Information and timing

Original article (link) posted: 03/08/2005

With imperfect monitoring, shrinking the period length implies less discounting from one period to the next, but also leaves less time for players to observe signals relevant to behavior.
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So there are two effects of reducing the period length: an effective increase in patience, which we know from the monotonicity result tends to increase the average value set, and a worsening of information, which Kandori (1992) elegantly shown to decrease the set of equilibrium values. Either of these two effects can dominate in a particular case.
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If the period of fixed action is a year, under plausible parameter values cooperation could be sustained very profitably. But suppose that instead auctions can be changed daily. The only way to encourage cooperation is to punish the event that there is no goods news, which has probability near 1 whether anyone shirks or not.
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Ironically, in this case the player's ability to respond quickly to information destroys all possibility of cooperation. This suggests that delaying the release of information might actually be valuable in partnerships; Abreu, Milgrom and Pearce (1991) show that for high "delta", information delays can virtually eliminate the inefficiency that Radner, Myerson and Maskin (1986) identified.
(Pearce (1992), p.156)

Abreu, Milgrom and Pearce (1991) "Information and Timing in Repeated Partnerships" Econometrica, 59
Kandori (1992) "The Use of Information in Repeated Games with Imperfect Monitoring" RES, 59-3
Radner, Myerson and Maskin (1986) "An example of a Repeated Partnership Games with Discounting and with Uniformly Inefficient Equilibria" RES, 53