Contamination between experiments: playing social preference games in sequence.

Transcription

1 Contamination between experiments: playing social preference games in sequence. Pedro Franco de Campos Pinto 16 de março de 2009 Abstract Many methodological issues remain in experimental economics. This paper deals primarily with the issue of contamination between experiments, which we define as altered behavior by participants in a experiment due to experience in a previous experiment. This is tested in the case of Social Preference games and we cannot reject the possibility of contamination having occurred. We propose three channels for this contamination, via an expectations update of players, through an wounded pride/spite model and through fatigue. We test these hypothesis by having participants play either an Ultimatum or an Dictator game or participate in a Test, followed by a novel game design, an Altered Public Goods (APG) game, and compare the results with that of players who only play the APG game. We cannot reject the hypothesis of contamination via an expectations update. We find mixed evidence regarding the possibility that contamination occurs due to players behaving in an wounded pride/spite model. We find fatigue as possible contaminant to be non-significant, although there is evidence that the level of fatigue induced in participants was low. 1 Introduction The area of experimental economics is one of economic science s recent success stories, having grown significantly since the first experiments conducted in the 60s and 70s and achieving a The author wishes to thank Fransisco Costa, Joísa Dutra, Caio Abramo and Isabela Guarino for their contributions and above all to Leonardo Rezende, whose mentoring made this paper possible. The author also extends his thanks to CNPQ for funding and his personal thanks to Célia Gouvêa, Celso Pinto, Luis Franco, Eduardo Vanin and Tiago Lafer for their support. Author affiliation: Master s Program, Department of Economics, Pontificia Universidade Catolica do Rio de Janeiro, Rua Marques de São Vicente, 225, Rio de Janeiro, RJ, Brazil. 1

2 degree of mainstream acceptance during the past decade. When Kahneman and Smith won the 2002 Nobel prize in economics, it came as no shock to the economics community. The development of a methodology for how to conduct these experiments was naturally a slow process and the first standard textbook for experiments would only appear in 90s, with Davis and Holt s Experimental Economics in The process is still undergoing, as can be illustrated in the current debate concerning the issue of daily life game play and strategies and laboratory behavior in experiments, seen in Palacios-Huerta and Volij (2007) and Levitt, List, and Reiley (2008). Despite the advances of the literature in experiments and the continued interest in its development, this remains an incomplete and important task, as the improper use of methods can drastically change the results of an experiment. This can be illustrated in Burnham, McCabe and Smith (2000), who report that the change of a single word from "opponent"to "partner"in the instructions of their experiment was sufficienttomorethandoubletheleveloftrustinessdis- played by participants. This example demonstrates the importance of framing effects, something that the literature in experimental economics has been interested in since at least Smith (1976) and which remain an important area of study. The importance of methodology is also found as part of the debate of whether some findings, such as preference reversals, that contradict standard economic theory are the result of improper methods, as Binmore (2007) states may be happening in some cases, or if the limits of standard economic theory have been found, as defended by Loewenstein (1999). This is a key issue in the debate between orthodox experimental economists and behavioral economists. More studies into how specific methodological practices may affect experimental behavior may help advance this important debate, specially in games that present the most consistent violations. One methodological issue that remains is that of contamination 1 between different experiments. We define contamination as the possibility that a previous experience in a economic experiment might affect the manner by which participants play a game in future experiments. We now state our primary hypotheses of interest, which are all related to this concept. 1.1 Primary Hypotheses There are many channels through which contamination in games might occur and some of these are well understood and taken into account when designing an experiment, such as contamination in the random lottery incentives system due to learning effects, as seen in Cubitt, Starmer and Sugden (2004). Indeed, the existence of learning effects by participants is well understood and an important part of experimental procedure and was already being taken into account in Smith 1 This term was inspired by and is similar to that of used in Cubitt, Starmer and Sugden (2004). 2

