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Hello. The problem is related to maximization problem using Kuhn-Tucker conditions and game theory. .Can you please explain me the following

Hello. The problem is related to maximization problem using Kuhn-Tucker conditions and game theory.

.Can you please explain me the following questions :

1) What do we mean by Kuhn-Tucker conditions?

2) If I want to find the best response for each player , do I have to solve for ti or for tij ? I have solved for tij but the result is not satisfactory.



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Consider a game with two players, where each player i = 1,2 has preferences
u,- = after“, where c,- is consumption and s,- is social interaction. s,- is given by Si = H +Iij *Fji: where r,- is time spent by player i alone, and ray is the time player 1' spends with
player j. Player 1' has to decide how much of his or her time T to allocate between
work, haying time alone, ti, and social interaction, raj. Assume that for each hour, player 1' works, he or she earns the wage w, and assume that the price of the
consumption good c,- is normalized to p = l. i. Carefully define the optimization problem for player 1. Write down the
Kuhn—Tucker conditions and discuss these conditions. Explain why player
1 faces a strategic situation. Find the best—response functions for player 1
and 2. Graph these functions. ii Find all Nash equilibria when assuming that players make their choices si—
multaneously.

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