Risk aversion and incentive effects: Comment

Harrison, G. W., Johnson, E., McInnes, M. M., & Rutström, E. E. (2005). Risk aversion and incentive effects: Comment. American Economic Review95(3), 897-901.   [PDF] ucsd.edu ; [PDF] ucsd.edu;[本站PDF]

==noted by yinung==

這是 Harrison et al. (2005) 對 Holt and Laury (Risk aversion and incentive effects ,2002,  AER) 這一篇的挑戰:


Harrison et al. (2005, AER) 對 Holt and Laury (2002, AER) 質疑有「order effects」(An order effect occurs when prior experience with one task affects behavior in a subsequent task., p.897) 並重新做實驗,比較1x10x 和只有 10x 的結果,如下圖。
(註:Hypothetical 指只有實驗中的假設報酬數字放大,並沒有實際報酬的放大)。
不過,Harrison et al. (2005) 在畫下圖的時候,不是用實際的數字,而是用 ordered probit 預測結果畫的



Risk aversion and incentive effects

Holt, Charles A., and Susan K. Laury. “Risk aversion and incentive effects." American economic review 92.5 (2002): 1644-1655. [PDF] ucsd.edu; [PDF] alaska.edu;

see also

Harrison (2005) 對上一篇的挑戰: Risk aversion and incentive effects: Comment (2005,  AER)][PDF] ucsd.edu;[本站PDF]

以及 Holt 的回應 : Risk Aversion and Incentive Effects: New Data without Order Effects (2005,  AER)


==Noted by yinung==


decision task 1. 先答完10題,事後從中「隨機」選出一題來玩,並依結果付 payment。再問是否進行 decision task 2

decision task 2. 假的 20x 報酬,但和 decision task 1 相同 (high-hypothetical ONLY treatment)

decision task 3. 真的 20x 報酬,但和 decision task 1 相同 (high-hypothetical Real Only treatment)

decision task 4. 和 decision task 1 相同,用來驗證「原來在 task 1 的風險偏好是否因 wealth effects 改變」

low-payoff treatmen

high-hypothetical treatmen

  • 即使是 Holt, 在 AER 發表時,仍然要引用 Kahnenman and Tversky 的辯論 (引在最下方)
  • Incentive Effects? 什麼動機
    measured as the number of safe lottery choices in each treatment (p.1653)
  • safe (lottery) choices 安全選項(見下圖):
    指前4個選 Option



控制 wealth effects: 要進行第2個 high-payment 實驗時,要先放棄第1個實驗得到的錢
To control for wealth effects between the high and low real-payoff treatments, subjects were required to give up what they had earned in the first low-payoff task in order to participate in the high-payoff decision.

==Harrison et al. 對本篇的 procedures 概述==

The subjects in the HL design were given sequences of three or four tasks, as shown in Table 1. Task #1 involved choices over lotteries with a baseline level of prizes, which we will refer to as the “1X scale.” Task #2 involved hypothetical choices over prizes with a scaled-up level of prizes, either 20X, 50X, or 90X. Task #3 repeated task #2, but with choices that involved real payoffs. Task #4 was a return to the baseline task with real 1X prizes. In some sessions, subjects were not given task #2 or task #3.1。(yinung: 呵… 這比Holt 寫得還簡要清楚)

==Kahnenman and Tversky==

The implication, that low laboratory incentives may be somewhat unrealistic and therefore not useful in measuring attitudes toward “real-world" risks, is echoed by Daniel Kahneman and Amos Tversky (1979, p. 265), who suggest an alternative:

Experimental studies typically involve contrived gambles for small stakes, and a large number of repetitions of very similar problems. These features of laboratory gambling complicate the interpretation of the results and restrict their generality. By default, the method of hypothetical choices emerges as the simplest procedure by which a large number of theoretical questions can be investigated. The use of the method relies on the assumption that people often know how they would behave in actual situations of choice, and on the further assumption that the subjects have no special reason to disguise (掩飾) their true preferences. (在實驗中,受試者沒有特別理由要掩飾他們的真實偏好


Risk Aversion and Incentive Effects: New Data without Order Effects

Holt, Charles A., and Susan K. Laury. “Risk aversion and incentive effects: New data without order effects." American Economic Review 95.3 (2005): 902-912.  source: PDF [本站]