3 (1962). We will be focusing on contamination that might occur in social preferences games, which consists of games where the welfare of other participants and/or issues such as trust or equitable divisions are part of the decision making of participants. Examples of such sorts of games include the Ultimatum game, Trust games and Public Good games. Despite this focus, the methodological issues presented in this paper may be relevant in experiments involving other typesofgames,suchascoordinationgames. Within this scope, one natural way of testing contamination would be to find subjects that have participated in experiments involving social preference games and compare their outcomes with that of a control group with no prior experience. Due to the novel nature of an economics experiment being performed at Pontificia Universidade Catolica do Rio de Janeiro (PUC-Rio) 2, this was not possible due to the lack of previous participants. Nevertheless, this remains a valid way of testing the hypothesis and might yield important results. Instead, the scope of this hypothesis was reduced to a smaller time frame and so the experiments tests contamination between games within a single experimental procedure. Thus, the main hypothesis this experiment will test is whether participating in two social preferences games in sequence alters the behavior of participants in the second game. If this hypothesis proves to be false, a case may be made that contamination is most likely weak or non-existent in these types of games, but accepting this hypothesis does not mean that contamination will necessarily occur in all experiments, since the possible effects time has on this factor could not be measured. This hypothesis may be stated as: Hypothesis 0: Contamination occurs when social preference games are played in sequence. The literature has dealt with a similar issue before, most recently by Cubitt, et al. (2004), who investigate the random lottery incentive system, which consists of presenting participants in a experiment with a series of games/tasks, but only paying for one of the tasks which is selected after the experiment by a random draw. The authors are concerned that if the independence axiom of expected utility theory is violated, subjects in this system might treat all tasks as a single game, instead of separately, which leads to cross task contamination, as first proposed by Holt (1986). That is, participants might end up playing games in a manner that is different than what would happen if the games were presented separately and with a guaranteed payoff for each one. The authors deal with contamination in the case of preference revelation tasks, which permits the generalization of their findings within the scope of single players games/tasks. 2 Guarino (2008), the only other economics experiment conducted by a member of the PUC-Rio Economics Department, was done at the department of economics of the Fundação Getúlio Vargas. 3

4 This paper, in comparison, concerns itself with contamination in games with multiple players and focus on effects stemming from interaction between players as a cause for contamination. Our definition of contamination can be extended, if it is accepted that people play games in their day-to-day life. Such a belief allows us a broad scope for the application of game theory. However, there is no consensus if we can make such a claim, as the extent of the validity of experiments as proxies for real life and, analogously, how much real life situations can be modeled as through games, is an issue that the literature still holds in contention. The debate between Palacios-Huerta, et al. (2007) and Levitt, et al. (2008) is an example of this. If we accept that experiments are sufficiently close to real life experience and vice versa, then the participants day-to-day experience before an experiment could potentially affect their game behavior significantly if contamination exists. An example of this might occur if participants were playing with friends, of whom they have significantly more knowledge regarding their preferences and/or which might lessen or magnify their potential emotional reactions. Contamination, is this more general sense, could be an important factor in most experiments. To test our zero hypothesis, the experiment made use of 3 differenttreatmentsandonecontrol group. The control group played solely an Altered Public Goods (APG game), which consists of a multiple rounds Public Good game with an extra action available to players, the possibility of withdrawing from the Public fund each round, as well as being able to contribute to the fund. In all treatments, the APG game was also played, but only after taking part in either a Test, a multiple rounds Ultimatum game or a multiple rounds Dictator game. Each treatment was named for the firstgameplayed,thusthetreatmentconsistingofthetestfollowedbyapggame is named the Test and APG treatment. The payoff of each game is separate from one another, to avoid issues similar to that of the random lottery incentive system. If the results in the APG game in the treatments differ significantly from that of the APG control group, there will be cause to believe that contamination exists. Whatarethepotentialexplanationsfortheoccurrenceofthemorerestricteddefinition of contamination? We propose three separate channels through which it might occur. The first, based on Kreps, Milgrom, Roberts and Wilson (1982), assumes that since participants have incomplete information on the type of player they are playing with in a game, they adopt strategies that are optimal when taking this into account, but which are not optimal when compared to a game with Nash rational 3 players with complete information. Contamination would occur between games due to the previous experience in a differentgameleadingplayers to revise their expectations of other player s behavior and adjust their optimal strategies. Thus: Hypothesis 1: Contamination occurs due to revised expectations about other player s types. 3 Players that adopt strategies that lead to Nash equilibrium. 4

