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santa bar Server Ne × Establishe × Winery Ta × Japanese × EDOMAS! × NEW-Bis × Breakfast × New resta × Server Ne × W Beyoncé x Course: E × Prob 10.4 x b Prob 10.6 × Prob 10.4 https://gauchospace.ucsb.edu/courses/pluginfile.php/727601/mod-resource/content/1/Prob%2010.4-6.pdf Apps A Beginner Mass Ga R Information for the V Netflix Watch TV ShYouTube-Broadcast Bank of America Ho M Gmail Mint > Over e Music UCSB Bills & rent Black Desert Beta BI Research for Royer Internships Prob 10.4-6.pdf valuation is 5, 5 when her valuation is 7, and 6 w Determine whether it is a symmetric BNE for a bidder to a. Determine hen her valuation is 10 bid 4 when her valuation is 5, 6 when her valuation is 7, and 9 when her valuation is 10 4. Consider a first-price, sealed-bid auction, and suppose there are o three feasible bids: A bidder can bid 1, 2, or 3. The payoff to a lo there are ony yoff to a losing bidder is zero. The payoff to a winning bidder equals his valuation minus the price paid (which, by the rules of the auction, is his bid). What is private information to a bidder is how much the item is worth >2, to him; hence, a bidder's type is his valuation. Assume that ther only two valuations, which we'll denote L and H, where H3 > L2 Assume also that each bidder has probability.75 of having a high valu- ation, H. The Bayesian game is then structured as follows: First, Nature chooses the two bidders' valuations. Second, each bidder learns his valuation, but does not learn the valuation of the other bidder. Third, the two bidders simultaneously submit bids. A strategy for a bidder is a pair of actions: what to bid when he has a high valuation and what to bid when he has a low valuation. a. Derive the conditions on H and L whereby it is a symmetric BNE for a bidder to bid 3 when he has a high valuation and 2 when he has a low valuation. b. Derive the conditions on H and L whereby it is a symmetric BNE for a bidder to bid 2 when he has a high valuation and 1 when he has a low valuation. c. Derive the conditions on H and L whereby it is a symmetric BNE for a bidder to bid 3 when he has a high valuation and 1 when he has a low valuation. 4:29 PM d)) . ENG 5/28/2016 Search the web and Windows NEExplanation / Answer
a. Derive the conditions on H and L whereby it is a symmetric Bayes–Nash equilibrium for a bidder to bid 3 when he has a high valuation and 2 when he has a low valuation.
It is to find the condition such that (3, 2) is a symmetric BNE. That is, every bidder with valuation H bids 3 while that with L bids 2.
For H Type, the expected payoff of bidding
3: .75×(H-3)/2+.25×(H-3)=5(H-3)/8
2: .75×0+.25×(H-2)/2=(H-2)/8
1: .75×0+.25×0=0
To bid 3 is the best if H13/4.
For L Type, the expected payoff of bidding
3: .75×(L-3)/2+.25 ×(L-3)=5(L-3)/8<0
2: .75×0+.25×(L-2)/2=(L-2)/8
1: .75×0+.25×0=0
To bid 2 is the best if L2 which is true because H>3>L>2.
Hence (3, 2) is a symmetric BNE if H13/4.
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