這篇是 Holt 回應 Harrison et al. (2004) 對先前發表(Holt and Laury, 2002, AER),有無 order effects 的質礙


payment 愈高,risk averse 愈明顯,但沒有 order effects。

==notes by yinung==

  • 用這來判斷 risk averse: The average number of safe choices(查細設定?)
  • 此新實驗改用 a single lotterychoice menu?
  • 1st treatment(odered choices): low-pay -> high-payment (20X)
  • 另外4個 (unordered) TM
  • 用兩個無母數檢定


==Game online==



  • Harrison, G. W., Johnson, E., McInnes, M. M., & Rutström, E. E. (2005). Risk aversion and incentive effects: Comment. American Economic Review, 95(3), 897-901.
  • HOLT, Charles A.; LAURY, Susan K. Risk aversion and incentive effects. American economic review, 2002, 92.5: 1644-1655.

The Lure of Authority: Motivation and Incentive Effects of Power*

Fehr, Ernst, Holger Herz, and Tom Wilkening. 2013. “The Lure of Authority: Motivation and Incentive Effects of Power." American Economic Review, 103(4): 1325-59. DOI: 10.1257/aer.103.4.1325; ******;

Supplementary Materials:
Online Appendix
(469.58 KB) | Download Data Set (3.84 MB) | Author Disclosure Statement(s) (90.26 KB)


共玩10回合 (先玩 7 回合的 sigle-player; 再玩正式的 10 回合)

0.1. 配對 principal 和 agent

0.2. 兩者看到36張牌, 代表36個projects; 其中有一張牌翻開, 代表 outside option (很小的報酬); 其餘 35 張牌看不到, 但其中有一張紅色牌 Project 1代表 principal 最偏好的, 而另一張藍色 project 2 代表 agent 最偏好的; 其它 33張牌報酬皆 = 0. 這個報酬設計是讓 subject 兩者會選 outside option, 相對於隨機選 project。


1.  principal 決定是否授權 (但 agent 尚不知道)

2. 雙方 “各自" 選擇努力水準 E/e (in a quadratic cost function, E/e ~ {0,5,10,… 95, 100}) , 努力水準和得知 project 的結果成正比

努力成本: gP(E)=25(E/100)^2;   gA(e)=25(e/100)^2

得知結果機率 pr(E)/pr(e); 不知結果: 1-pr(E/e)

3. 問雙方對對方努力水準之預期

principal 依授權決定, 先被問不授權 (授權) 下之 “預期 agent" 之努力水準, 再問授權 (不授權) 下之 “預期 agent" 之努力水準

agent 則被同時問; (預期對和錯與 payoff 無關)

4. agent 得知是否被授權; 並且 subject 依其努力水準, 隨機得知所有 project 的 payoffs (但還不知對手的努力和是否知道 project 之結果)

5. principal/agent 建議一個 project (但如果 agent/principal 是否知道 payoff, 取決於上一個 stage 4)

6. principal/agent 做出 project 的選擇, 並計算雙方的 payoffs

==notes by yinung==

這篇是討論 principal 對保留權力 (power) 的實驗, 也算是 group behavior 的創意研究。終於有人進行和我之前研究想法很類似的實驗研究了….


principal 願意犧牲一些利得,以保留決策權

… the principals are willing to sacrifice some of their earnings to keep authority suggests a preference for the decision right.

principal 在 “被知會但沒有決定權" 和 “未被知會" 兩種情況, 理論上效用應該無差異

Conditional on effort, an expected utility maximizing principal who is the subordinate of an informed agent should thus be indifferent between the case where she is informed and overruled by the agent and the case where she remains uninformed.

H0: 若 principal 對於被 overruled 有負效用, 則下一次會保留授權

… If, however, a principal experiences a nonpecuniary disutility from being overruled, her behavior after these two outcomes may differ: the principal may be less willing to delegate in the next period if overruled.

…an individual may maintain control in order to mitigate the potential for regret. (subjects want to avoid ex post regret about their choices—a hypothesis that was introduced by Loomes and Sugden (1982)… Regret aversion is a form of reference dependent utility and is based on the idea that subjects derive disutility from regret that arises by comparing their actual ex post outcomes with those the subject could have had by choosing a different action.


