Economics Challenge Series 2024 – Challenge 3: Pick-a-Door

5 months ago

Hi Everyone,

Welcome to the Economics Challenge Series for 2024. For July and August, I am running an economics challenge series. The series consists of seven challenges. All the challenges will commence in July and early August. I will publish and announce the results in August.

Six of the seven challenges from last year's Challenge Series return. The Tax Game from 2022 is replacing the business version of the Buying and Selling Game. Below is the list of challenges.

Challenge 1: Ice Cream Game
Challenge 2: Game Theory Game
Challenge 3: Pick-a-Door
Challenge 4: Complement vs. Substitute
Challenge 5: The Buying and Selling Game
Challenge 6: Even-to-Win
Challenge 7: Tax Game

Each challenge could reward winners with as much as 60 Hive Power. The value of the prize will depend on the level of participation. For each new participant, the prize will increase by 5 Hive Power. This will continue until 60 Hive Power 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 Power. The value of the prize will equal the sum of the number of participants across all challenges. This will continue until 80 Hive Power is reached.

For more information on the challenge series and the upcoming challenges, I recommend that you read my post from last year. This year’s Challenge Series is run the same way as last year’s.

Welcome to the Pick-a-Door Challenge

How to Play?

In this challenge, participants are required to make decisions based on expected payoff and risk. Participants are presented with 12 doors. Behind each door, there could be a prize (expressed in dollars). Each door has a possible prize worth a different amount. As the value increases, the probability of the prize being behind the door decreases. For example, there might be an 85% chance there is a prize worth $30 behind Door 3, and there might be a 30% chance there is a prize worth $100 behind Door 7. If the prize is not behind the door, the participant will receive a value of zero.

Opening a door incurs a cost. Each participant is given a budget of $80. Therefore, each participant can only open as many doors as their budget permits. Participants are not compelled to use all of the budget. If a participant opens 2 or more doors that have zero value behind them, they are eliminated from the challenge. If not eliminated, the winner is the participant with the highest total value expressed in dollars (i.e., the combined value of prizes minus the cost of opening doors).

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 ($20 for this challenge). Not opening a door has zero cost.
If it is revealed that the door does not have a prize behind it, the value is zero and the fee required to open the door is lost.
Based on the budget allocated and the cost of opening each door, each participant can only open a maximum of 4 doors. However, the participant may choose to 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 in which the doors are opened does not affect the probability of a prize being behind them.

What Information is Provided?

All possible prize values behind each door are provided.
All probabilities that these prizes will occur 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 model generating all relevant values. The winner will be announced in both the video and the written post.

Challenge Prizes

The total prize for this challenge could reach as high as 60 Hive Power. The number of participants determines the value of the prize. For every entry, the prize is increased by 5 Hive Power until a value of 60 Hive Power 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 15 points, and third place 5 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 the 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 that this will occur.

Figure 1: Value of Prizes and Probability

The cost of opening each and every door is $20. 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 1
Door 2
Door 6
Door 10

The closing date and time for this challenge is 6PM coordinated universal time (UTC) 26/07/2024. Responses after this time will not be accepted. The results of the challenge will be announced in a separate post.

I hope everyone has fun and enjoys this third challenge. If you have any questions, feel free to ask in the comments section. I look forward to your participation in the next challenge. It will be available in a few days.

My New Book, Sapien Loop

I have published an ebook on Amazon; it is titled ‘Sapien Loop: End of an Era’. The book is fiction. I do not normally write fiction. However, I felt it was appropriate considering what is happening in the world today. Freedom is the most important thing we have, but we are gradually losing it. I have covered this in many of my posts.

In the story, most citizens do not understand the concept of freedom because they have never really experienced it. In essence, the story is about an alien world that might represent our not-so-distant future. There are many other elements to the story that are an abstract and exaggerated version of our reality. I believe this book to be an important read, and I believe it has the potential to change the way you think.

Brief Summary of Sapien Lopp

This story is based on the fictional planet Sapia and its sole country, Sapey. Sapey is portrayed as a form of utopia for all its citizens. No poverty. No war. Almost no crime. Opportunities for all.

This was enough for most citizens, but not all. In one of the small regions, some of the citizens had become discontent. They felt something important was missing in their lives. Their discontent did not go unnoticed. Some of the Sapey elite wanted to weaponise this discontent to gain more power. This created more chaos than they anticipated. This led to further widespread social unrest.

On top of the chaos, ambition and greed provoked another enemy. This enemy was on a mission to settle both new and old scores.

If you want to buy a copy of the book, below are links to the relevant Amazon websites for each country it is available in. The book is priced at approximately US$5.08.

I am also running monthly contests where participants are required to answer questions based on the book. The prize is 30 Hive Power plus upvotes for the first twelve entries. You can recover the cost of the book with just one win.