Bayesian analysis of Price is Right showcase

Suppose you're a contestant on a popular game show called the Price is Right. You've made it to 'The Showcase' round where you're tasked with guessing the price of a group of prizes (typically trips, cars, furniture, etc.). The rules for the round (simplified a bit for this question) are as follows:

• There are 2 contestants competing in a showcase round
• Both contestants are shown unique groups of prizes (2 groups of prizes shown in total)
• After seeing the prizes, each contestant is asked to bid on what they think the value is of their unique set of prizes
• Whichever bid is closer, without going over, wins. If a contestant bids over, then their bid is disqualified from winning

This game provides an interesting example of balancing uncertainty with risk (since if we bid even 1 dollar over the true price of the items we are disqualified).

Given this information, you're tasked with using Bayesian inference to build a model and select your final bid in the showcase. Below are some details for your specific showcase round (the exact #s are not important, but will be helpful for plugs/structuring your own bets):

• You can assume that you have data on the 'true prices' of past Price is Right Showcase prizes, and they are normally distributed with a mean of 23,000 and a standard deviation of 4,500

• The two prizes in your prize package for today are:

• Trip to Hawaii

• Set of living room furniture

Note that this is an example of a 'case study' type question that is pretty open-ended, so focus on structuring your process/logic more so than your actual numerical answer. At a high level we'll step through comparing our estimate for this specific prize package to the historical mean/standard deviation (using Baysian inference), and we'll then set up functions to quantify and account for risk before arriving at our final bid.