Evolution of Fairness and Group Formation in Multi-Player Ultimatum Games

Date: 2015-08
By: NISHIMURA, Takeshi
OKADA, Akira
SHIRATA, Yasuhiro
URL: http://d.repec.org/n?u=RePEc:hit:econdp:2015-06&r=net
Group formation is a fundamental activity in human society. Humans often exclude others from a group and divide the group benefit in a fair way only among group members. Such an allocation is called in-group fair. Does natural selection favor an in-group fair allocation? We investigate the evolution of fairness and group formation in a three-person Ultimatum Game (UG) in which the group value depends on its size. In a stochastic model of the frequency-dependent Moran process, natural selection favors the formation of a two-person subgroup in the low mutation limit if its group value exceeds a high proportion (0.7) of that of the largest group. Stochastic evolutionary game theory provides theoretical support to explain the behavior of human subjects in economic experiments of a three-person UG.

Ignorance and bias in collective decision:Theory and experiments

Ignorance and bias in collective decision:Theory and experiments
Date: 2014
By: Alexander Elvitar (Centro de Investigación y Docencia Económicas, (CIDE))
Andrei Gomberg (Centro de Investigación Económica (CIE), Instituto Tecnológico Autónomo de México (ITAM))
César Martinelli (Centro de Investigación Económica (CIE), Instituto Tecnológico Autónomo de México (ITAM))
Thomas R. Palfrey (California Institute of Technology)
URL: http://d.repec.org/n?u=RePEc:cie:wpaper:1401&r=net
We consider a committee with common interests. Committee members do not know which of two alternatives is the best, but each member may acquire privately a costly signal before casting a vote under either majority or unanimity rule. In the lab, as predicted by Bayesian equilibrium, voters are more likely to acquire information under majority rule, and attempt to counter the bias built in favor of one alternative under unanimity rule. As opposed to Bayesian equilibrium predictions, however, some committee members vote for either alternative when uninformed. Moreover, uninformed voting is correlated with a lower disposition to acquire information. We show that an equilibrium model of subjective prior beliefs may account for this correlation, and provides a good fit for the observed patterns of behavior both in terms of rational ignorance and biases.
Keywords: Condorcet jury theorem, rational ignorance, homemade priors
JEL: D72 D83

An experimental study of sorting in group contests

YNY: 這是一篇比較 group 之組成成員能力不同下, 所形成 overbidding 的實驗文獻。

Date: 2014-01
By: Philip Brookins (Department of Economics, Florida State University)
John Lightle (Department of Economics, Florida State University)
Dmitry Ryvkin (Department of Economics, Florida State University)
URL: http://d.repec.org/n?u=RePEc:fsu:wpaper:wp2014_01_01&r=net
We study experimentally the effects of sorting in contests between groups of heterogeneous players whose within-group efforts are perfect substitutes. The theory predicts that higher aggregate effort will be reached when variation in ability between groups is lower, i.e., by a more balanced sorting. In the experiment, we assign subjects to four types — A, B, C, and D — ranked by their cost of effort, with A having the lowest and D having the highest cost, and conduct contests between two groups of two players each. In the Balanced treatment, (A,D) groups (i.e., groups comprised of a type A and a type D player) compete with (B,C) groups, whereas in the Unbalanced treatment, (A,B) groups compete with (C,D) groups. We find substantial heterogeneity and overinvestment of efforts by all types in both treatments, including the “underdog" (C,D) group which surprisingly is not demoralized by the unbalanced matching. Despite strong overbidding, relative aggregate efforts are remarkably close to equilibrium predictions both between treatments and between groups within each treatment. The results confirm the prediction that balanced sorting leads to higher aggregate effort.
Keywords: contest, group, sorting, heterogeneous players, experiment
JEL: C72 C91 M54 D72