5 In this experiment, participants will play a first game in the Dictator and APG treatment and the Ultimatum and APG treatment where deviations from Nash equilibrium are common and persistent, which should lead to a revision of expectations where participants believe with a higher probability that they are playing with non-rational players. As consequence, in these two treatments, this should lead to players deviating more from Nash equilibrium in the second APG game, by contributing more, when compared to the APG control group, as this will increase their payoff duetothewaytheapggameisdesigned. Another possible cause of contamination, based on Pillutla and Murnighan (1996), is that participants behave in a wounded pride/spite model. This model was created in an attempt to explain the large number of rejections and the division mode that the literature has found to happen in Ultimatum games. It proposes that participants will irrationally punish 4 other participants, by refusing offers, due to having received what participants perceive as unjust offers. We propose that contamination would thus occur as the literature reports that players in the first game will usually receive unfair offers and would thus opt to punish others for this in the second game. This hypothesis may be stated as: Hypothesis 2: Contamination occurs due to perceived injustices, which lead to irrational punishments. TheAPGgameallowsthetestingofthishypothesisinamannerthatisindependentfrom the first hypothesis, as the design of the game allows players to punish irrationally other players. If this hypothesis is true, then the level of punishment dealt should be significantly higher in the groups consisting of contaminated participants, which should be the case of participants of the Dictator and APG treatment and of the Ultimatum and APG treatment. In the former, as half the participants are incapable of taking any action during the first game, the effect should be strongest; in the latter, as players can reject unfair offers, the effect, if it exists, should be significantly weaker. One caveat regarding this model stems from the proposed explanation by Binmore (2007) for resultsthatcontradictstandardeconomictheory,whichisthatparticipantssuffer from a "rolling gait". This is the idea that since humans play games in real life all the time, they have developed optimal strategies for these games. If subjects play a laboratory game that is sufficiently similar to one they have an optimal strategy, participants might take significant amount of time to adjust their strategies, going through with their rolling gait/natural tendencies initially. In the case of social preference games, as human society depends on the mutual cooperation of its members to exist, it has been proposed, by Binmore (1999), that humans have adopted a 4 By irrational punishment we mean a punishment that reduces the payoff of the player who is punishing the other. 5

6 tit-for-tat strategy regarding cooperation in many social interactions. Thus, if presented with a game where cooperation is not optimal, they might use this tit-for-tat strategy, perceiving offers significantly less than 50% as non-cooperation, which is a strategy similar to what is expected from the wounded pride/spite model. In a different experiment, where players have more opportunities to take actions that might be perceived as potentially pride wounding, it may be possible to distinguish between these two models, since the rolling gait would eventually end as players finally learn not cooperate, but not in the wounded pride/spite model; this is beyond the scope of this experiment. Another channel through which contamination might occur is fatigue of participants. By participating in a game or test, participants should become fatigued and this might affect their actions in the second game. So as to control for the possibility that this is happening in the Dictator and APG and Ultimatum and APG treatments, we test for fatigue via the Test and APG treatment. The study of fatigue may also be relevant as it may be present in the experimental procedure used in the past, such as Cherry, Frykblom and Shogren (2002), who use a test to make participants in a dictator game earn their money. It is possible that they, and other similar procedures, might be capturing the effects of fatigue and not the consequences of having players earn money. This is, as far as we can tell, the first Economics Experiment that deals with the issue of fatigue in Social Preference games, although there is a growing literature that deals with fatigue in repeated choice experiments, as can be seen in Savage and Waldman (2008), and some studies explicitly try to prevent fatigue in their experimental design, such as Morrison (2002), although no model for fatigue is usually presented in such cases. As such, the literature has created models dealing with consistency of choice and choice set complexity, valid in the case of fatigue induced by repeated choice experiments, with consequences limited to within the scope these experiments. Given the difference between these type of experiments, which consist of simple preference revelation choice games with a single player, and experiments with Social Preference games, we turned to the Experimental Psychology literature, which has studied the consequences of fatigue to a greater extent, for our model and predictions. We opted to create fatigue caused by a test situation, as this procedure has been used before, such as in Cherry, et al. (2002), and because of the ease of performing a test. Kruglanski, Richterb and Webstera (1996) report that such participants fatigued through a test in a psychological experiment were more prone to making snap judgments of other participants and used poorly the available information when making their decisions. Given that both these conclusions can be considered an important part of the decision making in Social Preference games, there is a possibility that fatigue contaminate the APG game by these channels 5.Thus: 5 A caveat, however is that Kruglanski, et al., as with most psychology experiments, did not make use of 6

7 Hypothesis 3: Contamination occurs due to fatigue in players stemming from the first game. Note that unlike the previous hypotheses, it is more difficult to predict beforehand in what ways mental fatigue might affect participant s actions. If participants make less use of information when taking decisions, they might be slower in their learning process, which would lead to a slower convergence to Nash equilibrium in the APG game, if such convergence occurs, and thus a higher level of non-optimal behavior. However, if an increase in ill will as a consequence of snap judgements due to fatigue occurs, the opposite effect and/or an increase in punishments might occur, as players should be confronted, in the APG game, with non-generous behavior 6 from the very start of the game. We shall now state our secondary hypotheses. 1.2 Secondary Hypotheses In addition to the primary hypothesis, two secondary hypotheses are investigated. The first of these hypotheses deals with the new possible action for each player, punishment, in the APG game and checks if this significantly alters the results of player s behavior, when compared to the results that are usually found in the literature of a standard Public Goods game. This will be possible due to the control group s experimental procedure consist of solely playing the APG game. The hypothesis is thus stated as: Hypothesis 4: The APG game has a significantly altered game play when compared to a Public Goods game. Since the added action is non-optimal to a rational player playing Nash equilibrium in the design used, players should never opt to punish and player s behavior should be similar to that of normal Public Goods game. The second hypothesis which is tested is whether individual characteristics of participants affect the way they play. Past results, such as Buchan and Croson (2004), show that the gender of a participant may affect the actions taken during Social Preferences games and it has been reported that culture differences affect how players perform in such games, such as in Henrich (2000). Thus: Hypothesis 5: Individual characteristics of participants affect the actions taken. financial incentives, which should mitigate the effects of fatigue. 6 We define this as behaviour in which the pareto optimal action is not taken by players. 7

