The Public Goods Game

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This is an adapted excerpt from Dan Ariely’s Predictably Irrational

This thought experiment offers an interesting example The Tragedy of the Commons. Imagine that I offer you and three other people £10 each, which is yours to keep. But I also give you an opportunity to make more money. You can put as much of your £10 as you want in the “group pot”. Once all the players have privately decided how much of their money to put in the group pot, all the money doubles and then is split evenly among the four participants, regardless of how much money each individual contributed. How much of your £10 would you put into the group pot? If all four of you put in £10, the group pot would double from §40 to £80, be divided four ways, and each of you would take away a nice £20.

So let’s say you put in your £10, thinking that the other players will do the same. Once the pot is divided, however, you only get £15 back, not £20. What happened? It turns out that one of the other players, Bernie, decided to cheat. At the beginning of the game, Bernie realized that he would make the most money if he withheld his £10 while everyone else contributed to the central pot. So Bernie kept his £10 while the other three players placed their £10 in the central pot, making the total £30. This doubled for a total of £60, subsequently split four ways (remember, Bernie gets the proceeds of the group pot, whether or not he contributes), and each of the three contributors get £15. Bernie, meanwhile, has £25 ( his original £10 plus £15 from the split), more than any other player.

If given a chance to play the same game again with the same players ( I give you all new £10 bills), how would you play this time? You don’t want to be too trusting because you know Bernie might defect again. So you only put in 4£. It turns out that the other three players feel the same way and make the same decision, making the total in the group’s pot £12 (Bernie again does not put in any money). The pot doubles to £24, which is split evenly among four people. Each of the three contributing players gets £6 (In addition to the 6£ they kept for themselves), while Bernie winds up with £16 in total.

Now, your trust has been eroded. You play a few more games, but you don’t put in any of your money. Each time you end up with the 10£ you started with. You don’t lose anything, but since you don’t trust others to behave in a cooperative way, and neither do the other players, you don’t gain anything either. In contrast, if you and the others had acted cooperatively, each of you would have wound up with as much as £20 per game.

Viewed this way, the Public Goods Game illustrates how we, as a society, share the public good of trust. When we all cooperate, trust is high and the total value to society is maximal. But distrust is infectious. When we see people defect by lying in their ads, proposing scams, etc., we start acting similarly: trust deteriorates, and everybody loses, including the individuals who initially gained from their selfish acts.

Further “reading”

See Nicky Case’s The Evolution of Trust for a memorable visualization of this concept.

Related

• See my Google Colab notebooks for a version of this game :)