Assignment:
Partnership Game Lee (Player 1), and Julie (Player 2), are business partners. Each of the partners has to determine the amount of effort he or she will put into the business, which is denoted by ei, i = 1, 2, and may be any nonnegative real number. The cost of effort ei for Player i is cei, where c > 0 is equal for both players. The success of the business depends on the amount of effort put in by the players; the business’s profit is denoted by r(e1 ,e2) = e1α1 e2 α2 where α1, α2 ∈ (0, 1) are fixed constants known by Lee and Julie, and the profit is shared equally between the two partners. Each player’s utility is given by the difference between the share of the profit received by that player and the cost of the effort he or she put into the business. Answer the following questions:
(a) Describe this situation as a strategic-form game. Note that the set of strategies of each player is the continuum.
(b) Find all the Nash equilibria of the game.
Provide complete and step by step solution for the question and show calculations and use formulas.