Bó, Pedro Dal (2005) “Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games." American Economic Review, Volume 95, Number 5, December 2005 , pp. 1591-1604(14). ; brown.edu 提供的 [PDF] ; DOI: http://dx.doi.org/10.1257/000282805775014434 ;另見本站另一篇同作者在 2005AER 的文章;
==notes by yinung==
本篇以有限重覆賽局 PD game 為對照,比較無限重覆賽局之影響。
主要針對 equilibrium actions and equilibrium outcome ,而非 equilibrium strategies (可能要參考 Dale O. Stahl II (1991))
本文採用之賽局結構
PD1 PD2 ============================= ============================= 合作 背叛 合作 背叛 合作 (65, 65) (10, 100) 合作 (75, 75) (10, 100) 背叛 (100,10) (35, 35) 背叛 (100,10) (45, 45) ============================= =============================
有限賽局的設計(Finitely Repeated Games):
共有 1, 2,4 回合三種
子賽局均衡之推導,參見 Dale O. Stahl II (1991)
the set of subgame perfect equilibria can be calculated using the results in Dale O. Stahl II (1991).
主要發現:
高隨機繼續玩機率,會有較高的合作率。
…find strong evidence that the higher the probability of continuation, the higher the levels of cooperation.
引文:
針對 one-shot PD game; 合作率 9%; 無限重覆 (繼續機率=3/4) 合作率 38%。
…in the one-shot prisoner’s dilemma games studied here, the cooperation rate is 9 percent, for a probability of continuation of 3/4, it is 38 percent.
在有限重覆賽局中,也有終局效果 end-game effect,在最後一回合,合作率較低。
I find that the level of cooperation in the final round of the finitely repeated games is similar to the level of cooperation in one-shot games.
Abstract:
While there is an extensive literature on the theory of infinitely repeated games, empirical evidence on how “the shadow of the future" affects behavior is scarce and inconclusive. I simulate infinitely repeated prisoner’s dilemma games in the lab with a random continuation rule. The experimental design represents an improvement over the existing literature by including sessions with finite repeated games as controls and a large number of players per session (which allows for learning without contagion effects). I find that the shadow of the future matters not only by significantly reducing opportunistic behavior, but also because its impact closely follows theoretical predictions.
References
- 子賽局均衡之推導和 rate of cooperation outcome 的定義 (??)
Stahl, Dale O., II. “The Graph of Prisoner’s Dilemma Supergame Payoffs as a Function of the Discount Factor." Games and Economic Behavior, 1991, 3 (3), pp. 368 – 84.