Experimental Economics - Science topic

Dear Ligen Yu, thanks for the comment. I love Tao.

Information without understanding will cause mental constipation.

Indirect reciprocity is one type of conditional cooperation. Direct reciprocity is also one type of conditional cooperation. Thus, conditional cooperation is more broad than indirect reciprocity.

Indirect reciprocity is to cooperate under the condition that the opponent's reputation is good, roughly speaking. Direct reciprocity is to cooperate under the condition that the opponent cooperated, roughly speaking. Both indirect reciprocity and direct reciprocity are conditional cooperation.

Davor Mance I really like the differentiation by Elinor Ostrom that you stated in the end. Do you, by any chance, have the reference for this distinction?

Hi David,

Thanks for your input!

I looked at some of his research, yes.

I followed your suggestion and zeroed in on Axelrod's work. However, it's all simulations as well. Always algorithms vs. algorithms.

Oh well, thanks nevertheless!

Please let me know if these references/sites are helpful to you:

1.  Theories of Fairness and Reciprocity - Massachusetts Institute of ...

by E Fehr - ‎Cited by 951 - ‎Related articles

point out open questions, and to suggest avenues for future research. ..... For these experiments the equilibrium is computed under the assumption that all ... called Ultimatum Game invented by Güth, Schmittberger and Schwarze (1982). ...... 1) Evidence from the Third Party Punishment Game and the PGG with punishment ...

2.  Minimally Acceptable Altruism and the Ultimatum Game

by JJ Rotemberg - ‎2004 - ‎Cited by 111 - ‎Related articles

Apr 4, 2004 - experimental results of ultimatum and dictator games. Moreover ... (1991), for example, Levine (1998) computes that even splits ..... At that point, the proposer is indifferent to the allocation of A between the two parties .... low offers in a dictatorship game that these individuals were playing with third parties. In.

Dennis

Dennis Mazur

What, precisely, should your experiment reveal that is not already known?

You wrote that 11 factors are known to affect such a choice, and that you will test all of these. This "affection" must be related to something, and this something is a control (situation/condition). Thus, to give an effect of any of these factors you have to relate the response to some control. Otherwise you can only compare the responses between different experimental conditions, what will become very messy with 11 factors, some of which might be continuous or have several different levels. And apart from this it might be that some factors interact (there are already possible 110 two-way interactions, not to think about higher-order interactions).

I think you should be much much more specific in your research question and then try to find an experimental design that addresses this specific question robustly and with high precision and gives an interpretable and practically useful answer.

Ha, actually I read about the slider task a while ago but I completely forgot about it. I'm not sure about this one because I read an article which said that women perform worse than men in this task, which might induce a gender bias.

Anyway, thanks for the suggestion, I will definitely consider it.

If you have data for firms in different countries you could also add investor's perception about the risk of investment in that country together with measures of corruption and a good environment for doing business. You can find measures for all these variables in the International Country Risk Guide 

Good day, Matty.

I have successfully designed and analyzed hierarchical choice modelling experiments for structuring and bundling telco service contracts for small-to-medium and large business clients. The hierarchical choice modelling approach might suit the problem type as market contract choice might involve top-down hierarchical decisions, e.g. "I see you chose this <broad type> alternative, which <options/features> from this <pop-up menu> would you then choose?". A nice side-benefit is the generation of inclusive value estimates - an estimate of the value of including a sub-menu of options as a feature of a higher-level set of alternative choice attributes. A few nice features of the nested choice designs or sub-menus is that they often need no additional experimental design and add little in terms of participant cognition load and therefore overall completion time. They can often be implemented as a 'tick one or more' list, optionally displayed if a participant chooses a higher-level alternative, often with explicit additional option prices and, for online surveys, a dynamic price or cost implication summary of boxes ticked. Lastly they can model real choice contexts with better fit. Ever tried to buy a Subway (tm) sandwich? Ha! I have been thinking of, but not had success in gaining the funding to research, a similar problem of how best to structure self-funded irrigation schemes to optimize scheme success, and I thought the above approach could work. What do you think?

Cheers.

Damien

Well, there are a lot of options available such as C++, Matlab, Python etc. but it depends upon the scenario and requirements of economic analysis as well to opt for the most suitable language. C++ has been suggested as the preferred language for the economic analysis. Nevertheless, you may want to consider what your requirements are to assess the suitability of a programming language. Please refer to following links for some references.

