Roger B. Myerson Prize Lecture

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that individuals can misrepresent their types, and unfortunately this plan is 

not incentive compatible; that is, honesty by both traders is not an equilibrium 

of this game. For honesty to be an equilibrium in the sense of Nash (1951), 

it must be that each individual would find honesty to be the best policy when 

the other is expected to be honest. It is easy to see that a strong type can never 

gain by claiming to be weak: a seller who thinks that the object is worth $80 

would only be asked to sell at a loss if he pretended that the object was worth 

$0 to him. But let us look at the problem from the seller’s perspective when 

he knows he is weak. If the buyer were expected to be honest in this plan, 

then a weak seller could get a higher expected profit by claiming to be strong. 

If the weak seller honestly admitted weakness under this plan, his expected 

profit would be 0.5(10–0)+0.5(50–0) = 30, because the buyer has probability 

0.5 of being weak and probability 0.5 of being strong. But if the weak seller 

claimed to be strong, then he would have a 0.5 probability of getting profit 

$90–0, and so his expected profit from lying would be 0.5(90–0) = 45, which is 

strictly greater than the 30 that he would expect from honesty. (Throughout 

we assume here that individuals are risk-neutral, seeking to maximize their 

expected profits.) Thus, honesty is not an equilibrium of this mediation plan. 

That is, this simple split-the-difference plan is not incentive compatible.

3.2 Incentive constraints for symmetric mediation plans

Let us now consider other mediation plans. For simplicity, let us consider 

plans which treat the seller and the buyer similarly or symmetrically. To be 

specific, let us suppose that the conditional probability of trading when one 

individual is weak and the other is strong is some number q that does not 

depend on which of them is the weak one. Also, let us suppose that the ex-

pected profit margin of a weak individual who trades with a strong individual 

is some number y that does not depend on which individual is the weak one. 

For simplicity, let us suppose that two weak individuals, who are maximally 

eager to trade, would trade with probability 1 at a price $50, which is half-way 

between their two values. We can assume that trade does not occur when 

both are strong, as the seller would then value the object more than the 

buyer. So the general symmetric mediation plan with these two parameters q 

and y is as shown in Figure 3.

[strong]

[weak]

$20

$100

Seller

’

s value

“$20”

“$100”

[strong]  $80

“$80”

0, *

q, $100-y

[weak]  $0

“$0”

q, $y

1, $50

Buyer

’

s value

 P(trade), E(price if trade)

Figure 3. General symmetric mediation plan or mechanism.

For the plan in Figure 3 to be an incentive-compatible mechanism, q and y 

must satisfy three inequalities or constraints. First, the number q must satisfy 

the probability constraints 

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0 < q < 1.

(In each cell, the probability of trade could also be interpreted as the condi-

tional expected number of objects that the buyer would get in this case, and 

so q < 1 here can also be interpreted as a resource constraint, expressing the 

fact that there is only one object that they can trade.)

Under the symmetric plan in Figure 3, a strong buyer with value $20 would 

trade only at the price y, which would be an unacceptable loss for the strong 

buyer if y were greater than 20. So for a strong trader (buyer with value $20 

or seller with value $80) to be willing to participate in this plan, y must satisfy 

the participation constraint 

y < 20.

For honest reporting to be a Nash equilibrium in Figure 3, we need to verify 

that each individual would be willing to report his type honestly if he ex-

pected the other to be honest. It is easy to see that a strong type of seller or 

buyer would never want to pretend to be weak under this plan, as it would 

only result in trading at a loss. But a weak type might be tempted to pretend 

to be strong, to get a better price. Consider the weak seller, for example. 

(All calculations for the weak buyer are similar.) Under this plan, against 

an honest opponent, the weak seller’s expected profit if he reports honestly 

is 0.5q(y–0)+0.5(1)(50–0), but his expected profit if he falsely claims to be 

strong is 0.5(0)+0.5q(100–y–0). Thus, to make honesty an equilibrium, q and 

y must satisfy the informational incentive constraint 

0.5qy + 0.5(50) > 0.5q(100–y).

This constraint is algebraically equivalent to the inequality

q < 25/(50–y).

3.3 Incentive-efficient trading plans

The incentive constraints q < 25/(50–y) and y < 20 together imply that the 

largest feasible probability of trade is achieved by letting y = 20, q = 5/6. 

Figure 4 shows this incentive-compatible mechanism. The informational 

incentive constraint is satisfied as an equality here, as a weak type’s expected 

profit from honesty is (0.5)(5/6)20+(0.5)50 = 33.33, which is just equal to 

the expected profit (0.5)(5/6)80 that a weak type could get from lying.

3

 

3 

The incentive-compatibility of Figure 4 depends on the two traders communicating separately 

with the mediator. In general, incentives to lie to the mediator could be exacerbated if one 

individual learned the other’s report before submitting his own. In Figure 4, if the seller learned 

that the buyer reported her weak type before reporting his own, then the weak seller could get 

higher expected profit by pretending to be strong, because (5/6)80 > 50. 

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