Two buyers are bidding against each other in an auction for a painting. Buyer 1 values...

 

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Two buyers are bidding against each other in an auction for a painting. Buyer 1 values the painting at 8 million YTL and Buyer 2 values it at 6 million YTL. The rules of the auction are that each buyer i will simultaneously choose a bid b, from the set {0, 1, 2,..., 10} million YTL. The buyer with the highest bid wins the painting and pays a price equal to the second highest bid. If the two bids are equal, each buyer gets the painting with 0.5 probability. The payoffs of the buyers are as follows: for b₁ and b2 in {0, 1, 2, ..., 9, 10} u₁(b₁,b₂) 8-b₂ if b₁ b₂, 0.5(8b₂) if b₁ = b₂, if b₁ b₂. 0 { uz(b1, b2) 6-b₁ if b₂b₁, 0.5(6b₁) if b₂ = b₁, 0 if b₂ <b₁. { (a) Calculate and graph the best response correspondence of Buyer 1. (b) Write down the dominant strategies of Buyer 1 if there are any. Are they weakly or strictly dominant? (c) Calculate and graph the best response correspondence of Buyer 2. (d) Write down the dominant strategies of Buyer 2 if there are any. Are they weakly or strictly dominant? (e) Combine the two best response graphs to analyze if the game has any Nash equilibria. Write down all the nash equilibria you obtain, if there are any. (f) Write down all dominant strategy equilibria, if there are any. Two buyers are bidding against each other in an auction for a painting. Buyer 1 values the painting at 8 million YTL and Buyer 2 values it at 6 million YTL. The rules of the auction are that each buyer i will simultaneously choose a bid b, from the set {0, 1, 2,..., 10} million YTL. The buyer with the highest bid wins the painting and pays a price equal to the second highest bid. If the two bids are equal, each buyer gets the painting with 0.5 probability. The payoffs of the buyers are as follows: for b₁ and b2 in {0, 1, 2, ..., 9, 10} u₁(b₁,b₂) 8-b₂ if b₁ b₂, 0.5(8b₂) if b₁ = b₂, if b₁ b₂. 0 { uz(b1, b2) 6-b₁ if b₂b₁, 0.5(6b₁) if b₂ = b₁, 0 if b₂ <b₁. { (a) Calculate and graph the best response correspondence of Buyer 1. (b) Write down the dominant strategies of Buyer 1 if there are any. Are they weakly or strictly dominant? (c) Calculate and graph the best response correspondence of Buyer 2. (d) Write down the dominant strategies of Buyer 2 if there are any. Are they weakly or strictly dominant? (e) Combine the two best response graphs to analyze if the game has any Nash equilibria. Write down all the nash equilibria you obtain, if there are any. (f) Write down all dominant strategy equilibria, if there are any.

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A a The best response correspondence of Buyer 1 can be calculated as follows b2 0 1 2 3 4 5 6 7 8 9 ... View the full answer