8 Note that not in all past experiments individual characteristics were deemed relevant in explaining participants behaviors; as such, if no such link is found, it will be consistent with these previous results. Section 2 will deal with the experimental design and procedures. Section 3 will present the results of the experiment, section 4 will summarize these results and discuss them. Tables and figures will be presented in the first Appendix and all instructions used during the experiment will be presented via an second Appendix. 2 Experimental Design and Procedures The experiment was conducted at the department of economics of the Pontificia Universidade Catolica do Rio de Janeiro during the months of September (3 sessions) and October (2 sessions) of 2008, for a total of 5 sessions. In two of these sessions, participants were part of the control group and each of other 3 sessions consisted of a single, different treatment. The total number of participants was 12 for each session, except the second session for the control group, held in October, which had only 8 subjects due to absent and late students. Participants were recruited from all departments of the University via posters, leaflet distribution and advertising by professors, which instructed the interested to access a site with further instructions. Emphasis was given that participants would only be required to play simple games and/or a participate in a test and that the only requirement for participation was that of having a university student ID card. The site supplied more information regarding the experiment for candidates, but without detailing the games. Candidates were instructed to send an and were allowed to select which sessions they desired to participate. Each participant was only allowed to participate in a single session. In addition to the required and randomly selected 12 students for each session, 1 to 2 extra students were selected per session. Selected subjects were informed that in the event of more than 12 people being at the experiment, the last to arrive would only receive the participation feeof8reais(4.7dollars) 7. This was done so as to avoid delays and/or missing participants, the latter being crucial for the APG game (which requires groups of four people). The majority of selected students came from 3 courses, Economics (29%), Law (21%) and Social Communication (13%), which was expected, as the Social Communications and the Law courses have respectively the largest and second largest number of undergraduate students at PUC-Rio and students from Economics courses were expected to be more interested in a Economics Experiment. In addition, 63% of students were from the first and second years and 64% 7 Theexchangeratefluctuated significantly during the September and October; for the purpose of this paper, an exchange rate of 1.85 reais per dollar was used. 8

9 of students were male. The three different treatments were designated as the Ultimatum and APG treatment, the Dictator and APG treatment and the Test and APG treatment. Players in the control group only played the APG game, where as each of the three treatments consisted of playing a game or performing an test immediately followed, with no breaks, by the APG game. Subjects participating in the treatment groups were informed they would play a second game after the first, but no information was given regarding the game. This was done so that each game would be treated separately by each player and avoid the issues discussed in Cubitt, et al. (2004). Both the tests and the games were conducted via a network of computers using the z-tree program 8, as distributed by the University of Zurich and referenced in Fischbacher (2007) 9. In all sessions, instructions were displayed on the computer screen and were printed out for reference, and after reading the instructions, a small test was conducted to check that participants had understood the instructions. In addition, a sheet of scrap paper and a pen was provided for each participant. Computers were separated by cardboard screens. Participants were instructed, before the beginning, not to talk at any time during the experiment and in case of any doubts, to raise their hands and await a experimenter to come to them. During all sessions, these instructions were complied with. Participants in all sessions were paid after the experiment was finished and were informed of earnings via a token system in the instructions and during the experiment. The exchange rate between tokens and reais was that of 100 tokens for each 1.5 reais, equal to 0.81 US dollars. A priori average payoff to each subject per hour of participation was calibrated to be between 20 to 25 reais (10.8 to 13.5 dollars), although maximum potential earnings was a high as 46 reais (25 dollars) per hour. A description of each game and the test, as well as details concerning their applications, follows. We then summarize the predictions for the APG game for each treatment. 2.1 The Test The intention of applying this test was to create a significant degree of fatigue, in a similar manner to that of Kruglanski et al. (1996) and Cherry et al. (2002). The test consisted of 15 GRE-like quantitative math multiple choice questions, with a time limit of 2 minutes for each question for a total of 30 minutes. A clock indicated the amount of time left for each question. 8 Those interested in receiving the programs created may contact the author via . 9 The z-tree program is well suited for running social preference games, but it was significantly more difficult to program the Test, due to the inability of the z-tree to display image files. We would not recommend its use in applying future tests. 9

