An afternoon game

2005-10-10

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 £4 to £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: £9.80, B: £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 (£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 £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 £7.40, while rejecting it would mean getting £7. That said, for the B to accept costs all five Cs one token each, for a total loss among the Cs of £1. For the A, transferring seven tokens means getting £8.60 if the transfer is accepted and £6.80 if it is rejected (which would be against the interest of the B, provided they don’t care about the Cs).

In the end, I won £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 £7.30, I got £3 just for playing.

The outcome of my section of the game, therefore, left me with £6.80, the B with £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 £1.60. Our collective gain of £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.

{ 5 comments… read them below or add one }

B October 10, 2005 at 2:22 pm

Milan:

Maybe Staples is playing a “minimum offer for clear mutual gain” strategy?

Milan October 11, 2005 at 12:46 am

As consumers, we might be most like the Cs in this game: not particularly able to better our lot, in the face of possible collusion between retailers, but quite capable of suffering as the result of successful negotiations between them.

Milan July 22, 2007 at 9:43 pm

Economists often refer to this sort of behaviour as irrational. In fact, it is not. It is simply, as it were, differently rational. The things that money can buy are merely means to an end—social status—that brings desirable reproductive opportunities. If another route brings that status more directly, money is irrelevant.

Money isn’t everything

Jul 5th 2007
From The Economist print edition

. November 7, 2007 at 10:03 am

Tim Darling’s “Surefire Strategy” for winning at Monopoly sounds plausible — a great way to suck all the fun out of the game, leaving behind nothing but the relentless pursuit of victory.

* At the beginning of the game, focus on acquiring a complete C-G (Color Group) in Sides 1+2, even if it means trading away properties on Sides 2+3. After acquiring one of these C-Gs, build 3 houses as quickly as possible: no more houses, no less!
* Once your first C-G starts to generate some cash, focus on completing a C-G and building 3 houses in Sides 3+4.
* Note: 3 houses is the “sweet spot” in the game as shown in Table 1 below. That’s where you’re making the best use of your money.
* Single properties are the least good investment if you don’t build on them.
* The only exception to the above rules are when you need to acquire stray properties to prevent your opponents from completing their C-Gs to accomplish the above strategy.

. January 2, 2009 at 3:52 pm

“Economists were long puzzled, for example, by the routine outcome of a game in which one player divides a sum of money between himself and a competitor, who then decides whether the shares are fair. If the second player decides the shares are not fair, neither player gets anything.

What is curious about this game is that, in order to punish the first player for his selfishness, the second player has deliberately made himself worse off by not accepting the offer. Many evolutionary biologists feel that the sense of justice this illustrates, and the willingness of one player to punish the other, even at a cost to himself, are among the things that have allowed humans to become such a successful, collaborative species. In the small social world in which humans evolved, people dealt with the same neighbours over and over again. Punishing a cheat has desirable long-term consequences for the person doing the punishing, as well as for the wider group. In future, the cheat will either not deal with him or will do so more honestly. Evolution will favour the development of emotions that make such reactions automatic.”

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