium, the employer offers w=o if q=ql, and w=(1-β) β(qh-ql)ql, if q=qh.

Keys:
(i) what is the effort given the worker’s belief about q?
(ii) how much must the good employer type pay to prove qh?