Literature about Tournaments from John List’s syllabus


• Bull, Clive, Andrew Schotter and Keith Weigelt, “Tournaments and Piece Rates: An Experimental Study." JPE, 1987, 1-33.
•  Schotter, Andrew and Keith Weigelt, “Asymmetric Tournaments, Equal Opportunity Laws, and Affirmative Action: Some Experimental Results." QJE,
1992, 511-39.
•  Nalbantian, Haig and Andrew Schotter, “Productivity Under Group Incentives: An Experimental Study." AER, June 1997, 314-341.
•  Gneezy, U., and R. Smorodinsky “All-pay auction: An experimental study."  Working paper, University of Chicago.
•  Orrison, Alannah, Andrew Schotter, and Keith Weigelt. “On the Design of Optimal Organizations Using Tournaments: An Experimental Examination.”
1998, Management Science.
•  List, John A. et al., 2009. “Toward an Understanding of Optimal Contest Design,”
working paper, University of Chicago.

Bias in judgment: Comparing individuals and groups

Kerr, Norbert L.; MacCoun, Robert J.; Kramer, Geoffrey P. (1996) “Bias in judgment: Comparing individuals and groups." Psychological Review, Vol 103(4), Oct 1996, 687-719. http://psycnet.apa.org/?fa=main.doiLanding&doi=10.1037/0033-295X.103.4.687. uci.edu 提供的 [PDF]

==original abstract==

The relative susceptibility of individuals and groups to systematic judgmental biases is considered. An overview of the relevant empirical literature reveals no clear or general pattern. However, a theoretical analysis employing J. H. Davis’s (1973) social decision scheme (SDS) model reveals that the relative magnitude of individual and group bias depends upon several factors, including group size, initial individual judgment, the magnitude of bias among individuals, the type of bias, and most of all, the group-judgment process. It is concluded that there can be no simple answer to the question, “Which are more biased, individuals or groups?," but the SDS model offers a framework for specifying some of the conditions under which individuals are both more and less biased than groups.

Are N+1 heads better than one? The case of mutual fund managers*

Prather, L.J., Middleton, K.L., 2002. Are N+1 heads better than one? The case of mutual fund managers. Journal of Economic Behaviour and Organization 47, 103–120. DOI.


Recent studies find that mutual funds exhibit differential and persistent performance which is frequently attributed to superior managerial decision making. We extend the literature by examining the impact of the fund’s management structure on performance outcomes. Specifically, we examine directly whether superior outcomes, in terms of risk-adjusted returns, may be explained by behavioral decision making theory that asserts that teams make better decisions than individuals. Empirical results are consistent with the classical decision making theory and the efficient market hypothesis.

Group Performance and Decision Making*

Norbert L. Kerr and R. Scott Tindale (2004) “Group Performance and Decision Making," Annual Review of Psychology. 2004. 55:623–55. doi: 10.1146/annurev.psych.55.090902.142009.


Theory and research on small group performance and decision making is reviewed. Recent trends in group performance research have found that process gains as well as losses are possible, and both are frequently explained by situational and procedural contexts that differentially affect motivation and resource coordination. Research has continued on classic topics (e.g., brainstorming, group goal setting, stress, and group performance) and relatively new areas (e.g., collective induction). Group decision making research has focused on preference combination for continuous response distributions and group information processing. New approaches (e.g., group-level signal detection) and traditional topics (e.g., groupthink) are discussed. New directions, such as nonlinear dynamic systems, evolutionary adaptation, and technological advances, should keep small group research vigorous well into the future.

Are teams prone to myopic loss aversion? An experimental study on individual versus team investment behavior*

Matthias Sutter (2007) “Are teams prone to myopic loss aversion? An experimental study on individual versus team investment behavior."Economics Letters, Volume 97, Issue 2, November 2007, Pages 128–132. DOI; ***

==notes by yinung==

此文之實驗研究細節,可參考 Team decision making under risk and myopic loss aversion 一文, or see 2005-Sutter-team decision-working paper

==original abstract==

Myopic loss aversion (MLA) has been found to have a persistent influence on individual decision making under risk. In this paper I show that team decision making attenuates MLA, but that teams are also prone to MLA