Hope this helps!

In my opinion, it is never a good idea to have a fixed number of rounds. If you do, you will have two different kinds of effects: learning effects in the starting rounds of the game and end effects in the final rounds of the game. In the final rounds, participants tend to behave more selfishly. Refraining from being too selfish makes sense if you do not want to destroy the prospects of long-term future cooperation. If the future is very brief, this incentive disappears. You can prevent end effects (to a certain extent) by not specifying the number of rounds N beforehand, but by terminating the game with a certain probability alpha per round. If you choose alpha=1/N, the expected number of rounds is N, but at every stage of the game the expected time horizon of the game is still the same.

I would make the (expected) number of rounds dependent on the complexity of the setting. In complex settings, it may take a long time before the players understand the situation and before they can make sense of the behaviour of the others. In other words, there will be a long learning phase, that is, it takes a long time before a group of players arrives at a stable pattern of behaviour. You can reduce this phase by changing the description of the game or by giving the players the opportunity of gaining experience (e.g. in separate training sessions). But be careful that this does not interfere with the intentions you have with your experiment. In very simple settings, it does not take more than 3 to 5 rounds before most groups settle at a stable behavioural pattern. If you are mainly interested in such equilibrium behaviour (studying the learning phase might actually be more interesting...), then it suffices to run, say, 10 rounds on average, giving you about 5 rounds for studying this equilibrium behaviour. Increasing the number of rounds does often more harm than good: participants get bored by the situtation and start doing "strange" things just in order to create novel situations.

Franjo Weissing

You may try to check this meta-analysis from 2011:

Johnson, N. D., & Mislin, A. A. (2011). Trust games: A meta-analysis. Journal of Economic Psychology, 32(5), 865-889, http://noeldjohnson.net/www.noeldjohnson.net/Research_files/Trust%20Games.pdf

Thanks Diego. I will check these links

Hi Stefan,

as Sacha, I would simply propose to employ an analysis, which was already done in similar investigations. So simply check your references, where your theory stems from and do the same. It is of course reasonable to expect the occurance of an effect based on assumptions, methods and analyses of previous studies.

However, if you want detailed advice beyond, you should lay out your design, method and procedure. And... usually chosing a specific statistical analysis should be considered during designing the experiment. ;). This is a presrequesit to determine statistical Power/sample size, and is a matter of scientific reliability. Furthermore, you could otherwise end up with a design on which no statistical test applies (it happened to me in my first-ever-experiment :)).

Best, René

Check this page. You can find a version of the trust game coded in z-Tree.

Dear Aisha

Rob has answered your query in a very elaborate way, clarifying the pros and cons of the proposition.

I would, however, like to add as well as to differ on your hypothesis. The Keynesian 'paradox of thrift' is a generalization that suggests that on a macro economic scale the income generated in the process of production needs be spent on the output so as to keep the equilibrium level of income and employment going on. However, it will be very heroic and naive to assume that overspending can accelerate income levels. Because what is important is also the nature of spending like whether it is on capital goods or on consumer goods. The equilibrium occurs with the aggregate income being equal to output and aggregate spending. Rather than the quantum of spending the nature of spending is very important for long-term perspective.

There is one more thing. Overspending can lead to wastage and a false consumer self like a narcissist self. Overspending is not a way for the maintenance of long-term equilibrium. Rather a blend of saving and spending is. If one wants to help the economy she should save for her future and for herr future spending by investing the same in productive streams.

Hello Otilia,

As I understand, you are looking here to use the experimental game theory. For this you can refer to the studies of  Blomfield (1997); Zimbelman and Waller (1999); King (2002); Fischbacher and Stefani (2007) and Bowlin et al. (2009). Those authors use experimental game theory in audit field.

Attached some references:

Bowlin, K. 2011. Risk-Based Auditing, Strategic Prompts, And Auditor Sensitivity To The Strategic Risk Of Fraud. The Accounting Review, 86, 1231-1253.

Blomfield 1995. Strategic Dependence And Inherent Risk Assessment. The Accounting Review, 70, 71-90.

