REVISIÓN, MEJORA Y RESULTADOS DEL PROGRAMA

One reason that there is no use for dynamic signaling is that the evidence type in period 1 is payoff irrelevant. Recall the entrepreneur releasing customer reviews to an investor. In addition to signaling value to investors at the angel round, the entrepreneur may make an early disclosure in order to obtain funding from separate investors at the seed round. The entrepreneur must balance the incentive to get early funding with how his early disclosure will affect funding in later rounds. Does the seed investor benefit or suffer from the entrepreneur’s dynamic incentives? Is the amount of seed funding negatively or positively related to the amount of angel funding?

7.2.1. Model

I augment the previous dynamic model with an additional receiver who takes an action a1 ∈ A, following the first period disclosure. The period 1 and period 2 receiver’s preferences are represented by U¹, U² : T × A → R respectively. For period 1 and period 2 action choices, a1, a₂ the sender’s utility is given by δa1+ (1 − δ)a₂. The timing is as follows. The sender obtains type t1in period 1 and makes a disclosure d1 ∈ M (t₁). Receiver 1 observes d1, takes an action a1, and obtains utility U¹(a1, t1). Then the sender obtains t2in period 2 and discloses d2 ∈ M (t₂). Receiver 2 observes d1and d2, takes an action a2, and obtains utility U²(a2, t2).

The sender’s strategy is a first period reporting strategy, σ : T → ∆T ; and a second period conditional reporting strategy, γ : T² → ∆T . Receiver 1’s strategy is a1 : T → Aand Receiver 2’s strategy is a2 : T² → A. I assume that in period 2, γ and a2 are played according to the receiver 2 optimal equilibrium. Thus the equilibrium action in period 2 for type t after a disclosure s in period 1 is given by πhs(t|U²), where hs∈ ∆T is the interim distribution over period 2 types given σand after observing s in period 1. For tractability I focus on interval equilibria.

Definition 7. An interval equilibrium is one in which {t : a1(t) = c}is is an interval for every c ∈ R.

Lemma 3. If (T, d)satisfies the UEPP, then any interval equilibrium (a1, σ)has, t dt⁰ =⇒ a₁(t) ≥ a1(t⁰). More over if t _dt⁰ and a1(t) > a1(t⁰)then ht≥_{M E} h_t⁰.

This result says that if the sender makes a disclosure in period 1, then he must be given a higher action than if he did not disclose (or disclosed less). The idea is that the period 1 disclosure induces

the receiver to believe that the sender has more evidence. Since this induces more skepticism in the receiver the sender must be compensated in the form of a higher first period action.

Since first period actions are increasing in the disclosure order, increasing δ, the sender’s weight on the first period action, further dis-incentivizes the sender from withholding. Thus any equilib-rium action profile under δ will also be one under δ⁰ > δ.

Proposition 8. Let (T, d)satisfy the UEPP. Define Π(δ) to be the set of interval equilibrium period 1 action profiles, i.e. all a1such that there exists σ with (a1, σ)constituting an equilibrium.

∀δ < δ⁰, Π(δ) ⊂ Π(δ⁰).

Let E¹(δ)be the equilibrium that is optimal from the perspective of the period 1 receiver. A straightforward corollary is that receiver 1’s expected utility from E¹(δ)increases in δ. Thus, pe-riod 2 incentives harm the pepe-riod 1 receiver. The intuition is that because the sender can always wait to disclose, he will never be induced to disclose more in period 1 by dynamic incentives.

Moreover, all else equal, the sender would prefer to wait to disclose because first period disclo-sures induce more skepticism in receiver 2. Therefore, the sender’s dynamic incentives make him to ”disclose less”.

8. Conclusion

This paper has two main contributions: (i) it characterizes the receiver optimal equilibrium in a large class of verifiable disclosure games and (ii) it shows that distributions which induce greater skepticism in the receiver are characterized by the more evidence relation. While quite general, the disclosure model does not incorporate all related examples from the literature. A prime ex-ample is that I do not allow for message dependent disclosure costs such as that of Verrecchia (1983). With disclosure costs, the equilibrium action for any type is not pinned down by the set of types with with which he pools. This impedes the equilibrium partition approach. Another open generalization is allowing the sender to have type dependent preferences.

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