10 Participants were paid 1,5 reais (0.81 dollars) for each correct answer and no penalties were applied to wrong ones. To minimize possible distractions and facilitate running the experiment, it was made impossible to advance to the next question before the two minutes were up, so that all subjects finished thetestatthesametime. Thiswasdonebyallowingafinal answer to be selected before the two minutes passed, but providing a new question only after the two minutes passed. Because students were not exclusively recruited from the economics department, the use of GRE-like math questions was meant to stimulate students of all areas of study to try to answer all questions, while at the same time providing a reasonable degree of challenge to all participants. It was expected that an average player would get 40% of the questions right. 2.2 The Ultimatum Game The design of this game deviated from the standard game, as in Güth, Schmittberger and Schwarze(1982), by having multiple rounds and players having multiple, random and anonymous partners. At the start of the experiment, participants were randomly and anonymously designated the roles of either Player A or Player B for the duration of the game. The use of the terminology Player A and Player B was used to avoid framing issues. At the start of each round, each Player A received 3 reais (1.62 dollars) in tokens, information which was common knowledge to all participants, and were instructed to divide the tokens with a randomly selected, anonymous Player B, who also did not know who his partner was. The amount of tokens that could be divided had to be a multiple of 10, to avoid identification tactics between players. After each Player A made their decision, their offers of tokens were conveyed to the partner of that round, who would then choose to accept or refuse the offer. A refusal meant that neither player received tokens that round, whilstanacceptancemeantthatthedivisionof tokens between players happened as proposed. After each Player B made their decision, their decision and the amount of tokens received that round were displayed to each player, after which a new round began. During each decision phase of each round, a clock displaying a countdown of 30 seconds was shown, so as to expedite the decision of players, although players were explicitly informed that no penalty would be applied should any player take longer than 30 seconds. Due to the way the z-tree random partner generator works, all Players A and Players B were matched at least once during the experiment. The game lasted for a total of 15 rounds. Nash equilibrium predicts that all Player A participants will offer either zero or the smallest non zero amount possible to a Player B, who will accept any positive offer. Past results in experiments, such as reported in Pillutla et al. (1996), show that players tend to reject of- 10

11 fers significantly below 50%, which itself tends to be the mode of offers. However, different methodologies can produce different results, as can different cultures/sample compositions. The choice of making the ultimatum game a multiple partner and multiple rounds game was so that players could potentially discover more information regarding other players types. We opted for making partners anonymous to each other so as to simulate more closely how an average participant would have to process information regarding their previous experience in a experiment, since their participation in a new experiment would most likely lead them to play with subjects they had not played with before, thus only having access to aggregated information concerning other players. 2.3 The Dictator Game The game design also deviated from the traditional version, as first stated in Kahneman, Knetsch and Thaler (1986). The format was identical to that of the Ultimatum game, including design aspects such as multiple rounds, random and anonymous partners and with the same amount of money at stake each round. The only difference was that, as in all standard Dictator games, Player B subjects did not have veto power over the division proposed by Player A participants (the dictators), a fact which was common knowledge. Nash equilibrium predicts that Player A subjects will give nothing to a Player B. Past results reported by the literature shows that dictators, on average, give out non-zero amounts of money to Player B subjects. However, even more so than the Ultimatum game, methodological practices such as double blind procedures, as seen in Hoffman, McCabe and Smith (1996), and earning theamounttobegivenout,asincherry,et al(2002),cansignificantly alter the amounts given out, in both these cases leading to outcomes closer to the Nash equilibrium. The nearly identical design between the Dictator Game and the Ultimatum Game was chosen so as to facilitate comparisons between the treatments that use them. The reasons for making the dictator game a anonymous, multiple partner and multiple rounds game was the same as that of the Ultimatum Game. 2.4 The Altered Public Goods (APG) Game Inspired by the design used in Bochetb, Pagea and Putterman (2006), the design of the game is altered significantly from the standard Public Goods game by introducing a new action for all players, the possibility of withdrawing from the public fund. The game consisted of 20 rounds and in each round groups of 4 people were formed in randomly, with each member of the group anonymous to one another. Each group is allocated 1.2 reais (0.65 dollars) to a public fund and each player receives 0.3 reais (0.16 dollars) into a private account. 11

