Signalling

1. Signalling Often a player wants to convey his private information to other players. It might be information about his own payoffs (“My costs are low, so I can profitably undercut your price”) or about another player’s (“If you hire me, your payoffs will be high because I am so hard-working”) A SIGNAL is an action that a player takes to credibly convey to other players some information that he has but they do not. For the signal to work, it must be more costly if the player is a liar than if he is telling the truth. Also, it must not be too costly for the truthful player, or he will prefer to keep his information private.

2. Definitions Suppose there are two types of sellers, good (high quality) and bad (low quality). A particular seller shows up in front of a buyer. ADVERSE SELECTION. The good type of seller leaves the market to sell somewhere else where his quality can get a higher price. The bad type remains in this market. SIGNALLING. The good type of seller demonstrates his type by doing something (the signal) too costly for the bad type to want to imitate. SCREENING. The buyer offers to pay the seller more if the seller does something (the signal) too costly for the bad type to want to do.

3. Game Trees

4. Education As Signalling • Nature chooses 60 percent of workers to have High ability, with marginal products of 200, and 40 percent to have low ability, with marginal products of 100. • Each worker chooses whether or not to get a diploma. The diploma costs 120 for the low-ability type, and 60 for the high- ability type. • Employers compete with each other to hire workers. They cannot observe ability directly. They chooses wages of N for workers without a diploma and D for workers with a diploma. This is an example from John Macmillan's book, Games, Strategies, and Managers.

5. A Separating Equilibrium • Low-ability workers choose not to get diplomas. • High-ability workers choose to get diplomas. • Employers offer N = 100 and D=200. • Payoff(High, Diploma) = 200 -60 = 140. • Payoff(High, No Diploma) = 100 -0 = 100. • Payoff(Low, Diploma) = 200 -120 = 80. • Payoff(Low, No Diploma) = 100 -0 = 100. • Employers all earn zero profits. (If one employer could get more productivity from workers, then that firm would hire all the workers at the equilibrium wages and make positive profits.) • This is an example from John Macmillan's book, Games, Strategies, and Managers.

6. A Pooling Equilibrium • Low-ability workers choose not to get diplomas. • High-ability workers choose not to get diplomas. • Employers offer N = 160 and D=160. Payoff(High, Diploma) = 160 -60 = 100. Payoff(High, No Diploma) = 160 -0 = 160. Payoff(Low, Diploma) = 160 -120 = 40. Payoff(Low, No Diploma) = 160 -0 = 160. • Employers all earn zero profits. (If one employer could get more productivity from workers, then that firm would hire all the workers at the equilibrium wages and make positive profits.) • (Note that D=200 would still maintain the equilibrium) • There is no high-signal pooling equilibrium in this game. • This is an example from John Macmillan's book, Games, Strategies, and Managers.

7. SCREENING • Suppose we keep everything the same, except we say that the cost of the diploma is 30 for the high-ability workers and 120 for the low-ability. • There is still a pooling equilibrium in which neither type of worker acquires a diploma, and the wages are N=D=160; and a separating equilibrium in which HIGHs get diplomas, LOWs do not, and N=200, D=100. • Suppose we start in the pooling equilibrium of the signalling game, but one employer is allowed to move first, offering an (N,D) pair. If that employer offers N=100 and D=195, he will attract all the HIGH workers, who will get diplomas, and none of the LOW workers. • In this SCREENING game, in which one or more employers move before the workers decide whether to acquire diplomas, the separating equilibrium is the only equilibrium.

8. Education Story Lessons • Not being able to distinguish different types of workers results in adverse selection. • Signalling can result in a separating equilibrium in which high ability workers are paid more, but must pay for a costly signal. • It is essential that the signal be costlier for the low-ability worker than for the high-ability worker. Otherwise, signalling will fail. • If nobody expects signalling to work, it won't. No worker will acquire education, and that will be self-confirming, because no employer will want to pay workers with diplomas a higher wage. All workers will be ``pooled'' with the same low wage. • If an employer can move first, before workers make their education decisions, then he may be able to break out of pooling by offering higher wages for educated workers. This is called ``screening''.

9. Strikes as Signals • Suppose all unions like money and job security, and hate strikes, but some hate strikes more than others, because there are two types of unions: • Type 1: Likes Money Best. Risk Loving. High wages are most important, strikes are not so bad. • Type 2: Likes Security Best. Risk -Averse. High wages are not so important, but strikes are very bad.