Zimbelman, M. F. & Waller, W. S. 1999. An Experimental Investigation Of Auditor-Auditee Interaction Under Ambiguities. Journal Of Accounting Research, 135-155.

For example,  Zimbelman and Waller (1999), after collecting data using experiment, they have used Ordinary least squares (OLS) and logistic regressions to analyze the different results. 

Hope that I have answer to your questions, really sorry I am not economist I am accounting researcher and I am interested on using game theory in accouting and tax purposes. 

All the best

Very interesting question. There is no reason at all that social experiment are always disputable on ethic grounds. First of all, there always are  unintend ed experiments, just beacuse there are policy variations across jurisdictions etc. These are quasi-experiments (see e.g. how we studied reforms of electricity and other sectors in Florio M, ' Network Industries and Social Welfare. The Experiment that reshuffled European Utilities', OUP, 2013. Second, in some cases the policy maker or the analyst doesn' attach any ethical value to one variant against the other, and is truly uncertain about outcomes. You can think to a lot of examples. And think to experiments with placecebo in medicine, which are much more widespread, despite potential ethical issues. However, it is true that social experiments are costly, but they would be much more informative than laboratory experiments in economics, which sometimes are cheap and silly. In my opinion the true reason why there aren't many social experiments is legal, not ethical. Social planners simoly do not know how to write the legislation in a form that allows social experiments and do not want to take risk. Thus, this is often much more a political economy issue than an ethical one. 

i think that current  markets aren't very optimal.moreover to frictions and costs that you hinted, there are other problems with markets. MICHAEL J. SANDEL from Harvard has a good book named What Money Can’t Buy. in this book, he critique markets from a moral view. and all of his claim are thinkable.

but we must know that markets already are good place for exchange and we haven't better alternative. I think that change in market concept will be evolutionary rather than revolutionary.

Dear Alexander,

Today bankers are not interested in implementing PEBs, because they will lose the possibility of unauthorized use of clients' money. 

Calculate your sample size needed. Sample size calculator are available

Good luck

Béatrice

See also the this article from The Guardian on the problem of replicabiliy in psychology. It presents a nice summary of how psychology is changing.

Denis makes sense to me.

In economic models, there are endogenous variables, and exogenous variables. The model is in essence a theory about how the endogenous variables behave. The theory is based on the view that the exogenous variables determine the endogenous variables. Consumption behaviour of a group of people, for example, is determined by their incomes, the prices of the consumption goods they buy, and environmental factors like the weather that are influence their consumption behaviour. A natural question to ask in a model of this sort is this: how would a change in one exogenous variable affect the endogenous variables. The natural way to answer such questions is to change the exogenous variable of interest, holding other exogenous variables constant, and then observe what the model predicts with respect to the endogenous variables. In other words, the ceteris paribus assumption is what one needs to interrogate or explore a theory in which changes in certain variables are thought to be caused by changes in other variables.

The F-statistic in a multiple linear regression weighs the reduction in the residual some of squares (RSS) that is achieved by adding a number of covariates into the regression against the additional parameters needed to estimate their effects (the overall F-statistic compares the full model against the null model including only an intercept and no covariates) . If the overall reduction in RSS is moderate and the number of parameters large, the F-statistic may not be significant even if one or more of the betas are. With a single variable, the t-test of the hypothesis that beta=0 and the F-test for the simple linear regression are equivalent and a significant beta implies a significant F-statistic. The more "insignificant" or random explanatory variables you add to the model (i.e. the larger p, the number of parameters, becomes) , the less likely it is that the reduction in RSS achieved by the one significant variable justifies the addition of many (p) variables.

For example, if the null model (intercept only) has RSSnull=20 and a simple linear regression with variable x1 has RSS=15, the t-statistic becomes:

F = (RSS_null - RSS) / (p-1) / (RSS / (n-p))

With p = 2 and, for example, n=20:

F = 6

which is significant with a p-value of 0.0248

If adding a single random variable x2 to the model does not result in an appreciable reduction in RSS (say RSS=14.5), the overall model with p=3 is no longer significant:

F = 3.22

p = 0.0650

Thus the addition of random explanatory variables essentially "dilutes" the significant effect of a single important variable to the point that the overall model is no longer signficant.