12 Players are then presented with three possible actions: they may put up to 0.3 reais into the public fund; they may withdraw up to 0.3 reais from the public fund and put it in their private account; or they may do nothing. If a player withdraws money from the public fund, only 25% of the amount taken out is put in the privateaccount,soaplayertakingout0.3reais would only receive reais. After all participants made they decision, the total amount in the public fund was then doubled and divided equally between all members of that group. Aggregate data concerning how many tokens were allocated and taken from the public fund and how many tokens the participant received that round is displayed and the next round begins. As in the Ultimatum and Dictator games, a time control was used to expedite play, with players having 45 seconds to make their decisions, but again players were explicitly informed that no punishment would be applied to players that took more than the allocated time. The Nash equilibrium of this game is derived as follows. Each participant has a 0.3 reais stake in the public fund that they may take, with penalty, or leave there. If they opt to leave, this amount will double and be divided among the four members of the group, so that each player receives 0.15 reais. If they take the money, due to the penalty they only receive reais, so the optimal action is to leave the money. Similarly, if the participant contributes his 0.3 reais to the public fund, that amount will be doubled and divided in four, leaving him with 0.15 reais, meaningthatitisoptimalnotcontribute tothepublicfund. Asthisgamehasafixed number of rounds, which is common knowledge, Nash equilibrium predicts that players will not contribute in the last round and, as consequence, in any round. Some observations are in order, however. The Pareto optimal decision for players is for all of them to contribute maximally to the public fund in all rounds, since the amount in that fund is doubled, thus increasing the pie to be divided. This also means that when a participant opts to remove tokens from the public fund, although he only receives 25% of the amount removed, he punishes other members of his group, as the money ceases to be available to the others (100% loss of that money). This provides a irrational punishment mechanism for participants, since although the cost of punishment is significant, the level of punishment is considerably higher, as for each token a player loses by punishing, other players lose a combined total of 6 tokens. It is the possibility of withdrawal that will allow the testing of the wounded pride/spite model. Note that every token contributed to the fund is worth more than every token removed, so contributing tokens to the public fund is better for an participant than to take tokens from it. One possible criticism 10 towards the use of this game is that participants may not have perceived that withdrawing tokens from the public fund would also punish others, since this is not made completely explicit in the instructions. This was a dilemma of sorts, as classifying the withdrawalsasapunishmentintheinstructionsmighthaveleadtoundesirableframingeffects, 10 As suggested for me by Francisco Junqueira Moreira da Costa, of the LSE economics department. 12

13 specially by creating new dynamics in the APG game when compared to the standard Public Goods game. Instead, the instructions emphasized that the money in the public fund was to be divided between all members of the group and that withdrawals reduced the amount gained significantly. 2.5 Predictions for the APG game The literature reports that in the standard Public Goods game, without the possibility of withdrawals, players usually begin by contributing significant amounts of tokens from their private accounts, but as the rounds pass, end up reducing the amount contributed until the majority of players are contributing zero or very close to zero amounts. This is attributed to a learning process through which players undergo during the game. A priori expectation was that participants in the APG control group would behave in a similar manner in all sessions and that withdrawals should be close to zero and insignificant throughout this session, due to their irrational nature. If the expectations update hypothesis is true, then players in the Test and APG treatment should not differ significantly in game play when compared to the APG control group, as they can obtain no new information regarding other players through the test. In comparison, the Dictator and APG and Ultimatum and APG treatments should present significantly higher levels of contributions, but similar levels of withdrawals, as the first games in these treatments should present high levels of deviations from Nash equilibrium. This will lead players to increase the probability in their personal belief that they are playing with non-rational players. As higher levels of contributions result in a higher payoffs when playing with non-rational players, it will be optimal for participants to contribute more. If the wounded pride/spite model is true, then we can expect similar behavior in the Test and APG treatment and the APG control group. In the Dictator and APG treatment, as 50% of players can only receive offers and have no actions, and these offers should be significantly lower than 50%, players should opt to punish these offers when offered the opportunity in the APG game. This should lead primarily to an increase of withdrawals, which provide a strong though costly mechanism for punishment, specially in the first rounds of game play, although contributions might also be significantly lower. In the Ultimatum and APG treatment, similar behavior in the APG game might happen, specially if there are significant amounts of low offers, but the effect from this hypothesis should be weaker. If the fatigue model is accurate, then we might expect its effects to be present in all the treatments, assuming that the fatigue effects from the Ultimatum and Dictator games are similar to that of the test. The model predicts that players may converge more slowly to equilibrium, due to players using available information more poorly. It also predicts that an increase in 13