… these papers (含 Bartling and Fischbacher 2012, Coffman 2011) study the assignment of punishment in response to the allocation choices of either a principal or a delegate, our article studies the willingness of the principal to delegate and the willingness of a principal and an agent to invest effort in response to the assignment of decision rights.

this literature (指 the literature on the hidden costs of control by Fehr and Rockenbach 2003; Fehr and List 2004; Falk and Kosfeld 2006; Charness et al. 2012) shows that the exercise of control reduces an individual’s positive reciprocity towards the principal, our article shows that lack of control has demotivating consequences on subordinates that induce them to act against their material self-interest.


Authority and power permeate political, social, and economic life, but empirical knowledge about the motivational origins and consequences of authority is limited. We study the motivation and incentive effects of authority experimentally in an authority-delegation game. Individuals often retain authority even when its delegation is in their material interest—suggesting that authority has nonpecuniary consequences for utility. Authority also leads to overprovision of effort by the controlling parties, while a large percentage of subordinates underprovide effort despite pecuniary incentives to the contrary. Authority thus has important motivational consequences that exacerbate the inefficiencies arising from suboptimal delegation choices.

On the Theory of the Competitive Firm Under Price Uncertainty*

Agnar Sandmo (1971) “On the Theory of the Competitive Firm Under Price Uncertainty."  The American Economic Review, Vol. 61, No. 1 (Mar., 1971), pp. 65-73.  URL: http://www.jstor.org/stable/1910541; lse.ac.uk 提供的 [PDF];****

==note by yinung==

這篇利用 risk-averse 的 utility function 假設, 證明完全競爭廠商, 在有 price uncertainty 下, 最佳決策是


where c'(x),邊際成本, is increasing in x

Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games

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))

I focus on equilibrium actions and outcomes instead of equilibrium strategies,
I find that the percentage of outcomes in which both subjects cooperate is almost 19 percent when it is an equilibrium, whileit is less than 3 percent when it is not.


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).


…find strong evidence that the higher the probability of continuation, the higher the levels of cooperation.


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.


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.


  • 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.

The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence

Dal Bó, Pedro ; Fréchette, Guillaume R. (2011) “The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence." The American Economic Review, Volume 101, Number 1, February 2011 , pp. 411-429(19). DOI: http://dx.doi.org/10.1257/aer.101.1.411;brown.edu 提供的 [PDF] ; Download Data Set (355.92 KB) | Online Appendix (284.08 KB);

==notes by yinung==

此文用的 PD game,進行無限重覆賽局的實驗。see also 另一篇也在 AER 2005 年刊出的和有限重覆 PD game 之比較(或參目本站的另一篇 note)。

          合作     背叛
 合作    (R, R)   (12, 50)
 背叛    (50,12)  (25, 25)
繼續玩之機率:1/2, 3/4


The 18 experimental sessions were conducted between July 2005 and March 2006. A total of 266 New York University undergraduates participated in the experiment, with an average of 14.78 subjects per session, a maximum of 20 and a minimum of 12. The subjects earned an average of $25.95, with a maximum of $42.93 and a minimum of $16.29. In the treatments with δ =
1/2 and δ = 3/4 the average number of rounds per match was 1.96 and 4.42 respectively, and the maximum was nine and 23 respectively.


…each subject participated in between 23 and 77 infinitely repeated games

…Previous experimental evidence has shown that subjects often fail to coordinate on a specific equilibrium when they play a small number of infinitely repeated games



…the level of cooperation decreases with experience and converges to low levels

…the level of cooperation does not necessarily increase and may remain at low levels even after significant experience is obtained.

…this evidence suggests that while being an equilibrium action may be a necessary condition for cooperation to arise with experience, it is not sufficient.

若 cooperation 是 risk dominant, 則合作隨著經驗增加而上升

If we consider together all sessions for which cooperation is risk dominant, we find that cooperation increases on average as subjects gain experience….Risk dominance has been used as a selection criterion in the study of coordination games.


