Megabucks and CashCow are the only two irms in a market Each frm must decide whe
ID: 2439679 • Letter: M
Question
Megabucks and CashCow are the only two irms in a market Each frm must decide whether to price high or price low The payoftfs from each strategy combination are shown to the right-in millions of dolars The frst number in each pair is Megabucks profit, the second is CashCow's prot Price HighCash CowPrice Low if the frims cooperate, he strategy that Megatucks wll choose is price highand he stategy that CashCow ail choose is s50 s75 t the lirms behave opporiunistically, the strakegy that Megabucks will choose is price high and the strategy that Cas Cow w choose is pnce high $50 ? 53 510 $75 $10Explanation / Answer
(1) If the firms cooperate, the result would be just as an infinitely repeated Prisoner's dilemma, where the outcome is not the nash equilibrium, but where the total earning is highest. The table for that is as below, which sums up the profits of both firms per decision.
As can be seen, combined profits are higher where both firms keeps high profits. Hence, if the firms cooperate, the stratergy that Megabucks will choose is price high, and the stratergy that CashCow will choose is price low.
However, if the combined profits were higher in the 1st row and 2nd column and/or in 2nd row and 1st column, than the high price cell, then the equilibrium would be there, even in the case where the profits were higher and the same in the stated rows, in which case, each cell would be chosen half of the time. Also, in the short run, one firm may cheat so as to get higher profit of $75, but so will the opposite firm, and they would in the long run would decide to choose high price, as that increases their total profits.
(2) Now, if each player behaves opportunistically, meaning independently or non-cooperatively, then the decisions would be where the Nash equilibrium lies. As can be seen, Megabucks's dominant stratergy is - price low, as the profits are higher in this row in compared to the price high row ($75 > $50 and $10 > $3). Also, the CashCow's dominant stratergy is - price low, as the profits are higher in that column in compared to the price high column ($75 > $50 and $10 > $3). Hence, the Nash equilibrium is in the cell where both firms keeps the price low.
Thus, if the firms behaves opportunistically, the stratergy that Megabucks will choose is price low, and the stratergy that CashCow will choose is price low.
CC-Price high CC-Price low M-Price high $(50+50) = $100 $(3+75) = $78 M-Price low $(75+3) = $78 $(10+10) = $20