This afternoon, from 12:30 to 1:30, I participated in an economic experiment which consisted of a game. Within the game, there were three groups of five. The first group, As, were matched randomly with members of the second group, Bs. Each of these players started with 35 tokens, each worth 1/5th of a Pound. There was a third group, Cs, who got 25 tokens.
The game was only played once (ie. not iterated).
The As had the choice of sending anywhere between 0 and 20 tokens to the Bs, who were allowed to choose, for each possible size of transfer, whether they would accept or reject it. If the B accepted, the A got 50-X tokens, where X was the size of the transfer. (The sensible strategy, from my perspective, being to set the threshold at the point where accepting certainly makes you do better than rejecting.) The B, in this case, would get 30+X. If the B rejected, the B would keep 35 tokens and the A would lose one. For each A-B pair where a transfer took place, all Cs lost one token. Cs did not make any choices over the course of the game.
The Cs, therefore, would end up with somewhere between 20 and 25 tokens, depending on how many pairs cooperated, and therefore earn Â£4 to Â£5. The As, if they transferred one token and the transfer was accepted, would earn 49 tokens, while the paired B would get 31 (A: Â£9.80, B: Â£6.20). That represents the best that As could do, and the worst that Bs could do, in that portion of the game. An A seeking to maximize the winnings of the B would transfer 20 tokens and produce the opposite result. For a transfer of ten tokens, the A and the B would each end up with 40 tokens (Â£8).
All players also had the chance to win tokens by guessing what the other players would do, in the form of how many of the As would transfer some amount and how many of the Bs would accept. Getting one right earned you 50p and getting both right earned you Â£1. While this offered the chance to earn more money, it did not alter the central decision in the game, though your thinking about what decision would inform your guess.
My thinking was that, firstly, every A would make a transfer because the worst they could do is lose four tokens and they could gain as many as 19. Additionally, each B would accept a transfer, for precisely the same reason. Moreover, it would be awfully boring to sit in a room for an hour listening to rules and then not actually play the game in an active way.
I was an A, one of the two actively deciding groups. I decided to transfer 7 tokens, one above the minimum amount where the payoff to the B of accepting exceeded the amount that would be had from rejecting. For a B, accepting 7 tokens means earning Â£7.40, while rejecting it would mean getting Â£7. That said, for the B to accept costs all five Cs one token each, for a total loss among the Cs of Â£1. For the A, transferring seven tokens means getting Â£8.60 if the transfer is accepted and Â£6.80 if it is rejected (which would be against the interest of the B, provided they donâ€™t care about the Cs).
In the end, I won Â£7.30, which means that my offer was rejected but that I guessed properly that the four other As would all make an offer. In addition to the Â£7.30, I got Â£3 just for playing.
The outcome of my section of the game, therefore, left me with Â£6.80, the B with Â£7, and did not reduce the number of tokens held by the group of Cs. Had by B accepted, they would have walked away with another 40p and I would have earned another Â£1.60. Our collective gain of Â£2 would have been twice the collective loss of the Cs. I suppose either concern for the Cs or the fact that I would earn more from the transaction caused them to reject my strategy of the minimum offer for clear mutual gain.