…These results show how difficult it is for experienced subjects to sustain high levels of cooperation. They cast doubt on the common assumption that agents will make the most of the opportunity to cooperate whenever it is possible to do so in equilibrium.

…In fact the impact of repetition on rates of cooperation was rather modest, leading Roth to conclude that the results are equivocal (Roth 1995). (註:這些結果皆來自於隨機結束的賽局 randomly terminated game. All of these papers used games with a randomly determined length.)


A usual criticism of the theory of infinitely repeated games is that it does not provide sharp predictions since there may be a multiplicity of equilibria. To address this issue, we present experimental evidence on the evolution of cooperation in infinitely repeated prisoner’s dilemma games as subjects gain experience. We show that cooperation may prevail in infinitely repeated games, but the conditions under which this occurs are more stringent than the subgame perfect conditions usually considered or even a condition based on risk dominance.


  • Bereby-Meyer,Yoella, and Alvin E. Roth. 2006. “The Speed of Learning in Noisy Games: Partial Re-inforcement and the Sustainability of Cooperation.” American Economic Review, 96(4): 1029–42.
  • Dal Bó, Pedro. 2005. “Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games.”American Economic Review, 95(5): 1591–1604.
    這篇比較無限和有限重覆 PD game, 發現無限重覆賽局,在同樣條件下會有較高的合作率

    [this paper] compares infinitely repeated and finitely repeated prisoner’s dilemma games of the same expected length and finds that cooperation is larger in the former as theory predicts.
  • Dal Bó, Pedro. 2007. “Tacit Collusion under Interest Rate Fluctuations.” RAND Journal of Economics, 38(2): 533–40.

Stationary Concepts for Experimental 2×2-Games

Selten, Reinhard; Chmura, Thorsten (2008) “Stationary Concepts for Experimental 2×2-Games." American Economic Review, Volume 98, Number 3, June 2008 , pp. 938-966(29). DOI: http://dx.doi.org/10.1257/aer.98.3.938; zju.edu.cn 提供的 [PDF];

==notes by yinung==

此文之觀念, 適用於 長期 或 repeated 賽局之均衡解

mixed equilibrium 可視為是動態均衡解 (stationary concept)

Mixed equilibrium has several interpretations. One interpretation is that of a rational recommendation for a one-shot game. Another  interpretation  looks at mixed equilibrium as a result of evolutionary or learning processes in a situation of frequently repeated play with two populations of randomly matched opponents. One may speak of mixed equilibrium as a behavioral stationary concept.

這篇以 2×2 賽局實驗, 比較5種 stationary concept:

Quantal response equilibrium (Richard D. McKelvey and Thomas R. Palfrey 1995)

策略選擇比例是 exponential form

assumes that players give quantal best  responses  to  the behavior of  the others  (see Section  IB).  In  the exponential form of quantal response equilibrium considered here, the probabilities are proportional to an exponential with the expected payoff times a parameter in the exponent.

Action-sampling  equilibrium

從觀察對手的 7 種 (神奇數字) 可能的策略, 來決定自己的最佳策略

…in  a  stationary  situation,  a player takes a sample of seven observations of the strategies played on the other side, and then optimizes against this sample.

Payoff-sampling equilibrium  (Osborne and Rubinstein 1998)


…envisions a  stationary  situation in which a player takes two samples of equal size, one for each of her pure strategies. She then compares the sum of her payoffs in the two samples and plays the strategy with the higher payoff sum…. The best fitting sample size turns out to be six for each of both samples. The name  “payoff-sampling equilibrium" refers to the sampling of own payoffs for each pure strategy.

Impulse balance  equilibrium

和 prospect theory 觀念結合的均衡

proposed  by Selten  is  based  on  learning direction  theory  (Selten  and  Joachim Buchta 1999)…   is  applicable  to the repeated choice of  the same parameter  in  learning situations  in which  the decision maker receives feedback, not only about the payoff for the choice taken, but also for the payoffs connected to alternative actions.
…. The decision maker is assumed to have a tendency to move in the direction of the impulse….

此觀念有別於 reinforcement learning

… that impulse learning is very different from reinforcement learning.

