Three students are participating in a project. Each of the three students simultaneously chooses whether or not to complete the task assigned to her. The project is successful if and only if all three students complete their tasks. Each student ranks the outcomes from best to worst as follows:1. Any outcome in which the project is successful and she does not complete her task. 2. Any outcome in which the project is successful and she completes her task.3. Any outcome in which the project is unsuccessful and she does not complete her task. 4. Any outcome in which the project is unsuccessful and she completes her task.

Answer the following questions.(a) Formulate this situation as a three-player matrix game.(b) Find all pure strategy Nash equilibria of this game. Show your work.

QUESTION B2 (6 marks total) Alice is an investor. She has $100 to invest in the Wonderland stock market which has three stocks to invest in: Wheat, Corn, Tea. Being an economy based mainly on agriculture, the return of the investment in Wonderland depends on the weather condition and the availability of water. The weather is either good with probability or bad (each happens with equal probability), and water is either enough or not (each happens with equal probability). The weather condition and the availability of water are not related (they have independent probability distributions). She only cares about her return and is to decide to invest $100 in one of the stocks. Her payoffs are as follows. 1. If the weather is good and there is enough water: then the rate of return of Wheat is 30%, Corn is 10% and Tea is 30% (that is, she receives $120 if she invests in Wheat, $110 if she invests in Corn, and $130 if she invests in Tea); 2. If the weather is good and there is not enough water: then the rate of return of Wheat is 20%, Corn is 10% and Tea is 20%; 3. If the weather is bad and there is enough water: then the rate of return of Wheat is 10%, Corn is 20% and Tea is 5%; 4. If the weather is bad and there is not enough water: then the rate of return of Wheat is 0%, Corn is 5% and Tea is 0%; Answer the following questions. (a) (1 mark) Formulate Alice's problem as a decision problem under uncertainty. (b) (2 marks) Does Alice have and weakly or strongly dominated action? Explain. (c) (2 marks) Which stock is the best choice for Alice? (Hint: Compare her expected utilities.) (d) (1 mark) If Alice is allowed to divide $100 among the three stocks, will she choose to do so, or will she continue to invest only in one stock? Explain. END OF ONLINE TEST