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# Hello. My question is related to maximization problem using Kuhn-Tucker conditions and game theory. I have upload the question and my solution.

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

I have upload the question and my solution.Can you please explain me the following questions :

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

2) The terms tij and tji are the same?

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

4) Also, there are some cultures that emphasize social interaction more than others. In this exercise how can I determine the role of '' culture'' if exists?

Consider a game with two players, where each player i = 1,2 has preferences
u,- = ﬁxer”, where c,- is consumption and s,- is social interaction. 5,- is given by \$:H+W*Wr where r,- is time spent by player i alone, and ti}- 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, having time alone, ti, and social interaction, If}. 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.

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