Economics 7 Week Challenge Series 2022 – Challenge 7: Pick-a-Door

Hi Everyone,

Welcome to the Economics 7 Week Challenge Series for 2022. Over 7 weeks, in the months of August and September, I will be running an economics challenge series. This series will consist of 7 challenges. Five of these challenges will be returning from last year’s Challenge Series and two of them are completely new. Below are the list of challenges.

Challenge 1: Auction
Challenge 2: Buying and Selling Game (Business Version)
Challenge 3: Tax Game (New)
Challenge 4: Game Theory
Challenge 5: Make Me Happy
Challenge 6: Buying and Selling Game (Original Version)
Challenge 7: Pick-a-door (New)

Each challenge could reward winners with as much as 60 Hive. The value of the prize will depend on the level of participation. For each new participant, the prize will increase by 5 Hive. This will continue until 60 Hive is reached (12 participants). The first 12 participants will also receive a 50% upvote from this account. In addition to the prize money, the top few participants will be given points. These points will be used to determine the overall challenge series winner. This winner may receive as much as 80 Hive. The value of the prize will equal the sum of the number of participants across all challenges. This will continue until 80 Hive is reached.

For more information on the challenge series and the upcoming challenges, I recommend that you read my post Spectrumecons Seven-Week Challenge 2022 (Coming Soon) and watch my video.

Welcome to Challenge 7: Pick-a-door

How to Play?

The challenge series is focused on economics. An important aspect of economics is dealing with the unknown. We do not know how people will respond to changes. We can only predict behavioural changes and the extent of these changes based on the information we have. In this challenge, participants need to make decisions based on expected payoff and risk. Participants are presented with 12 doors. Behind each door there could be a prize (expressed as a dollar value). Each door will have a possible prize worth a different dollar value. As the dollar value increases the probability of the prize being behind the door decreases. For example, for Door 3, there could be a 72% chance of a prize worth $40 and for Door 7, there could be a 40% chance of a prize worth $88. If the prize is not there, the participant will receive a value of zero.

To open a door costs $10, each participant will be given a budget of $40. Therefore, each participant could open as many as 4 of the 12 doors; however, they are not compelled to use all of the budget. The winner will be the participant with the highest dollar value at the end (i.e. combined value of budget not spent and prize values). However, if a participant opens more than 1 door that has a zero value behind it, they will be eliminated from the challenge. The winner will receive 2/3 of the prize and second place will receive 1/3 of the prize.

All entries must be made in the comments section of this post.

Each account is only permitted one entry.

Objectives of the game

The objective of the game is to obtain the highest prize value minus costs without opening more than one door that has a value of zero. The participant who can do this will be the winner.

Game Assumptions

The value revealed behind each door is what each participant who selected that door wins. There is no sharing of prizes in this challenge.
All doors cost the same amount to open ($10 for this challenge). Not opening a door has a zero cost.
If it is revealed the door does not have a prize behind it, the value is zero and fee required to open the door is lost.
Each participant can only open a maximum of 4 doors. However, the participant can open less.
If a participant opens more than one door that does not have a prize, he or she is eliminated from the challenge regardless of the value accumulated from the doors that have prizes behind them.
The order the doors are opened does not affect the probability of a prize being behind it.

What information is provided?

All possible prize values behind each door are provided.
All probabilities that these prizes will eventuate are provided.
Cost of opening doors is provided.

How are the results of the game determined?

A Microsoft Excel Model is used to determine if the prizes are behind the doors. The model will calculate each participant’s winnings as well as determine the overall winner. The results post will contain a video of the generation of the values. The winner will be announced in both the video and written post.

Contest Prizes

The total prize for this challenge could reach as high as 60 Hive. The number of participants determines the value of the prize. For every entry, the prize is increased by 5 Hive until a value of 60 Hive is reached. The winner will receive 2/3 of the prize and second place will receive 1/3. The first 12 entries will be given upvotes. The winner of this challenge will be given 40 points, second place 20 points, and third place 10 points. These points will be tallied at the end of the challenge series to determine the overall winner.

Let the challenge begin

Participants can choose to open up to 4 of 12 doors for a chance to win prizes valued in dollars. Figure 1 contains the twelve doors, the value of the prizes that might be behind them, and the probability this will occur.

Figure 1: Value of prizes and probability

The cost of opening each and any door is $10. The fee is deducted from the value won to determine the overall value gained

Entry format

For this challenge, I expect to see entries made in the following format:

Doors Opened:
Door: W
Door: X
Door: Y
Door: Z

Example of entry

Doors Opened:
Door 4
Door 5
Door 8
Door 10

The closing date and time for this challenge is 6PM coordinated universal time (UTC) 18/09/2022. Responses after this time will not be accepted. The winners will be announced in the results post along with the video containing the generation of values for each item.

I hope everyone enjoyed this final challenge as well as the previous 6 challenges. That brings the 2022 Economics 7 Week Challenge Series to an end. Over the next 2 weeks, the results of the final four challenges (4, 5, 6, and 7) will be posted. The overall winner will be announced in the final results post. May the best participant win.

If you want to read any of my other posts, you can click on the links below. These links will lead you to posts containing my collection of works. These 'Collection of Works' posts have been updated to contain links to the Hive versions of my posts.