What Is the Shadow of the Future in Game Theory?
Robert Axelrod's phrase for how the expectation of meeting again shapes what you do now. Tit for Tat won two computer tournaments on it, and a 2015 reanalysis says the win has conditions.
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Two people share a flat for a year. One of them leaves dishes in the sink on a Monday. The other can wash them, leave a note, or stack them on the other’s bed, and the choice depends mostly on whether there is a Tuesday. Take away the Tuesday, say by making this the last day of a sublet with no forwarding address, and the dishes stay where they are.
That Tuesday is what Robert Axelrod called the shadow of the future in The Evolution of Cooperation (1984). In his computer tournaments of the repeated prisoner’s dilemma, the expectation of meeting the same opponent again made present cooperation pay, and a negligible chance of another meeting made defecting the safe choice every time.
The winner of both tournaments, Tit for Tat, was the simplest entry: cooperate first, then copy the other player’s last move. It was submitted by Anatol Rapoport and won a field of 14 entries in the first round and 62 in the second. Copying only pays if the game goes on, which is what the term says. Fehr and Gächter’s experiment at the University of Zurich split subjects the same way, between groups that stayed together and groups reshuffled every round.
Lobstermen who fish one bay for decades live under a very long shadow, and their warnings start with a rope on a buoy. The result has a limit. Rapoport, Seale and Colman (PLoS ONE, 2015) argue that Tit for Tat’s success depends on the tournament’s design, the criterion for success and the payoff values.
Frequently asked questions
How were Axelrod’s tournaments run?
Each program played every other for about 200 rounds, and all eight top-ranked entries in the first tournament were “nice”, meaning they never defected first. Tit for Tat was one of them; the first field also included a random baseline.
Does Tit for Tat always win?
No. Rapoport, Seale and Colman (PLoS ONE 10(7): e0134128, 2015) argue that its success depends on three things: how the tournament was set up, which success criterion is used and the payoff values chosen in the prisoner’s dilemma matrix.