Roger B. Myerson Prize Lecture

328

(y=20, q=5/6)

Seller

’

s value

$20 [s]

$100 [w]

EU(str)=$0

[s]

$80

0, *

5/6, $80

EU(wk)=$33.33

[w]

$0

5/6, $20

1, $50

 P(trade), E(price if trade)

Buyer

’

s value

Figure 4. An ex-ante incentive-efficient mechanism.

One of the basic contributions of mechanism design to economic analysis 

is an extension of how we think about efficiency in markets and other systems 

for economic transactions. In Figure 4, the probability of the mediator fail-

ing to achieve a mutually beneficial trade is strictly positive (it is (2/4)(1/6) 

= 1/12). Ex post, after the traders have reported their types and one of them 

has reported weakness, any such failure to realize mutually beneficial gains 

from trade would be allocatively inefficient, as the object is not being allo-

cated to the person who can make the most valuable use of it. Such was the 

classical view of efficiency that economists regularly applied before mecha-

nism design. But now we understand that, when the participation constraints 

and informational incentive constraints are taken into account, no incentive-

compatible mediation plan can have a lower probability of such ex-post al-

locative inefficiency here than this mechanism in Figure 4. 

When the expected profits are calculated ex-ante, before either indi-

vidual’s type is determined, the expected profit for each individual is 

[0+0+(5/6)20+(1)50]/4 = 16.67 in this mechanism. In fact, there is no incen-

tive-compatible mechanism that could yield a higher ex-ante expected profit 

for both individuals here. So in this sense (following Holmström and Myerson 

1983), we may say that this mechanism is ex-ante incentive efficient.

Notice that this concept of incentive efficiency applies to the mechanism 

for determining how the resource allocation will depend on people’s infor-

mation, not just to a particular resource allocation, and it takes incentive 

constraints into account in asking whether any other feasible mechanism 

could be better for these individuals. In ex-ante incentive efficiency, each 

individual’s welfare is evaluated at the ex-ante stage, before anyone learns his 

or her type.

The incentive-efficient mechanism in Figure 4 would not look so good to 

the seller if he knew he was the strong type, however, because this plan never 

allows the strong seller to get any positive profit from selling the object for 

more than his value of 80. So if we care about individuals’ welfare as they 

assess it in the game itself, when each knows his own type, then we need to 

admit other mechanisms as incentive-efficient. 

Figures 5 and 6 show other symmetric mediation plans that have y<20, and 

so allow a strong individual to get a positive profit margin against a weak op-

ponent, but keep the incentive constraint binding with q = 25/(50–y), so that 

the trading probability q is as large as possible given y. These mechanisms 

are better for the strong types than Figure 4, and they are interim incentive 

efficient, in the sense that there is no other incentive-compatible mechanism 

that would be preferred by each possible type of each individual in the game. 

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329

(The word interim here refers to the fact that we are evaluating each indi-

vidual’s welfare at a time when he has learned his own type but has not yet 

learned any others’ types; see Holmström and Myerson, 1983.) The mecha-

nism in Figure 6 (which is the best among these for the strong types), is the 

solution identified by a natural generalization of Nash’s (1950) bargaining 

solution, as defined by Myerson (1984).

Seller__’__s_value__$20_[s]__$100_[w]___EU(str)=$3.125'>(y=10, q=5/8)

Seller

’

s value

$20 [s]

$100 [w]

EU(str)=$3.125

[s]

$80

0, *

5/8, $90

EU(wk)=$28.125

[w]

$0

5/8, $10

1, $50

Buyer

’

s value

 P(trade), E(price if trade)

Figure 5. An interim incentive-efficient mechansim.

(y=0, q=1/2)

Seller

’

s value

$20 [s]

$100 [w]

EU(str)=$5

[s]

$80

0, *

1/2, $100

EU(wk)=$25

[w]

$0

1/2, $0

1, $50

Buyer

’

s value

 P(trade), E(price if trade)

Figure 6. An interim incentive-efficient mechanism (generalized Nash bargaining solu-

tion).

3.4 Dishonest equilibria and the revelation principle

The above analysis assumes that the mediator should get information by pro-

viding incentives for the traders to be honest. But even for mechanisms that 

are not incentive-compatible, the traders may convey information by rational 

strategies that form an equilibrium of their reporting game. For example, 

consider again the simple split-the-difference plan from Figure 2. We saw that, 

if the buyer were expected to be honest, then the seller would prefer to always 

claim to be strong. But if the seller is expected to always claim “strong” in this 

mediation plan, then the buyer would prefer to be honest, because an hon-

est admission of weakness could at least get 100–90 = $10 profit for the weak 

buyer. Thus, the simple split-the-difference mediation plan has a reporting 

equilibrium where the seller always reports strong but the buyer is honest. 

With this equilibrium of this mediation plan, the outcome of the mediation 

will depend on the traders’ actual types according to table shown in Figure 7.

Seller

’

s value

$20 [s]

$100 [w]

[s]

$80

0, *

1, $90

[w]

$0

0, *

1, $90

Buyer

’

s value

 P(trade), E(price if trade)

Figure 7. Incentive-compatible mechanism equivalent to an equilibrium of split-the-

difference.

The plan in Figure 7 is itself an incentive-compatible mediation plan. In ef-

fect, the plan disregards the seller’s reported type and has trade occurring at 

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