14 withdrawals, or a decrease in contributions, may occur due to an increase in ill will, due to fatigued players being more prone to making snap judgements and that in the APG game, non-generous behavior is present from the start. These effects should also be stronger as players tire more. 3 Experimental Results To present the results found, a general overview will come first, followed by several subsections dealing with each hypotheses tested. The Test proved to be easier than expected, with participants averaging a 67% correct answer ratio (one participant managed to a 100% ratio) and, on average, participants selected a final answer with 27 seconds left before the next question was presented. In addition, during the payment phase, participants were informally asked if they felt tired after the experiment, the majority of which replied that they did not. This evidence seems to indicate that the test probably was not successful in generating a significant amount of fatigue on participants. In the Dictator game, results were similar to that found in the literature, as can be seen in Table 1,where the average offers of each round in the Dictator and Ultimatum games are shown. Player A participants consistently gave out a significant percentage of their allocated amount, around to 20% of the total, although there was an unexpected increase of the average amount given during the last round. Participants in the Ultimatum game also performed as in other studies, as can be seen in Table 1. Player A participants made offers significantly below a division, with a significant rejection rate, during the first few rounds, but subsequently increased their offers and converged to just below the expected 50% division, with an accompanying decrease in rejection rates, which endedupnearzerointhefinal rounds. The APG game presented results that were the most surprising. As can be seen in Table 2, where the average withdrawals in the APG game of all sessions are shown, participants persistently opted to take out tokens from public fund in all cases, but a downward trend appeared in most sessions, except in the Dictator and APG treatment, a possible explanation for which may be that of a learning effect. A similar downward trend was present in all sessions when considering the average amount of tokens being contributed into the public fund, which is presented in Table 3. This result is in accordance to previous results in the literature. Figures 1, 2, 3 and 4 present the average contribution made by each player in the APG game in each session, accompanied by the corresponding variance. In all cases, the variance of the contributions in each session can be seen as the result of both the variance of each participant s action and from the dispersion of averages of each participant. 14

15 3.1 Hypothesis 0: Contamination between social preference games To test this hypothesis, we compare the average results of the APG game in the three treatments and the control group. These are presented in Tables 4 and 5. The null hypothesis in each test is that an average contribution/withdrawal is equal across sessions, done via the T-Welch test. Also performed is the Mann-Whitney test with the null that the distribution of averages across the sessions are equal. As Tables 4 and 5 show, both average withdrawal and average contributions are significantly different from zero in all cases and average withdrawals are significantly smaller than average contributions, between half to one quarter as large. The tests between sessions also shows a quite robust result: we reject in all cases with high significance that the APG control group and that the Ultimatum and APG and the Dictator and APG treatments are statistically equal, although when we compare the average withdrawal, we cannot reject that the treatments and the control group are equal. We also reject that average withdrawals in the Test and APG treatment are statistically different from that of the APG control group, although we cannot reject that average contributions of the treatment is equal to the control group. We thus have evidence that contamination occurred in all our treatments and, because the effects encountered occurred in different variables, this evidence suggests that the channels through which contamination occurred was different in the Test and APG treatment, when compared to the Dictator and APG and the Ultimatum and APG treatments. Thus, we do not reject the hypothesis that contamination in social preference games exists. 3.2 Hypothesis 1: Contamination via expectations update As Table 4 and 5 show, we reject in all cases that average contributions of the Ultimatum and APG and the Dictator and APG treatments are statistically equal to the APG control group, but we do not reject that average withdrawals in the treatments are equal to the control group. These results are as predicted by the contamination via expectations update hypothesis. In addition, we reject that average contributions and average withdrawals in the Test and APG treatment are statistically equal to the Dictator and APG and Ultimatum and APG treatments, which also conforms to this hypothesis. We also cannot reject that the Ultimatum and APG treatment and the Dictator and APG treatment have equal contributions in all cases and that the average contribution made by participants in these two treatments is greater than that of the other two sessions. In addition to these tests, T-Welch and Mann-Whitney tests were performed excluding the first five rounds of play for all games, with the same null hypotheses as the tests when all rounds are included, and which are presented in Tables 6 and 7. These additional tests are done as 15

16 robustness tests, as we attempt to account for learning effects occurring in the APG game and thus verify the robustness of the encountered expectations update effects. We are assuming that participants on average converge to an equilibrium after the first five rounds. We find the same results when comparing the average withdrawals on all sessions. We also reject that average contributions made in the Dictator and APG treatment are statistically equal to the APG control group; however, we cannot reject that average contributions in the Ultimatum and APG treatment are equal to our control group. As the majority of our results closely correspond to the predictions of the contamination via expectations update, there is a strong case for accepting this hypothesis. 3.3 Hypothesis 2: Contamination via irrational punishment As is presented in Tables 4 and 5, when considering all rounds, average withdrawals in the Dictator and APG and Ultimatum and APG treatments are found to be statistically equal to that of the APG control group and average contributions in both these treatments are found to be statistically higher than of the control group. These results are strongly against the predictions of this hypothesis. Since the effects of the spite/wounded pride model should be strongest in the first few rounds, T-Welch and Mann-Whitney tests were performed on the first five rounds of play in all sessions, under the same null hypotheses of the tests performed when all rounds are considered. These are presented in Tables 8 and 9 and we find the same results for average contributions made, with the exception of rejecting that average contributions are equal in the Dictator and APG and Ultimatum and APG treatments. Again, this is against the predictions of this hypothesis. However, when considering average withdrawals, we find that although the results when comparing the Ultimatum treatment and the control group have not changed significantly, the average withdrawal inthedictatorandapgtreatment arenowfoundtobesignificantly higher when compared to that of other sessions, which conforms to the predictions of this hypothesis. Given the mixed evidence found when testing this hypothesis, further tests were performed. Presented in Tables 10 and 11 are the coefficients of a series of univariate regressions between the average earningsandaverage offers made/received by each participant in the firstgamewiththeir subsequent average contribution and average withdrawal in the APG game in the Dictator and APG treatment and the Ultimatum and APG treatment. Each regression includes an intercept which is not reported. The results show that none of these coefficients are statistically different, which is against the predictions of this hypothesis, as players who were more hurt in the first game, through smaller offers and smaller earnings, should have punished more in the APG game. Finally, when paying the participants in all sessions, we informally asked them if they felt 16