League-Table Incentives and Price Bubbles in Experimental Asset Markets

Date: 2011-05
By: Cheung, Stephen L. (University of Sydney)
Coleman, Andrew (University of Sydney)
URL: http://d.repec.org/n?u=RePEc:iza:izadps:dp5704&r=net
We study experimental markets in which participants face incentives modeled upon those prevailing in markets for managed funds. Each participant’s portfolio is periodically evaluated at market value and ranked in a league table according to short-term paper returns. Those who rank highly attract a larger share of new fund inflows. Under conditions in which prices are close to intrinsic value, the effect of incentives is mild. However under conditions in which markets are prone to bubble, mispricing is greatly exacerbated by incentives. Even in experienced markets, prices climb to levels clearly indicative of speculation and do not always crash back.
Keywords: league tables, price bubbles, managed funds markets, tournament incentives, asset market experiments
JEL: C92

Summary by Yi-Nung (2011.12.31)


本文研究 “排行機制" 是否會使資產泡沫的情形更嚴重

…whether league-table incentives may contribute to the perpetuation of price bubbles in asset markets.
(p.5) … for league-table incentives to amplify price distortions in these markets


Such an event, and any ensuing crash back to intrinsic value, can have adverse consequences for the efficient allocation of capital, as well as distorting the distribution of wealth and propagating instability throughout the economy. For these reasons, the factors that contribute to the severity of price bubbles are of interest to policy makers and regulators.

為何要用實驗來研究 asset bubble 問題之原因:

an inherent difficulty of studying price bubbles using historical data is that an asset’s true intrinsic value is not observable even in retrospect. Thus any empirical assessment of a price bubble is necessarily contingent upon assumptions that must be made with regard to intrinsic value, leading to the possibility of specification error. As a result, there is always scope for disagreement over whether any given historical episode indeed constitutes a price bubble.

… a further challenge for empirical research is that the incentives facing market participants may be endogenous to the performance of the market under consideration, may differ between participants within a given market, and may in any case not be observable to the researcher.


… design of our experiments is based upon canonical studies by Smith, Suchanek and Williams (1988)(PDF) and Noussair, Robin and Ruffieux (2001)(PDF).


Baseline:                每人獲得每段期間 “與績效無關之" 固定報酬,
競賽 tournament: 每人獲得每段期間 “以帳面價值成長率為績效" 之報酬 (league-table incentives, 或 tournament incentives (James and Isaac. 2000, AER))
其它變因: experience in repeated markets, 不同的 market intrinsic value

In our baseline experiments, each trader receives identical periodic bonuses irrespective of their performance. These bonuses model the inflow of new funds under management, and in the baseline they do not vary as a function of relative performance. Thus under the baseline, a trader’s earnings depend only upon the intrinsic value of their holdings at the conclusion of the market. In our tournament condition, we introduce league-table incentives by allocating bonuses on the basis of each trader’s relative performance, as measured by the recent growth in the paper value of their portfolio. Once again, final earnings are assessed at intrinsic value; however the measure of return that is used to construct the league table is based upon market price. In this manner, we induce a tension between the pursuit of long-run and short-run measures of value under the tournament.


1. 在固定報酬值的環境下, 有價格泡沫; 但相對於遞減報酬值的環境下, 價格泡沫較小
In the constant-value environment with baseline incentives, we again observe that prices deviate somewhat above intrinsic value in inexperienced markets. However, and again consistent with previous research, these deviations are mild compared to what we observe in the declining-value environment.
2. 在固定報酬值的環境下且有經驗的市場中, 價格泡沫現象幾乎沒有
Moreover, in experienced markets with baseline incentives, prices track intrinsic value almost perfectly.
3. league-table incentive 下價格泡沫情況更趨嚴重
… confirms the potential for league-table incentives to amplify price distortions in these markets


資產泡沫的定義: (p.3)

A bubble in asset prices has been defined as “trade in high volumes at prices that are considerably at variance from intrinsic value” (King et al 1993, p.183).


James, D., R.M. Isaac. 2000. Asset markets: How are they affected by tournament incentives for individuals. American Economic Review. 90(4) 995–1004. [jstor.org提PDF]

這篇描述操作績效高於市場者, 其薪酬與績文呈正比; 但其它人則獲 flat rate 之薪酬