Game theory application

So today I participated in a paid experiment entitled "Game Theory, Culture and Institutional Path Dependence". A study funded by the National Science Foundation, it intends to provide insight into certain features of decision making. But that is none of my business really. I was signed up for it because of the enticing 15/hr rate, and also because Ren Jie had previously earned tonnes for just playing games. Since I have the time (well, did I?), I was like 何乐而不为?

Basically, the gameplay required me to make decisions choosing strategies in each individual game. Everything was done on the computer, and there was no way of knowing who your partners were. A total of 200 rounds were played, plus extra rounds given in a 90% chance basis. The payoff matrix was as followed:


Clearly, choosing B would be my dominant strategy, since it makes me strictly better of regardless of what player 2 chooses (I'm player 1). If the player 2 plays his dominant strategy too, both of us will end up achieving the Nash equilibrium. After playing the dominant strategy repeatedly for like 30 rounds, I got bored (because the partners kept on playing the same strategy too) and started thinking whether there was any other way to play the game. Then it struck me that I could actually apply my game theory skills in the game.

Instead of playing the dominant strategy, both me and my partners could actually be better off if we "collude". We could each take turns sacrificing our payoffs to make the others profit more. For instance, instead of getting (5,5) all the time, we could get (4,14) in the first round, (14,4) in the second round, (4,14) again in the third round and so on. In that way, the average payoffs would be higher for us.

Hence, I started sending out "signals" to my partners. I began to commit in playing A and B alternately, and to my delight, my partners took the hint after like just 2 rounds. So from that point onwards, we happily "colluded" all the way till the end of the game.

Too bad there was like only about 215 rounds. In the end I got 33 bucks from the game, plus a base pay of 5 bucks. That's a total of 38 dollars (tax free since it's in cash) in 70 minutes!! Only if they have such games every week...