7. In a first price sealed bid auction with 2 bidders, let v be the valuation ofbidder i and b; be her bid. The bids are made simultaneously and the payofffunction of player i is given as follows:if b; > bj,(v; – b:)/2 if b; =b;,if b; < b;.u:(b1, 62; V1, V2) =0.The optimization problem of player i is given by(a) maxb, (vi – b;)(b) mat, (v; – b:)Prob{b; > b;(v;)}(c) maxs, (vi – bi)Prob{b, > b;(v;)} + }(v; – b;) Prob{b; = b;(v;)}(d) mar, (v; – bị)Prob{b; > b;(v;)} +}(v; – 6:)Prob{b, < b;(v;)}

In the first price sealed bid auction, person i will win and pay his bid i.e. bi Now, the…

7. In a first price sealed bid auction with 2 bidders, let v; be the valuation of bidder i and b; be her bid. The bids are made simultaneously and the payoff function of player i is given as follows: Vi - - bi ui (b1,b2; V1, V2) = (v₁ - bi)/2 0 if bi > bj, if b₁ = bj, if bi < bj. The optimization problem of player i is given by (а) тахь; (v; — b;) (b) maxь; (vi — b₁) Prob{b; > b;(vj)} - (c) maxь, (vi — b₁) Prob{b; > bj(vj)} + ½ (vi − b;) Prob{b; = b;(vj)} (d) maxь; (vi — b₁) Prob{b; > b;(v;)} + ½ (v₁ − b;) Prob{b; < b;(vj)}

7. In a first price sealed bid auction with 2 bidders, let v; be the valuation of bidder i and b; be her bid. The bids are made simultaneously and the payoff function of player i is given as follows: Vi - - bi ui (b1,b2; V1, V2) = (v₁ - bi)/2 0 if bi > bj, if b₁ = bj, if bi < bj. The optimization problem of player i is given by (а) тахь; (v; — b;) (b) maxь; (vi — b₁) Prob{b; > b;(vj)} - (c) maxь, (vi — b₁) Prob{b; > bj(vj)} + ½ (vi − b;) Prob{b; = b;(vj)} (d) maxь; (vi — b₁) Prob{b; > b;(v;)} + ½ (v₁ − b;) Prob{b; < b;(vj)}

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following game 1\2 Y Z A 10,3 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (9/10,1/10) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, player 2 should respond by playing _____
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Please select the correct option and write clear. Thank you.
Determine all of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following game:
1. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects £2, with payoff functions ₁ and 7₂. Find the best response for P2, as the function î2 = BR₂(x1), for each given #₂: (a) (b) (c) T₂(x1, x₂) ) = (1400 — x1 — x2)x2 − 13x² T₂(x1, x₂) T₂(X1, X2₂) = : 100x2 + 3x1x2 − 14x1 – 30x1x² = 15x2 x² + x² +1
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(The All-Pay Auction). The seller has an item for sale. The valuations of the bidders are independently and identically distributed on R+ with a c.d.f. F. Find the symmetric equilibrium of an auction with two bidders in which both bidders pay their own bids but only the highest bidder wins the object. Show that each bidder’s expected payment is the same in this auction and in the first-price auction.
Assume that two collectors, X and Y are in a first prize sealed bid auction for a batch of vintage comic books. X and Y have different valuations (V) for this batch of comic books e.g. VX And VB are between $2000 and $4000. Both collectors know their own V but does not know the V of the other collector. All they know is that the other collector’s V is a uniformly distributed number between $2000 and $4000. Assume risk neutrality for X and Y e.g. expected payoff for X is: (VX – bX)Pr(bX) and expected payoff for Y is (VY – bY)Pr(bY). These collectors will make their bids strategically. Show how X’s bidding strategy is bX = ½ Vx + 1 and Y’s is bY = ½ Vy +1 in a Nash equilibrium.
P1| P2 Left Middle Right Left 4,2 3,3 1,2 Middle 3,3 5,5 2,6 Right 2,1 6,2 3,3 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played in the first period, followed by (Left, Left). e) (Middle, Middle) is played in the first period, followed by (Right, Right).
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