In reinforcement learning, the payoff obtained for a pure strategy played in the preceding period determines the increase of the probability for this strategy. … 完全取決於自己的報酬 (is  entirely based on observed own payoffs)

In  impulse  learning  it  is not  the payoff  in  the preceding period  that  is of crucial importance. It is the difference between what could have been obtained and what has been received, which moves the behavior in the direction of the higher payoff. … 取決於對手的策略和自己的報酬 (requires feedback on the other player’s choice and the knowledge of the player’s own payoff)

均衡成立時, 期望向上和期望向下 impulses 相同, losses 時 impulses 加倍計算
In  the  stationary distribution, expected upward impulses are equal to expected downward impulses. … losses are counted double in the computation of impulses as in prospect theory (Daniel Kahnemann and Amos Tversky 1979).

===五種 equilibrium 之差異===

The five concepts can be thought of as stationary states of dynamic learning models. Learning models differ with respect to their requirements on prior knowledge of the game and on feedback after each period.

reinforcement learning: Nash, quantal response, pay-off sampling equil. 屬之

其它兩種皆需要更多資訊: 自己的報酬 + 對手之選擇

one needs knowledge of one’s own payoff matrix, as well as feedback on the other player’s choice

==original Abstract:==

Five stationary concepts for completely mixed 2×2-games are experimentally compared: Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium (Martin J. Osborne and Ariel Rubinstein 1998), and impulse balance equilibrium. Experiments on 12 games, 6 constant sum games, and 6 nonconstant sum games were run with 12 independent subject groups for each constant sum game and 6 independent subject groups for each nonconstant sum game. Each independent subject group consisted of four players 1 and four players 2, interacting anonymously over 200 periods with random matching. The comparison of the five theories shows that the order of performance from best to worst is as follows: impulse balance equilibrium, payoff-sampling equilibrium, action-sampling equilibrium, quantal response equilibrium, Nash equilibrium.

How Strong Are Weak Patents?*

Farrell, Joseph; Shapiro, Carl (2008) “How Strong Are Weak Patents?" American Economic Review, Volume 98, Number 4, pp. 1347-1369 ( total 23 pages). DOI: http://dx.doi.org/10.1257/aer.98.4.1347. [PDF]



We study the welfare economics of probabilistic patents that are licensed without a full determination of validity. We examine the social value of instead determining patent validity before licensing to downstream technology users, in terms of deadweight loss (ex post) and innovation incentives (ex ante). We relate the value of such pre-licensing review to the patent’s strength, i.e., the probability it would hold up in court, and to the per-unit royalty at which it would be licensed. We then apply these results using a game-theoretic model of licensing to downstream oligopolists, in which we show that determining patent validity prior to licensing is socially beneficial.

Selection Criteriain Coordination Games: Some Experimental Results

Russell W. Cooper, Douglas V. DeJong, Robert Forsythe, Thomas W. Ross (1990) “Selection Criteriain Coordination Games: Some Experimental Results." American Economic Review, Vol. 80, No. 1 (Mar., 1990), pp. 218-233.  (In JSTOR: Page Scan PDF Summary)

Abstract by yinung

This paper studies a class of symmetric, simultaneous move,  complete information games called coordination games which exhibit multiple Nash equilibria that are Pareto-rankable. Coordinationgames are at the heart of a numberof recent models in industrial organization macroeconomics. These include models of network externalities (Michael Katz and Carl Shapiro,1985), product warranties under bilateral moral hazard (Cooper-Ross,1985), team production (John Bryant, 1983); and macroeconomic models of imperfect competition. A number of selection criteriahave been proposed for games of this natureand these are reviewed. These criteria provide a number of hypotheses regarding equilibrium selection in coordination games.

…The goal of this experiment to address the following questions.First, is Nash equilibriuma good predictorof observed behavior in strategic or game settings? Second, when there are multiple Nash equilibria does one arise “naturally"as the outcome?

The main results … are summarized as follows. First, we find that the observed pattern of play is accurately predicted by the Nash equilibrium concept. Second, we find that the Pareto-dominant Nash equilibrium is not always the experimental outcome.


Pareto-dominant Nash:

selected References

  • Farrell, Joseph, “Cheap Talk, Coordination, and Entry," Rand Journal of Economics, Spring 1987, 18, 34-39.