## Screening And Signaling Games

## Screening And Signaling Games

# Screening And Signaling Games

An agent with private information who takes a costly action in order to favorably affect the responses of others is “signaling.” A responding agent who precommits to a response that is contingent on the informed agent’s action is “screening.”

In Michael Spence’s seminal paper (1973), a worker signals her value by her choice of education. Firms base their beliefs about a workers’ productivity based on her educational choice and compete for her services. In the simplest case there are two types of worker, with values *v* _{1} and *v* _{2} > *v* _{1}. The cost of achieving an educational credential *z* for a type *t* worker is c_{t} ( *z* ). Spence asked under what conditions it would pay the high value worker to signal by choosing to add to her educational credentials, even in the extreme case in which the education had no direct effect on productivity. Suppose that there is such an education level *z* _{2} selected only by a high-value worker. That is, the equilibrium outcome separates the different types. Given that there is separating, competition by firms results in a wage offer of *v* _{1} for those without the educational credential and a wage offer of *v* _{2} to those with the credential. For this to be an equilibrium, each type of worker must have an incentive to take the anticipated action. Hence the following incentive constraints must be satisfied:

*IC* _{1}:*v* _{1}≥ *v* _{2}-*c* _{1}(z)

*IC* _{2}:*v* _{2}- *c* _{2}(z) ≥ *v* _{1}

Let ** Ź ** be the education level where the first constraint is satisfied with equality and let

**be the education level where the second constraint is satisfied with equality. As long as the high-value worker has a lower cost of education,**

*Ź*

*z**<*

**and any education level**

*Ź**z*

_{2}

**∈**

*[Ź,zŹ]*satisfies the two incentive constraints. Note that a smaller

*z*

_{2}is less costly for the high type. Thus, for Pareto efficient separating, the incentive constraint for the low type is binding.

## APPLICATIONS

From this basic idea a vast applied literature has emerged. In the insurance industry it has been argued that deductibles are used to separate risk classes, because a good risk has a smaller probability of incurring the deductible and hence a smaller cost of signaling. For new products, advertising has been explained as a signal, because if the quality is low, the firm will incur a loss of revenue due to reduced future sales, as consumers experience the good. Similarly, a high introductory price can signal high quality, as long as there are a sufficient number of fully informed consumers.

In the theory of bargaining between a firm and union, the delay between an offer and a counter-offer is a potential signal. Suppose that bargaining with full information leads to agreement over how the pie should be shared. The firm only knows whether revenue will be high or low. The opportunity cost of delay is lower for a low profit firm, so the union is willing to accept that the pie must be smaller and thus accept a lower wage.

Signaling theory has also been used extensively in finance to show how the underpricing of an initial public offering (IPO), the capital structure, and the issue of double-taxed dividends can all be used to signal a firm’s profitability.

In macroeconomic policy analysis it has been argued that a government can credibly signal its commitment to “tough” future economic policy by taking a tough action in the current period. The net cost to taking this action is lower for a government that really does value the future benefits of (for example) a sustained anti-inflationary policy. Similarly, a government can signal its long-term commitment to trade liberalization by taking a tough action in the current period.

## DEVELOPMENT OF THE THEORY

Spence’s original work followed largely in the Walrasian tradition. Michael Rothschild and Joseph Stiglitz (1976) argued for a formal game-theoretic foundation. In their analysis, the uninformed agents move first, making commitments as to how they will respond. That is, the firms make screening offers. They showed that in such a model there may be no Nash equilibrium, and concluded that competitive markets can perform poorly.

More recent theory has focused on signaling games in which the informed agent moves first. Suppose, in the Spence model, that the informed agent believes he will be paid a high wage if and only if he chooses an education of at least *z* _{2} ∈ [*Ź,Ź* ]. Given such beliefs, the two types separate. Because any education level on this interval will suffice, there is now a continuum of Nash separating equilibria. But what beliefs are plausible if the informed agent chooses a smaller education *ž* ? This question is at the heart of a large theoretical literature on refinements of Nash equilibria (Intuitive Criterion, Divinity, Stability). The most popular of these refinements is the Intuitive Criterion of In-Koo Cho and David Kreps (1987). Their basic idea is that an informed agent will take an out-of-equilibrium action when (1) she will be better off if the responders correctly infer her type, and (2) given this belief, all other types prefer their Nash equilibrium action. The efficient separating equilibrium is the unique Nash equilibrium that satisfies this restriction on beliefs. This is readily illustrated. Consider the education levels *z* _{2} and *Ź* *> z* on the interval [*Ź,Ź* ] By construction, a low-value worker is better off earning his true value *v* _{1} than paying for an education at these levels. Thus, by the Intuitive Criterion, a worker choosing zwill be perceived to be high value. Given such beliefs, high value workers have an incentive to choose the less costly education *ž* Arguing in this way, only the Pareto efficient separating Nash equilibrium can satisfy the restrictions on beliefs imposed by the Intuitive Criterion.

**SEE ALSO** *Evolutionary Games; Game Theory; Noncooperative Games*

## BIBLIOGRAPHY

Cho, In-Koo, and David M. Kreps. 1987. Signaling Games and Stable Equilibria. *Quarterly Journal of Economics* 102 (2): 179–222.

Riley, John G. 1979. Informational Equilibrium. *Econometrica* 47 (2): 331–359.

Riley, John G. 2001. Silver Signals: Twenty-Five Years of Screening and Signaling. *Journal of Economic Literature* 39 (2): 432–478.

Rothschild, Michael, and Joseph E. Stiglitz. 1976. Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information. *Quarterly Journal of Economics* 90 (4): 630–649.

Spence, A. Michael. 1973. Job Market Signaling. *Quarterly Journal of Economics* 87 (3): 355–374.

*John G. Riley*