I guess some hints can also come from the use of data generated from a computer software (e.g. the atomic coordinates of an atomic assembly).

Astonishingly those can be considered as "experimental data". Can they be considered as laboratory data? It's a matter of meaning of the words.. a computer software is in any case an "artificial environment" (even if it is not a physical one), and we "gather" the data from a computer, even if it is different than "recording" them

Correct

Thanks Richard, an update on this. We have tried to use a GEE approach as you advocate to deal with the autocorrelation. Our model is as follows

geeglm(Nash_decision~fishery+treatment+state_of_resource+period+Experience+Cumulative, family=binomial(link="logit"), data=data1, id=playerno., corstr = "ar1")

We recoded player and session (playerno.) to indicate a different player playing in each session (i.e. 1a - 8a for players 1-8 in session 1 and then 1b-8b for players 1-8 in session 2) and included period (i.e. round) in the model to cater for the time effect. We assume that playerno is the individual sample units in our dataset.

What we have found through testing however is that the QIC score is the same no matter what correlation matrix we specify (ar1 or exchangeable or independence).

geeglm(Nash_decision~fishery+treat+period+state_of_resource+Experience+Cumulative, family=binomial(link="logit"),

+ data=data1, id=playerno, corstr = "ar1")

> gee2 = update(gee1, corstr = "independence")

> gee3 = update(gee1, corstr = "exchangeable")

> sapply(list(gee1, gee2, gee3), QIC)

[,1] [,2] [,3]

QIC 871.02 871.02 871.02

Quasi Lik -434.02 -434.02 -434.02

Trace 1.49 1.49 1.49

px 1296.00 1296.00 1296.00

Also there is no Auto-correlation (checked with ACF) in each case, but if we remove period auto-correlation arises in some lags. Is this suggesting that the correlation between rounds is not so strong, so including period as factor is enough to deal with that? Is this an issue that the QIC is the same across the same models with different correlation structures?

Also do we need to consider the nesting factors (i.e. rounds nested within session)? We have read that you can ignore nested design through specifying the correlation structure correctly in GEE? Is this correct?

Thanks!

You can find the best answers to your question in here:

1) Keeney, R., & Raiffa, H. (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs: John Willey & Sons.

2) Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263-291. I think you can find these two in the Web.

Since a few years we have been starting an endeavor which is based on the interplay between Experimental Economics and Agent-based Economics to the study of how to model artificial agents using human behaviors. You will find the paper on:

The specifics of an experiment depend on what you want to observe. If you want to look at intuitive reactions, you would be best looking at quick decisions and compare them with slow ones [1]. If you are interested in seeing how a group evolves, then you want to experiment an iterated public goods. And so on.

As for the general motivations why people keep experimenting the public goods game as well as other social dilemmas, the reason is that social dilemmas formalise many fundamental situation of our society, from depletion of natural resources to climate protection, from security of energy supply to price competition markets, workplace collaborations, political participation, and international relations. Consequently, understanding how and why cooperation can evolve in a social dilemma is a topic of primary importance.

The standard model (Nash equilibrium) predicts that humans contribute nothing to the public good. However, fortunately, this is not what happens. A large body of experimental studies has by now confirmed that humans do contribute something and the amount of contribution typically depends on the parameters of the game (marginal return and size of the group). These data are so regular and robust that people are getting more and more convinced that cooperation does have also a strategic component that can be captured by suitable models [2],[3].

References:

[1] Rand DG, Green JD, Nowak MA (2012) Spontaneous giving and calculated greed. Nature 489, 427-430.

[2] Charness G, Rabin M (2002) Understanding social preferences with simple tests. The Quaterly Journal of Economics 117 (3), 817-869.

[3] Capraro V (2013) A Model of Human Cooperation in Social Dilemmas. PLoS ONE 8(8): e72427.

MINIMUM SAMPLE SIZE

There are two scenarios: (i) known population size: N and (ii) unknown population size. In scenario (i), population proportion is the most common approach, i.e. Cochran,'s equation, Yamane's equation or Scheaffer et al. However, the question concerns "infinite" population, i.e. unknown population size. The explanation for scnario (ii) follows:

MINIMUM SAMPLE SIZE WITH UNKNOWN POULATION SIZE

In infinite population, i.e. unknown or constantly changing population, the minimum sample size may be determined by: n = [Z square times sigma square] devided by sampling error square. Formally, it is given by:

(1) n = [(Z^2)s^2] / E^2

where ...

