Suppose we are interested in constructing an incentive compatibility constraint for an agent to announce his state truthfully.

Consider a simple case of the state space being $S=\{H,L\}$ and his payoffs to be $\pi_L,\pi_H$.

For the player to announce the state and payoff truthfully, is it correct to set the IC as:


If it is correct, why is it so, and if it isn't, what is the correct way of setting up the IC and why? Is there a general rule of thumb in constructing an IC? Any reference would be also helpful.

  • 1
    $\begingroup$ I am not clear about your notation. I believe that the payoffs should depend both on the true type and the announced type. $\endgroup$ – brunosalcedo Aug 12 at 15:01

As @brunosalcedo suggests in the comment, the agent's payoff, $\pi(a,s)$, should depend on i) the realized state $s$ and ii) the announced state $a$. Note that the announcement $a$ should in general be a function of the realized state $s$, i.e. $a:S\to S$. Incentive compatibility should thus be \begin{equation} \pi(s,s)\ge \pi(a',s),\quad\forall a'\ne s. \end{equation} In words, incentive compatibility requires that the agent's payoff when his announcement agrees with the state (i.e. the state is $s$ and his announcement is also $s$) be no lower than his payoff when his announcement disagrees with the state (i.e. the state is $s$ but his announcement is $a'\ne s$).

Check out the following book chapters for more detail:

  • Mas-Colell, Whinston, and Green (1995) (aka MWG) chapter 14.C discusses IC in the context of moral hazard
  • MWG chapter 23.B introduces IC for truthful implementation
  • Krishna (2010) chapter 5 is similar to the previous MWG chapter, but draws out more implications of IC.
  • $\begingroup$ (+1) could you write out MWG once? Just to make the reference clear... $\endgroup$ – Maarten Punt Aug 13 at 11:52
  • $\begingroup$ @MaartenPunt: Thanks. The reference has been added. $\endgroup$ – Herr K. Aug 13 at 17:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.