The Los Gatos Art Gallery has a valuable painting that it wishes to sell at auct

Question

The Los Gatos Art Gallery has a valuable painting that it wishes to sell at auction. There will be three bidders for the painting. The first bidder will bid on Monday, the second will bid on Tuesday, and the third will bid on Wednesday. Each bid must be accepted or rejected before the next bidder bids. If all three bids are rejected, the painting will be sold for a standing offer of $900,000. The Art Gallery’s chief auctioneer's estimates for the bid probabilities are contained in the table below: For example, the auctioneer has estimated that the likelihood that the second bidder will bid $2,000,000 is 90%. Show work:

a) Usea decision tree to determine the optimal decision strategy for which bid to accept.

b)Draw a risk profile for the optimal decision.

Amount of Bid Bidder 1 (Monday) Bid 2 (Tuesday) Bidder 3 (Wednesday) $1,000,000 0 0 0.7 $2,000,000 0.5 0.9 0 $3,000,000 0.5 0 0 $4,000,000 0 0.1 0.3

Explanation / Answer

SOLUTION :-

As per the data and information given in the question, there are three Bidders, one each on Monday, Tuesday and Wednesday.

Bidder 1 may bid on Monday either for $2,000,000 or $3,000,000 with probabilities 0.5 each

Therefore expected pay-off for Bidder 1 is $2,500,000 (2,000,000*.52 + 3,000,000*.5)

Bidder 2 may bid on Tuesday either for $2,000,000 with probability 0.9 or $4,000,000 with probability 0.1

Therefore expected pay-off for Bidder 2 is $2,200,000 (2,000,000*.9 + 4,000,000*.1)

Bidder 3 may bid on Wednesday either for $1,000,000 with probability 0.7 or for $4,000,000 with probability 0.3

Therefore expected pay-off for Bidder 3 is $1,900,000 (1,000,000*.7 + 4,000,000*.3)

Based on the comparison of the above mentioned calculations for the expected pay-off for the bidders, it is recommended that the optimal decision strategy among the bidders is to go for Bidder 1 with highest expected pay-off of $2,500,000 and accept the bid of Bidder 1.

Risk profile for the optimal solution is $2,000,000 with probability 0.5 and $3,000,000 with probability 0.5

Bid may be for $4,000,000 with probability of 0.1 by Bidder 2 or with probability 0.3 by Bidder 3

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