“Incentives for Unaware Agents,” E.L. von Thadden & X. Zhao (2012)

There is a paradox that troubles a lot of applications of mechanism design: complete contracts (or, indeed, conditional contracts of any kind!) appear to be quite rare in the real world. One reason for this may be that agents are simply unaware of what they can do, an idea explored by von Thadden and Zhao in this article as well as by Rubinstein and Glazer in a separate 2012 paper in the JPE. I like the opening example in Rubinstein and Glazer:

“I went to a bar and was told it was full. I asked the bar hostess by what time one should arrive in order to get in. She said by 12 PM and that once the bar is full you can only get in if you are meeting a friend who is already inside. So I lied and said that my friend was already inside. Without having been told, I would not have known which of the possible lies to tell in order to get in.”

The contract itself gave the agent the necessary information. If I don’t specify the rule that patrons whose friend is inside are allowed entry, then only those who are aware of that possibility will ask. Of course, some patrons who I do wish to allow in, because their friend actually is inside, won’t know to ask unless I tell them. If the harm to the bar from previously unaware people learning and then lying overwhelms the gain from allowing unaware friends in, then the bar is better off not giving an explicit “contract”. Similar problems occur all the time. There are lots of behavioral explanations (recall the famous Israeli daycare which was said to have primed people into an “economic relationship” state of mind by setting a fine for picking kids up late, leading to more lateness, not less). But the bar story above relies on no behavioral action aside from agents having a default (ask about the friend clause if aware, or don’t ask if unaware) which can be removed if agents are informed about their real possible actions when given a contract.

When all agents are unaware, the tradeoff is simple, as above: I make everyone aware of their true actions if the cost of providing incentive rents is exceeded by the benefit of agents switching to actions I prefer more. Imagine that agents can not clean, partially clean, or fully clean their tools at the end of the workday (giving some stochastic output of cleanliness). They get no direct utility out of cleaning, and indeed get disutility the more time they spend cleaning. If there is no contract, they default to partially cleaning. If there is a contract, then if all cleaning pays the same the agent will exert zero effort and not clean. The only reason I might offer high-powered incentives, then, is if the benefit of getting agents to fully clean their tools exceeds the IC rents I will have to pay them once the contract is in place.

More interesting is the case with aware and unaware agents, when I don’t know which agent is which. The unaware agents gets contracts that pay the same wage no matter what their output, and the aware agents can get high-powered incentives. Solving the contracting problem involves a number of technical difficulties (standard envelope theorem arguments won’t work), but the solution is fairly intuitive. Offer two incomplete wage contracts w(x) and v(x). Let v(x) just fully insure: no matter what the output, the wage is the same. Let w(x) increase with better outputs. Choose the full insurance wage v low enough that the unaware agents’ participation constraint just binds. Then offer just enough rents in w(x) that the aware agents, who can take any action they want, actually take the planner preferred action. Unlike in a standard screening problem, I can manipulate this problem by just telling unaware agents about their possible actions: it turns out that profits only increase by making these agents aware if there are sufficiently few unaware agents in the population.

Some interesting sidenotes. Unawareness is “stable” in the sense that unaware agents will never be told they are unaware, and hence if we played this game for two periods, they would remain unaware. It is not optimal for aware agents to make unaware agents aware, since the aware earn information rents as a result of that unawareness. It is not optimal for the planner to make unaware agents aware: the firm is maximizing total profit, announcements strictly decrease wages of aware agents (by taking their information rents), and don’t change unaware agents rents (they get zero since their wage is always chosen to make their PC bind, as is usual for “low types” in screening problems). Interesting.

2009 working paper (IDEAS). Final version in REStud 2012. The Rubinstein/Glazer paper takes a slightly different tack. Roughly, it says that contract designers can write a codex of rules, where you are accepted if you satisfy all the rules. An agent made aware of the rules can figure out how to lie if it involves only lying about one rule. A patient, for instance, may want a painkiller prescription. He can lie about any (unverifiable) condition, but he is only smart enough to lie once. The question is, which codices are not manipulable?

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