Note: Results updated at the end of the post

Hi Everyone,

Welcome to Week 6 of the Economics 7 Week Challenge series for 2022. We begin this week with the results post for Challenge 4: Game Theory. Unlike many of my other results posts, this post does not contain a video. All values were provided in the question. The winner is determined by the participants’ responses to each other’s decisions.

What is the Game Theory Challenge?

For the benefit of those who did not enter this challenge, here is a brief explanation of how the game works.

Participants are to choose 5 out of 9 boxes. Each box is assigned a value. The value of the box is equally shared amongst the participants who selected it (e.g. if a box has a value of 30 and 6 participants select that box, each participant obtains a value of 5). The sum of the values of the selected boxes, after being adjusted for sharing, will be the participant's score.

This challenge has several win conditions. These conditions are as follows:

The participant who obtains the highest value wins the challenge if no other players’ obtain that same value.
If more than one participant shares the highest value, the participant with the lowest value wins if no other players’ obtain that same value.
If more than one participant shares the highest value and if more than one participant shares the lowest value, the first and second participants to enter the challenge will be joint winners of the challenge and will share the prize evenly. This will occur regardless of the value they obtained from the boxes.

Responses to the challenge are made in the comments section of the challenge post. The account with the winning entry will receive Hive equivalent to 5 times the number of participants (e.g. if the challenge has 6 participants the prize will be 30 Hive (5 × 6)). The maximum prize for this challenge is 60 Hive. In addition to the winning prize, the first 12 entries are given upvotes. The winner also receives 40 points; this contributes to determining the overall challenge series winner.

The format of the required entry is explained in detail in the challenge itself.

For a more detailed explanation, you can access the challenge post using the following link.

Other challenges

There are seven challenges in this year's challenge series. Six of them are now closed. One is still running. See the links below.

Closed

Open (Until 18/09/2022)

Challenge 7: Pick-a-door (New)

Results of Challenge 4 (NO LONGER VALID)

Table 1 contains the selections made by all the participants for this challenge, the values of each box after sharing, each participant’s score, and the winner of the challenge.

Table 1: Results of Challenge 4

The winner of Challenge 4 is @adedayoolumide. @adedayoolumide won by achieving the outright lowest score of 11.27. The highest score of 18.43 was shared by @homesteadlt and @pana1; therefore, the winning criterion shifted to the lowest score. @adedayoolumide wins 60 Hive (more than 12 entries) and is awarded 40 points.

Challenge Tips and Analysis

There are many ways of approaching this challenge. It is difficult, as we cannot control the behaviour of other participants. Entering later enables a participant to observe many of the other participant’s actions. However, it is possible that a winning strategy will not be available for a participant entering late. In the case of this challenge, a new participant could have made a late entry and won. See Table 2 below.

Table 2: Late Entry Scenario

Another additional participant would be unable to win directly as both the highest and lowest possible scores based on existing selections had been achieved. If more people continued to enter, this could have changed as the value of different boxes would fall. Another participant could have entered the same combination of boxes as the participant with the lowest score; thus, causing another tie. On this basis, the first and second entrants would have been joint winners.

Unless participating second, entering the same boxes as another participant is a strategy that guarantees defeat. Yet, 4 participants entered the same boxes as a previous participant. Even if there is currently not a winning combination available, later entrants could alter the box values so that the combination you entered becomes a winning one. Entering the same boxes as another participant also blocks that other participant from winning.

On two occasions, the participant with a potentially winning entry was blocked. This looks like a deliberate attempt to manipulate the results. I believe some participants might be colluding to keep the winner within their own group. This is not in the spirit of these challenges but also not against the rules.

Results of Challenge (UPDATED)

A mistake has been made in the calculation of the results. A participant (@needlemover) was accidently not included in the initial calculation described in the previous section. The inclusion of this participant has changed the results of the challenge. Therefore, we have a new winner based on the second criterion of lowest score. That winner is @adeyemijan. See the Updated Results in Table 3.

Table 3: Results of Challenge 4 (UPDATED)

As I have already announced @adedayoolumide as the winner, the previous result will also stand. @adedayoolumide can keep the 60 Hive awarded as well as the 40 points. @adeyemijan will also be awarded 60 Hive and 40 points as well as an additional 10 points for informing me of the mistake. I hope both participants find this to be a reasonable solution for the mistake made.

Race to become the Challenge Series Champion (UPDATED BASED ON ABOVE CHANGES)

After four challenge, the overall scores for the Challenge Series are as follows.

Overall Series Score (UPDATED BASED ON ABOVE CHANGES)

Participants	Points
Adedayoolumide	50
Adeyemijan	50
Pana1	35
Fatherfaith	35
Temileke	30
Homesteadlt	20
Emeka4	10
Joshsticks28	5

This table will be updated in every results post.

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.