Suppose that a delivery person named Clifford (player 2) is to deliver a package to a house with a chihuahua (player 1) in the yard. The yard around the house is fenced, but the gate is unlocked. Clifford can either enter the yard and deliver the package (action D) or leave an “attempted delivery” notice on the gate (action A). There are two types of chihuahua that Clifford may face. The first has no teeth; call this type W for “weak.” The second has teeth and jaws similar to those of a steel bear trap; call this type G for “gnarly.” The chihuahua is equally likely to be each type. Prior to entering the yard, Clifford cannot tell which type of chihuahua he faces.

Clifford likes to deliver all packages, but he would not like to have an encounter with the gnarly type of chihuahua. If Clifford chooses action A, he receives the payoff of 0 regardless of the chihuahua’s type. Delivering the package with the weak chihuahua in the yard yields a payoff of 4 for Clifford, but delivering the package with the gnarly chihuahua in the yard results in a payoff of −4 for Clifford. That is, the gnarly chihuahua will bite Clifford, but the weak one will not. Both types of chihuahua would receive a benefit of 4 if Clifford delivers the package and a benefit of 0 if not.

Prior to Clifford’s choice (D or A), each type of chihuahua chooses whether to bark (B) or not bark (N). The gnarly chihuahua does not like to bark—the “steel trap” mouth makes barking difficult—so barking costs this type an amount c > 0. The weak chihuahua likes to bark and receives a benefit x > 0 from doing so. These costs and benefits are in addition to the chihuahua’s benefit of Clifford’s selection of D described earlier.

(a) Represent this game in the extensive form.

(b) For what values of x and c is there a separating equilibrium for which the saying “barking dogs never bite” holds true?

(c) How does this compare with the education signaling models?