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 (D) or leave an "attempted delivery" notice (A) on the gate. There are two types of chihuahuas 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 does not like to have an encounter with the gnarly type of chihuahua. So his payoffs are as follows. If Clifford leaves the "attempted delivery" notice A, he recives a payoff of 0 regardless of the chihuahua's type. Delivering the package with the weak chihuahua (W ) in the yard yields a payoff of 4 for Clifford, but delivering the package with the gnarly chihuahua (G) in the yard results in a payoff of 4 for Clifford. Think of this as Clifford is biten by the gnarly chihuahua, but he gets to pet the weak one. Both types of chihuahua like for Clifford to deliver the package and each receives a beefit of 4 from his doing so (D), and a benefit of 0 from him not delivering the package and leaving the "attempted delivery" notice (A).

Prior to Clifford's decision (D or A), each type of chihuahua chooses whether to bark (B) or to not bark (N). The gnarly chihuahua does not like to barkthe "steel trap" mouth makes barking difficultand bears a cost of c > 0 to bark. The weak chihuahua likes to bark at outsiders and receives a benefit x > 0 from doing so. (These are in addition to the chihuahua's benefits, described above, due to Clifford playing D or A. So the chihuahua's payoff is given by adding the above benefits and the cost/benefit described here.) Assume that Clifford is not close enough to be able to observe the chihuahua's teeth when it barks.

(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?