inthe"longpurse"predatorygame,supposethatthepreychoosestoexitortostayatthebeginning of the month, before the dominantfirm (or predator) decides tofight or to share. If the prey chooses to exit at the beginning of the period, it does not incur any cost and saves the $100,000 loss of being preyed upon.
As before, the prey can withstand only 3 months of predation and by the fourth month, must exit because its reserves would have run out.
Draw the new extensive-form game. What is the condition that must be satisfied for the perfect Nash equilibrium of this game to be one where the predator is always willing to predate? In the original timing, the condition was that it pays the predator tofight a price war for just one period, orpM-200>pD.
Now, suppose there is discounting in this game. The discount factor is given byd?(0,1). Let pDandpMbe the discounted value of an infinite stream of duopoly and monopoly payoffs. As before, assume that the prey has enough cash reserves to withstand at most 3 months of predation. How do the payoffs change? Draw the extensive form of the game with the discounted payoffs. How is the condition in the previous part of the question affected by discounting?