17 any hostility towards one another after the experiment, almost zero of which reported as such, whichweakensthecaseforthishypothesis. 3.4 Hypothesis 3: Contamination via fatigue When comparing the results of the Test and APG treatment with that of the APG control group in Tables 4 and 5, we cannot reject that contributions are equal, but we reject that withdrawals are equal. However, withdrawals are found to be significantly lower in the Test and APG treatment, exactly the opposite result of the prediction made by this hypothesis, as discussed in the Experimental Design and Procedures. Furthermore, as players tire more the longer they play, we performed tests by excluding the first five rounds of play, as presented in Tables 6 and 7. This also serves as a robustness test for this hypothesis and we largely find the same results. The single exception lies in the T-Welch test comparing the average contributions of the Test and APG treatment and the control group. Assuch,there isastrongcaseforrejectingthatfatigue,aswehavemodeled,affected participant s actions in the APG game, although some other factor, caused by the test, seems to have affected the actions of players. 3.5 Secondary Hypothesis Hypothesis 4: Subjects in the APG game play significantly different from a Public Goods game As can be seen in Tables 2 and 3, the general downward trend regarding the amount contributed is what came to be expected from past results as reported by the literature. In this regard, the introduction of a new action did not create any new dynamics regarding contributions. However, the average amount withdrawn was persistently positive, albeit with a similar downward trend in 3 sessions, and statistically significantly different from zero in all treatments. As such, there is cause to argue that the introduction of the punishment action has significantly affected the game play of the public goods game, since it is not possible to consider the withdrawals as non-significant. This is strengthened by the results in the APG control group and Test and APG treatment, where participants opted to withdraw, since there is no cause for punishment as the result of a previous game. On the other hand, there is little evidence that players were opting to punish other players as consequence of actions taken within the APG game, as the dynamics of the contributions was very similar to that commonly seen in the literature. As such, there is enough evidence to conclude that the APG game does significantly alter 17

18 game play, as players opt to take an irrational action, despite the fact that the mechanisms of contributions followed a pattern similar to that found in the standard Public Goods game Hypothesis 5: Individual characteristics of participants are correlated with the actions they take Tables 12, 13 and 14 show the results of T-Welch tests performed concerning the observed individual characteristics of each participant. This was done by aggregating sessions and then dividing this data into characteristic groups and testing whether contributions or withdrawals were significantly different between each sub-sample. The observed characteristics consisted of the sex of the participant, what was their area of study and their semester 11.Theresultsfound show that there is very little evidence to believe these characteristics were a significant factor regarding the decisions taken by them in the APG game, as in most of the tests performed it was possible to reject an equality in each sub-sample. The exceptions lie in 3 tests comparing the courses of each student, but with no clear pattern. Consequently, this hypothesis may be rejected. 4 Summary and Discussion The further development of methodology in experimental economics is an important step that still presents many questions to the literature. Contamination in experimental economics, which deals with the hypothesis that participant s previous experience in an experiment may alter their behavior in a second experiment, is one of these and this paper attempts to test this hypothesis, in the context of Social Preference games. We first propose that if contamination occurs in the time frame of weeks and months, it should also occur in a shorter time frame and we hypothesize that if players play two Social Preference games in sequence, contamination might occur between the first and second game. We test this by comparing the results of players that first play either an Ultimatum or a Dictator game, or perform a test, followed by an APG game, with the results of players that only play the APG game. The tests performed on these results give us strong evidence that contamination does happen in all cases and that there seems to be two different contamination channels acting, as the difference found when compared to the APG control group are similar in the Ultimatum and APG and Dictator and APG treatments, both of which are different when compared to the Test and APG treatment. 11 Pos-graduate participants were considered a part of the 5 semester and above group. 18