Thingamabob Game

Allow me to introduce you to the thingamabob game. Here are the rules:

1. There are 7 players, each with $1000.

2. There are 5 rounds. Each round, every player decides how many thingamabobs they will produce (independently of each other).

3. To produce 1 thingamabob costs $1. At the end of the round, all thingamabobs sell for $2. For example, if you have $1000, you could produce 250 thingamabobs, and the next round you would have $1250. Instead, you could produce 1000 thingamabobs and have $2000 dollars next round.

4. If you produce too little (say less than 10% of your maximum), your shareholders get angry and you are fired (you immediately lose).

5. For every 1000 thingamabobs produced, 2 ppm of carbon dioxide is released into the atmosphere.

6. The game starts at 430 ppm of carbon dioxide and if it passes a random number between 470 and 510 (that nobody knows), the world ends.

7. If the world ends, nobody gets anything, but if you make it to round 5 without the world ending, the top 5 players (ranked by money) get rewarded according to their placement.

Sounds simple enough right? Well, a few 8th grade classes got to play this game during World History, and so far NONE of them survived. This game was made to teach us how capitalism can encourage greed and working against the common good, and it did a very good job at that. However, I had an unanswered question: What is the optimal strategy?

To begin, I coded a simulation of this game in Python, along with basic AI players that would make choices according to three quantities: how much money it has, the amount of carbon released, and the average production amount of the other players. The AIs have different, fixed weights for each of these quantities. In other words, the importance they assign to each quantity varies. For example, one AI could care a lot about money, while one could care more about carbon. Each AI decides what percent of their money to spend in production for each round based on those numbers.

I decided to use an evolution algorithm for this project. The simulation is divided into eras. Each era, 100 games take place, each with 7 random players from a pool of 70 AIs. The top 10 players at the end of the era will pass on their weights, with small changes (aka mutations), to the next era. Here were the results.

The first thing I noticed was that win rates got astonishingly high. As high as 67%. However, the moment the win rate spiked, greed took over and it fell to below 20%. The fall was extremely sudden, happening in less than an era.

We can see that this decline was likely caused by a sudden change in both the average weight of a player for carbon and the average weight for money. However once this sudden change happened, the win rate never got above 40% again. Once the players discovered this greedy playstyle, they held onto it. It seems that the more the AIs care about the amount of carbon, the better their chances of winning.

Although the AIs may not have found the optimal playstyle for the thingamabob game, they did show how selfishness can easily spread. For the first three eras, we can clearly see that money had a very small weight, even going negative. Carbon also had a very small weight. Then, without warning, the players became more selfish, caring more about money and less about carbon. This led to everyone but the richest being worse off. Since only the richest would ever win, weights that encouraged more selfishness spread around, easily outcompeting any altruism.

What is even more concerning about this game is its relevance to real life. Companies who choose to act more ecofriendly have to spend more money, allowing them to be outcompeted by other companies. Although the thingamabob game isn’t a full representation of real life, we can still learn a surprising amount of knowledge. This seemingly simple game teaches us a lesson about money and carbon: maybe all we need to stop global warming is a change in our values.