Three Steps Ahead

Theoretical Economics, 10(1), 203-241

39 Pages Posted: 13 Jun 2012 Last revised: 5 Feb 2015

Date Written: March 28, 2014


We study a variant of the repeated Prisoner's Dilemma with uncertain horizon, in which each player chooses his foresight ability: that is, the timing in which he is informed about the realized length of the interaction. In addition, each player has an independent probability to observe the opponent's foresight ability. We show that if this probability is not too close to zero or one, then the game admits an evolutionarily stable strategy, in which agents who look one step ahead and agents who look three steps ahead co-exist. Moreover, this is the unique evolutionarily stable strategy in which players play efficiently at early stages of the interaction. We interpret our results as a novel evolutionary foundation for limited foresight, and as a new mechanism to induce cooperation in the repeated Prisoner's Dilemma.

Keywords: Limited foresight, Prisoner's Dilemma, limit ESS

JEL Classification: C73, D03

Suggested Citation

Heller, Yuval, Three Steps Ahead (March 28, 2014). Theoretical Economics, 10(1), 203-241, Available at SSRN: or

Yuval Heller (Contact Author)

Bar Ilan University ( email )

Dept. of Economics, Building 504
Bar Ilan University
Ramat Gan, 5290002
+972 5252 82182 (Phone)

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