Hans-Theo Normann, Brian Wallace (2012) “The impact of the termination rule on cooperation in a prisoner’s dilemma experiment." International Journal of Game Theory, August 2012, Volume 41, Issue 3, pp 707-718. link to Springer; working版本：ucl.ac.uk 提供的 [PDF]；hhu.de 提供的 [PDF]；
Note by yinung
這篇原是 DICE 的 working paper (see 本站另一篇 PO 文），現在刊出來了。
主要結論 （in abstract):
此文研究3種 PD game 實驗回合結束的方式 (告知結束回合、不告知結束回合、隨機結束)，比較合作率之不同。 1. 三種結束方式不影響合作率 2. 隨機結束方式不會提高合作率 (相對於告知結束回合)；不同繼續玩 (隨機結束) 之機率高低 (continuation probability) 亦不影響合作率 3. 結束方式會影響 over time 和 end-game 行為 4. 預期玩的回合愈長，合作率愈高
可引述
三種 termination rule:
- finite horizon: Flood (1952) and Rapoport and Chammah (1965) … it is well known that stable cooperation does occur also in finitely repeated games
- unknown horizon: Fouraker and Siegel 1963
- random-stopping rule: to terminate the experiment (Roth and Murnighan1978; Axelrod 1980)
End-game effects: Morehous (1966) … defection rates increase towards the end of the game when the horizon of the game is known to be finite. … used a probabilistic termination rule so that “end-game effects were successfully avoided” (Axelrod 1984, p. 42). Murnighan and Roth (1983, p. 284) argue that “consideration of end-game play is less critical” with the random termination rule. Holt (1985, p. 320) makes the same point. 也有人在分析結果時，去掉最後幾回合 贊同應用隨機結束 With finitely many periods, the theory is bland; by contrast, the random termination rule “permits the nature of the equilibrium outcomes to be controlled” (Roth and Murnighan 1978, p. 191) Selten and Stoecker (1983) further noted that subjects learn to anticipate the endgame effect in that this effect is shifted to earlier rounds when a supergame with a finite horizon is repeated several times (see also Andreoni and Miller 1993) 隨機結束機率高者，使合作率較高 （與本文結果不一致），但重覆的實驗不能確定此一結果 Roth and Murnighan (1978) found that a random stopping rule with higher continuation probability does lead to more cooperation in the prisoner’s dilemma. However, in the modified setup analyzed in Murnighan and Roth (1983), this could not be confirmed. Dal Bo (2005) 發現隨機結束機率(在 supergame 玩 10 次後) 有重要影響
本文之實驗
至少玩 22 回合 (??? 不知何義，待了解… 因為結束回合數不一定一樣), 4 情境、每情境有15組人
- Know
- Unknow
- RandomHigh (5/6 繼續機率)
- RandomLow (1/6 繼續機率)
supergame 不重覆 （？？）Subjects were rematched after the first supergame. 另外有 Shorter Horizon 額外較短實驗
- Known5 （9組，2人一組）
- Known10 （11組）
- Random5+5 (11組；至少5回，5/6 繼續機率，平均期望值＝10回，恰與 Known10 對照)
合作率 要小心合作率的定義！（各文獻不一定相同) 其 Table 2 中的合作率是 cooperte choices (不是 cooperate outcome, 所以22回合中才最多有 44 個 cooperate choices) 此文皆是利用 cooperate choice 來分析，Harvey Wichman (1970, J of Personality and Social Psychology) 也是用此定義 有的文獻合作率的數字是 cooperate outcome (兩人皆是 cooperate choice 才算合作） (引文)…In order to take the possible dependence of observations between paired players into account, we count each participating pair as one observation. Matrix of the game 從合作到背叛，邊際利得只有 1000－800 ＝ 200, 反而對手損失 750 較多；若因此而雙方開始不合作，每期邊際損失 250，根本不值得背叛；但是一旦被背叛，當次邊際損失 700， 要3次背叛才得以報復。
================================
背叛 合作
背叛 (350, 350) (1000, 50)
合作 (50, 1000) (800, 800)
================================
文中所述之 5 個 results
- Result 1. The termination rule does not significantly affect average cooperation.
2種隨機結束和告知回合、不告知 等 treatment 合作率無顯著不同 (Kruskal-Wallis test)
- Result 2. There is a negative and significant time trend in treatments Known and RandomLow.
Known 和 RandomLow 合作率有下降趨勢 (significant time trend)
- Result 3. A significant end-game effect occurs in all treatments except Unknown。
- Result 4 The termination rule does not significantly affect average cooperation rates in treatments Known5, Known10, Random5+5.
- Result 5 The length of the horizon of the game significantly increases cooperation rates.
本文所用無母數統計方法
Abstract
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