Q1 Market-clearing Prices Consider a standard position auction. There are two positions: Top (T) and Bottom (B). Position T receives ¤7 = 150 clicks per day and position B receives rB = 50 clicks per day. There are four bidders (B1-B4) with the following dollar values per click: v1 = 8, vz = 6, v3 = 4, v4 = 2. %3D (a) Find the efficient assignment. (b) Find the lowest per click market-clearing prices. (c) Find the highest per click market-clearing prices. (d) Fully specify and draw the complete set of ALL per click market-clearing prices.

Q17. What the information sets in the above game denote?  Player 2 does not observe the action of player 1, so he does not know in which decision node he/she is playing at.   Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and b, or one between c and d.   Player 2 does not observe the precise action of player 1, but he does know that player 1 has played one between a and c, or one between b and d.   Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and d, or one between b and c.

These are Multiple Choice Questions, only need to choose one (alphabet) answer (from A to D) for each question. ONLY answer 3 questions. Q1) Louey's Greasy Spoon restaurant charges $15 for each dinner entree and $5 for each dessert selection, and they offer a dinner special that provide an entree and dessert for $18. If a dinner at Louey's assigns zero value to dessert and $19 to an entree, what is their optimal decision? A) Buy the dinner Special B) Buy only the entree C) Buy only the dessert selection D) We do not have enough information to determine the optimal decision Q2) The Acme Oil Company is a vertically integrated firm. It explored for and extracts crude oil. It also refines the crude oil into gasoline and other products, and sells these products to consumers. There are many other firms that extract and sell crude oil so that the market for crude oil is regarded by Acme Oil as competitive. The internal price that Acme Oil uses when the crude oil that it extracts is "sold" to…

Which one of the following descriptions is correct according to this extensive form? (I think it's 3rd option but unsure)

See attachments for question context. Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how prices increase over time, does not change. What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.

3. This game is based on the book "Real Men Don't Eat Quiche" by Bruce Feirstein. There are two players sitting at a bar. The timing is as follows: i. Nature determines P1's type as "wimp" or "surly". P1 observes it, P2 doesn't. (and this is common knowledge) ii. P1 chooses whether to order a beer or a quiche. iii. P2 sitting next to P1, observes P1's choice. Then P2 decides whether to start a fight with P1 or not. The extensive form is given below. Let numbers p and q denote P2's conditional beliefs in the two information sets. 1,3 FB 2 FQ 2,1 BW 1W QW 2 P 4,0 NB 9. [0.3] wimp NO 0,0 1,0 FB 2,4 NB [0.7] surly FQ 1,2 1-q 2 B$ 15 Q 2 NO 0,1

Explain how the number of bidders in a common value auction affects the outcome of the auction. Relate this to the effect on price in different market structures based on the number of producers.

- First-Price and Second-Price Auctions - Consider an auction of a single indi- visible object with 5 bidders, 1, 2, 3, 4 and 5, whose personal valuations (willingness to pay) for the object are v₁ = 10, V₂ = 8, 03 7, 04 5 and 5 3. The bidders simultaneously submit their bids and the winner is the one with the highest bid. Suppose that, when the highest bidder is not unique, the bidder with the smallest number (highest valuation) wins. (a) Suppose that this is a second-price auction, where the winner pays the highest bid among those from her opponents, determine whether each of the following bidding profiles is a Nash equilibrium. Explain. (i) (b₁,b2, b3, b4, b5) = (10, 8, 7, 5, 3) (ii) (b1,b2, b3, b4, b5) = (8,8, 0, 0, 0) (iii) (b₁,b2, b3, b4, b5) = (10, 0, 0, 0, 10) (b) Now suppose that this is a first-price auction, where the winner pays their own bid, determine whether each of the bidding profiles above is a Nash equilibrium. Explain. = =

(a) Assuming that each fishery chooses fi ∈ (0, F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? 4 (c) Suppose that a benevolent social planner wants maximize the utility of both fisheries. In other words, the social planner solves the following problem: max w(f1,f2) w(f1, f2) = u1(f1, f2) + u2(f1, f2)                                    =2 ln(f1) + 2 ln(f2) + 2 ln(F − f1 − f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?

(b)  Assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game?