In modern game theory study, one of the first games to be introduced to students is the Nash Bargaining Game (named after the famous mathematician John Nash, the subject of the Hollywood film A Beautiful Mind).
Economists and in particular environmental economists love this game because the premise of it depends on a finite good (e.g. a limited amount of money) which is valuable to all players. There are many variations to this game, but the usual goal of the game is for each player to maximise the amount of the good they have by the end of the game (e.g. the person with the most amount of money wins), but there is also a maximum threshold level to which the all of the players’ goods must sum to (e.g. the sum of the accumulated money by all players has to be less than £100). In different variations of the game, bypassing this sum may mean a lose for all players involved, or missing out on a special bonus amount of money.
The actual play of the game is very simple: Every player starts with the same amount of good that, summed together, is above the threshold level. There are a defined number of rounds, and during each round each player (generally secretly) forfeits however much of the good they feel like (this can be 0), and at the end of each round the arbitrator announces how much money has been given up.
If that last two paragraphs were gobbledygook to you, I apologise! But perhaps a description of a new variation by zoologist Manfred Milinski will make sense to you; I encourage you to play it with your friends the next time they suggest a round of poker.
The rules of this game are:
- Each player starts out with a set amount of money. For the purposes of explaining, I will say £20 (raise or lower this according to the level of income of the poorest member of your group!).
- The group needs to collectively donate half of the total sum of the starting amount (so if you have six players who each had £20 to start off with, the group needs to donate £60, that is 6×20/2) to a ‘fund’. If this ‘fund’ is not met by the end of the game, there is a 90% chance that everybody will lose all their money. If it is met, everybody gets to keep the money they have left over after donating.
- You have ten rounds to do this. Each round consists of each player secretly donating their money to the fund, and at the end of the round an arbitrator announces how much money there is in the fund.
- Players are allowed to discuss strategy with each other.
It may not immediately become apparent to you, but this game is an attempt to emulate, at a very basic level, international climate change negotiations. Each player can be seen as a negotiator from a country, each trying to play the game to achieve what’s best for themselves. If the sum of their (expensive) pledged actions are not large enough, a climate catastrophe is upon us and all the money they did not spend (and more!) on helping to mitigate climate change will be spent attempting to adapt to it.
Unfortunately, only 50% of Milinski’s experimental groups managed to ‘save the world’. Can you and your friends do better?
I see a couple of ways you could play this game:
- The arbitrator (you could call them Gaia!) comes up with the money and hands it to everyone. All money that goes in the ‘fund’ goes back to the arbitrator. Similary, if everyone loses, all the money returns to the arbitrator. This is a slightly boring game though, and friends may feel more generous with their money, as it will be going back to the person who originally provided it. However, if this is the only way you can get your friends to play this game, this may be the way to do it. If not, however, to make things more interesting:
- Each player comes up with their own money. A ‘bad’ charity, that is a charity that no one would ever consider giving money to, is agreed on by everyone. An especially good ‘bad’ charity would be one that is against everyone’s beliefs. So if you’re with a bunch of environmentalists, maybe a coal lobby. Or if you’re with technologists, a luddite group. You get the picture. If the game is lost, all the money goes to this charity. If the game is won, the money in the fund can either go to funding your next party or to a good charity. I suggest funding your next party, because a good charity may also make everyone feel a bit more generous with their money.
Okay, go out there and see what your friends are made of! If you do play this game, please let me know how it goes.
The idea of a ‘bad charity’ is influenced by Ian Ayres’s StickK.com. This site allows you to name a charity you dislike and set yourself commitments. If these commitments are broken, you donate a set amount of money to a pre-named charity you dislike.
Podcast: Fixing Climate is Going to Cost You – Planet Money – npr.org