Remember from our class discussion that it is useful to think of players who come to a game possessing different private information as different types When credible signaling works in the equilibrium of the game the lessinformed players will be able to infer the information of the moreinformed ones correctly from the actions Hence in equilibrium the different types are correctly revealed or separated Therefore we call this a separating equilibrium In some cases however one or more types may successfully mimic the actions of other types so that the uninformed players cannot distinguish the different types by observing actions Then in equilibrium we say the types are pooled together and we call this a pooling equilibrium Finally at times it so happens that a new type of partially revealing or semiseparating equilibrium can emerge where the actions in the equilibrium convey some additional information about the players types but some ambiguity about these types remains In this question we will study Renees incentives when it comes to reporting unobserved income to the tax authority Renee works as a dance teacher Some of her students pay her in cash at the end of a class Accordingly Renee has the opportunity to earn cash income in addition to other forms of payments that she reports that are not reported to the Australian Tax Office ATO Her cash income is rather variable Suppose that in a good year G she earns a high income so her tax liability to the ATO is 5000 In a bad year B she earns a low income and her tax liability to the ATO is 0 The ATO knows that the probability of Renees having a good year is 06 and the probability of her having a bad year is 04 but it doesnt know for sure which outcome has resulted for Renee this tax year In this game first Renee decides how much income to report to the ATO If she reports high income H she pays the ATO 5000 If she reports low income L she pays the ATO 0 Then the ATO has to decide whether to audit Renee If she reports high income they do not audit because they automatically know theyre already receiving the tax payment Renee owes If she reports low income then the ATO can either audit A or not audit N When the ATO audits it costs the ATO 1000 in administrative costs and also costs Renee 1000 in the opportunity cost of the time spent gathering bank records and meeting with the auditor If the ATO audits Renee in a bad year B then she owes nothing to the ATO although she and the ATO have each incurred the 1000 auditing cost If the ATO audits Renee in a good year G then she has to pay the 5000 she owes to the ATO in addition to her and the ATO each incurring the cost of auditing