Z = standardized score at half-alpha;

s = population standard deviation

E = sampling error

STANDARDIZED SCORE AT HALF ALPHA: Z(a/2)

Use the Z-equation to determine the value for the Z(a/2): observed and compared this observed value to the standard value. For 0.95 confidence interval, this value of Z(a/2) is 1.96. See Unit Normal Distribution Table. The Z-equation is given by:

(2) Z(a/2) = (x^ - mu) / (s/sqrt. n)

where ...

Z(a/2) = 1.96;

n = initial sample size, i.e. 20, 30, 50, etc.

x^ = initial sample mean

s = population standard deviation: sigma

POPULATION STANDARD DEVIATION: SIGMA

The population standard deviation may be determined via the t-equation:

(3) t = (x^ - mu) / S/sqrt. n

where ...

mu = estimate population mean

S = initial sample standard deviation

n = initial sample size

Rearranging the equation to solve for assumed population mean: mu ...

(4) mu = t(S/sqrt. n) - x^

where ... t(a/2) = 1.83

NOW, solve for s (population standard deviation: sigma) in the Z-equation. By rearranging the Z-equation to express it in terms of sigma:

(5) s = [(x^ - mu)/Z] sqrt. n

With known Z(a/2) from the observation in the initial sample(s) and "sigma": s, now put it into equation (1).

SAMPLING ERROR: E^2

Sampling error is defined as the error between the measurements of sample and that of the assumed population. This example value is not known since N is unknown. We can only work with the estimate. The sampling error is gicen by:

(6) E = S / sqrt. n

where ...

S = Sample standard deviation

n = sample size

SAMPLING METHOD

Statements (1) through (6) may be used to detrmine the minimum sample size where N is infinite. In so doing, one asks: "what is the proper sampling method?' The sampling method employed may be in a form of Bootstrap process: resampling via series of small samples in order to obtain a fair characterization of the population. The following may provide some guidance:

Assume that in a sample space there exists a population N where the value of N is not known or infinite, series of samples called T (read theta) in a set T:{t1, t2, ..., tn} in various size are taken from unknown N pool. Each sample from the resampling set {t1, t2, ..., tn} may produce the following statistics:

t1: {mean t1, var, std}

t2: {mean t2, var, std}

...

tn: {mean tn, var, std}

NOW, do b-bar analysis for pair difference to test whether the population is homogeneous. If d-bar shows that the means: {(mean t1 - mean t2), (mean t2 - mean tn), ..., (mean tn-1 - mean tn)} is not significant then the population is homogeneous. If the d-bar test shows significant difference, continue wioth the resampling to double check whether the population is indeed non-homogenoeous. If subsequent bootstrap sampling coonfirms characteristics: homogeneity or otherwise, then collect of means from the bootstrap and use it as a single set of means, i.e. treating each mean as a single observation set: mean tn = x*. Set x* = x^ and calculate the minimum sample size using statements (1) through (6) following the steps outlined above. Note that x^ is the mean of a single sample and x* is the mean of a set of bootstrap means.

ASSUMPTION

The above explanation assumes that the population is normally distriuted. However, if the population is not normally distributed, the researcher is advised to use chi-square test for a single initial sampling or F-test for k-sample, i.e. if bootstrap process is used. To confirm whether the population may be normally distributed, see Anderson-Darling Test: A-square test.

Using one my model I have predicted successfully the very unexpected rejection of the 2005 French referendum on the project of European Constitution. I even have alert before hand on the danger of holding referendum about the European construction few years before. A piece from the conclusion of a 2004 paper:

"Applying our results to the European Union leads to the conclusion that it would berathermisleadingtoinitiatelargepublicdebatesinmostoftheinvolvedcountries. Indeed, even starting from a huge initial majority of people in favor of the European Union, an open and free debate would lead to the creation of huge majority hostile to the European Union. This provides a strong ground to legitimize the on-going reluctance of most European governments to hold referendum on associated issues. "

From: S. Galam, « The dynamics of minority opinion in democratic debate », Physica A 336 (2004) 56-62

Using another model I have predicted the repetitive occurrence of hung elections at fifty/fifty in 2004 and indeed it did occurred. From the 2004 conclusion:

"Accordingly the associated “hanging chad elections” syndrome could become of a common occurrence in the near future."

