Two individuals A and B have to simultaneously decide how much effort to exert in a partnership. If denotes the effort of A
and that of B, the value generated for each partner from the
partnership is. The cost of effort for A is and the cost of effort
for B is .
a) Write down the payoff functions for the two players and,
explaining your reasoning, derive their reaction functions.
Remember to include all your working and describe what a
reaction function is. Using words and mathematics, explain
whether this a game of positive or negative externalities.
Using words and mathematics, explain whether this game
exhibits strategic substitutes or strategic complements.