REPEATED GAMES - GAME THEORY

Outline of the Strategic Challenge

Recently, acureforarareconditioncausingmildgastrointestinaldistressknownasGhul'sdisease hasbeendevelopedbyFriesLaboratories.Unfortunately, the curedevelopedbyFrieshassevere side effectsit induces severe chills and shivering, which is worse than the gastrointestinal distress from Ghul's disease. However, Wayne Enterprises has recently developed a drug that suppresses the undesirable side effects of the cure developed by Fries Laboratories. Both Fries and Wayne plan to sell their product into the indefinite future. However, both are aware that aftereachperiod,thereisaone-in-fourchancethatacompetitorwilldevelopasuperior product for a lower price, driving both Wayne and Fries from the market. In each period, Wayne Enterprises will choose the price for its drug, and then Fries will announce its price.

The Problem for Wayne Enterprises

Your job istomaximizeprofitsforWayneEnterprises.Unfortunately, yourdrugiscostlyto manufacture,andsoyour per-period profitsaregivenby (ww),where w istheprice charged by Wayne Enterprises for the drug, w=2 is the manufacturing cost for the drug, and is the quantity sold.

The Problem for Fries Laboratories

YouexpectFriesLaboratoriestoalsotrytomaximizeprofits. Per-periodprofitsforFries Laboratories are given by (ff), where f is the price charged by Fries Laboratories for the drug, f=4 is their manufacturing cost for the drug, and is the quantity sold. Demand for the CureGhul'sdiseaseaffectsdifferentpeopletovaryingdegrees,andhencethereisalargedegreeof dispersioninthewillingness-to-payfortheFries/Waynedrugcombination. Hence, eachperiod demand is given by =18fw.

The Pricing Decision

You shouldformulateaplan forajointpricingstrategywithFries. Yourplanshouldtakeinto accountthepossiblemovesthat youand Friesmightmake(particularlythosethatcontradictthe plan),and whatactionsshouldbetakenin response tosimplifyyourinitialanalysis,assumethat youagreetousethesamepriceseachperiod(assumingthatnoonebreaksthedeal)andthatyou (Wayne) will set a price of w=6.