From: S. Galam, « Contrarian deterministic effect: the hung elections scenario », Physica A 333 (2004) 453-460

But of course those predictions do not validate the models of opinion dynamics as proved models but instead validate the approach behind them. I refer to my book "Sociophysics, A Physicist's Modeling of Psycho-political Phenomena" published by Springer in 2012 in which I discuss lengthy those questions.

One paper in French is attached. Unfortunately the system does not allow more attachments

Eric,

So the dominance requirement -- which is a methodological, experimental design condition on the 'peakedness' of the payoff function when testing null hypotheses derived from economic theories -- has tumbled down the priority list because of more general questions about whether incentives matter at all.

This seems eminently plausible.

I would also conjecture that it has fallen by the wayside because no recognised general-purpose procedure exists with which dominance may be verifiably implemented in our experimental designs. And many of our experimental design favourites -- such as the Random Lottery Incentive scheme -- create separate impediments. The closest approximation seems to be the inclusion of a "multiply payoffs by the factor X" treatment condition, where X is set sufficiently high (e.g. 10, or 100) so as to pre-empt any criticisms citing insufficient peakedness of the payoff function.

Incidentally #1: I particularly like the Hardnose paper/result. At first glance, there would seem to be some scope for trying this sort of approach in the decision making under risk and uncertainty context as well.

Incidentally #2: the Hardnose result reminds me of Winking & Mizer (2013) Natural-field dictator game shows no altruistic giving, Evolution and Human Behavior. These authors erase altruistic giving with a design that involves an experimenter with a bag of casino chips, a confederate, and an unaware member of the public standing at a Las Vegas bus stop.

Bikhchandani, Hirshleifer, & Welch 1992 cascades/herds are predicated on a binary action space. Todorova&Vogt 2012 show that this effect disappears when the action space granularity is increased from 2 to 1001. So with regard to information aggregation in an investment setting, the relevant transition in observable behavior occurs well before the infinite limit of a continuous action space is reached.

re: Pauline's answer: Yes, of course, I didn't mention it but you should always start w/ a power analysis to determine what your ideal final sample size would be. Also, if there are other groups that have done longitudinal studies on a similar population you can ask them for estimates of attrition, but bear in mind that specific social factors in one sample or another (e.g., what city you're in; how difficult it is to travel to your campus; how you're reimbursing participants) can greatly influence attrition in any particular study. So don't rely too much on generalizations from previous studies.

In the context of global value chains, I know the OECD has released some research on the role of SMEs. That might lend some ideas to your work, Matty. If you've come across any studies on upstream & downstream activities in agricultural value chains could you let me know. Thanks.

Thanks so much, I really appreciate your help. Caz

What the trust game measures is an ongoing controversy among many economists. Early results showed that the trust game does not measure trust at all, but rather trustworthiness (Glaeser, et al. (2000), "Measuring Trust"). More recent research suggest that the trust game measures the beliefs component of trust (how likely is it that an unknown other will cheat you). See, e.g., Sapienza, Toldra and Zingales (2012) "Understanding Trust"; or Butler, Giuliano and Guiso (2012) "Trust and Cheating."

Overconfidence is actually tricky to measure, ex-ante, and how to measure it will depend on which definition of overconfidence you want to use. E.g., if you are interested in overconfidence defined as believing your information is more precise than it is, then you could simply elicit each participant's belief distribution for an objectively-known random event (e.g., state lottery outcome) and compare the elicited distribution to the actual distribution using some measure of dispersion (e.g., variance) for statistical testing. If you are interested in a more intuitive measure of overconfidence, then you could match pairs of participants to compete on a task where performance is orthogonal to ability so that, objectively there is a 50/50 chance (or, whatever probability you want to design) of winning. Then you could elicit participant's beliefs about the chances of winning. Labeling individuals reporting values sufficiently higher than 50/50 as overconfident would be warranted here, I think, where the definition of "sufficiently" is up to the experimenter.

It would be great if Paul Ojeaga could actually give some examples of the many studies in this area that he is aware of.