Consider 2 player game that repeats the following stage game T times: Player 1 Player 2 L R U 3; 3 0; 5 D 5; 1 2; 2A) What is the unique sub-game perfect Nash equilibrium of this nitely repeated game? Now let's slightly relax the assumption of mutual rationality and see what happens. Say that player 1 believes that player 2 will play according to the strategy you found for them in a) with probability 9 10 , but that with probability 1, 10 player 2 will follow a `grim strategy'. Player 1 is considering two options. The rst is to play her own grim strategy until the last period and then play D in the last period. The second is to play according to the SPNE strategy. B) Find the smallest T such that player 1 prefers the rst option rather than the second. Explain the intuition for why the length of the game matters. C) If the payo in the case (U;L) had been (4; 4), how would you expect your answer to b) to change and why?

Ido not understand this project overview agricultural commodities are bought and sold through the stock exchange. the price of commodities changes all the time. investors buy many agricultural commodities before they are ready for shipping. when an investor buys an agricultural commodity that is going to be ready in the future, they call this purchasing futures. this might be a future crop, meat that has not yet been processed, or another type of agricultural commodity. for this project, you will have to decide how to spend $10,000. research the new york stock exchange. find one or more agricultural commodities that you are interested in. remember, it may be listed as a future crop. instructions identify the agricultural commodities that you think have the best chance of going up in price. think about what is going on with supply and demand. decide how you will spend your money. you may purchase only agricultural commodities. check the market every day for a week. record the price of your commodity or commodities each day. you may buy or sell your commodities at any time during the week. you may sell your commodities and buy different ones. feel free to experiment with the $10,000 by buying and selling commodities, but make sure to keep a careful record of your activities. at the end of the week, you will write a report on your investments. this report should be structured to include this information: page 1: explain how the stock market works. page 2: list all commodities purchased. describe each in detail. discuss why you selected these commodities. remember, they must be agricultural. page 3: create a chart or graph to illustrate the price of your commodity or commodities over the week’s time. list all of your activity buying and selling. make sure you include prices and details. page 4: write a summary of your experience. describe what you might do differently if you were using actual money. propose potential reasons why the price of each commodity may go up or down.