4.8 Incentives to Collect Information
In the previous sections we have analyzed communication incentives. In this section, we analyze players’ incentives to collect information. I restrict attention to a simple scenario and assume that M observes t and only A has to exert effort to learn q.
This allows a simple comparison of the effort exerted by the two kinds of agents.
The baseline model can be easily extended to include a stage in whichA has to exert costly effort to learn q. The timing is as follows. Nature determines t and q, and reveals t to M . In stage 1, A exerts effort πjA to learn q. In stage 2, the communication game of section 4.2 takes place. Payoffs are then realized.
Assume a quadratic cost of effort that is given by 12λ(πjA)2. Parameterλ > 0 captures the marginal cost of effort toA. I assume for simplicity that λ is common knowledge, and that both kinds of agents,v = 1 and v = 0, have the same marginal cost of effort. TermπjA∈ [0, 1] denotes the effort exerted by A, where the subscript j = v ∈ {0, 1} distinguishes the effort of A with v = 1 from the effort of A with v = 0.18 Effort πAj determines the probability with which A becomes informed.
If A exerts effort, then he successfully learns q with probability πAj, and remains uninformed with probability 1− πjA. IfA is uninformed, then he sends an empty message,m = φ, which is equivalent to babbling.
The expected payoff to the agent withv = 1 and v = 0 is respectfully given by,
EUA(v = 1) = π1A The first (second) term on the right is the expected payoff ifA finds (does not find) information, and the last term is the cost of effort. Notice that in case A
18I assume for simplicity that effort is observable, also that players observe whether the other player is informed or not. This does not effect our results since in our model a player does not have incentive to conceal whether he is informed or uninformed.
does not find information, then an informed M prefers to implement the project if t + E(q) > 0. The first-order-conditions of equation 4.13 and equation 4.14 with respect toπ1Aandπ0Arespectfully, imply that
πA1 =(N2− 1)(1 − N2b2)
12λN2 (4.15)
π0A=1− b2
16λ (4.16)
The higher is λ and b, the lower is the effort exerted by both kinds of agents.
It is not so obvious whether πA1 is larger or smaller thanπA0 since an increase inb results in a decrease inN . Figure 4.6 depicts the effort levels under v = 1 and v = 0 as a function ofb. The two curves intersect at b = 0.14. As can be seen, πA1 is larger (smaller) thanπ0Aifb is sufficiently small (large). Notice that the effort of an agent with shared values decreases (π1A→ 0) at a higher rate as b increases.19 The reason is that communication incentives of such an agent are more sensitive tob, as shown in the previous analysis. In fact, if the marginal cost of effort is the same for both types of agents, then π1A is relatively higher for the same range of b for which an agent with shared values reveals more information toM . The implication is that an agent with shared values does not necessarily exert higher effort to become informed.
Above we assumed that marginal costs of collecting information are symmetric.
This is likely not the case in reality. If an agent has a smaller (higher) marginal cost, then his effort is higher (the curve in figure 4.6 will shift up for allb). Whether agents within an organization have a larger (or smaller) marginal cost of collecting information in comparison to external management consultants is likely to depend on various factors. First, marginal costs will depend on the type of information that is required by the manager. For example, management consultants interact with numerous firms and industries, due to which they are likely to have easier access to information about consumer demand, best practices, and international markets. On the other hand, internal agents are likely to have easier access to information about the firm. Second, marginal costs of effort will also depend on concerns related to multi-tasking. An worker in the organization is likely to have a higherλ if doing so pulls him away from other tasks.
In the analysis above, we assumed thatM ’s information, t, is private knowledge.
In section ?? we showed that ift is common knowledge, then communication from an agent with shared values is strictly better than ift is private knowledge. Moreover,
19As can also be seen from the partial derivative of equilibrium efforts with respect to b.
4.8 Incentives to Collect Information 55
A achives his first-best outcome in case the project is implemented. If A is able to achieve his first-best outcome (conditionally), then it is likely that A will have stronger incentives to become informed. Indeed, this is true in our model. If A observest, then his expected payoff is given by,
EUA(v = 1) = π1A The first-order-condition with respect toπA1 implies,
π1A=2 + (6− 7b)b2
24λ (4.18)
It can be verified that equation 4.18 is strictly larger than the effort levels given in equations 4.15 and 4.16. Note that this is in line with Aghion and Tirole (1997).
If the agent is able to achieve his first-best (even if conditionally so as in our model), then it motivates the agent to exert higher effort. An implication of these results is that a manager will have incentive to reveal his information to an agent if doing so will improve the incentives of A to collect information. To put it another way, M can motivate an agent to exert higher effort by communicating with the agent. Note that this mechanism differs from the mechanism in Aghion and Tirole (1997). There, it is primarily delegation of decision rights that motivates the agent. WhetherM can credibly reveal his information fully toA is question for future research.