ECON3028 Advanced Experimental and Behavioural Economics
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Advanced Experimental and Behavioural Economics
ECON3028
Tutorial 3
This tutorial provides an opportunity for you to reflect on what constitutes a good (or not so good) answer to the type of question that you might be asked in Section B of this year’s Take Home Exam (THE). For the purpose of this exercise, we ask you to focus on one of the actual questions from the 2021 THE for this module.
Question 2 in Section B of last year’s Take Home Exam was:
“The best explanation of the experimental evidence of decay in contributions to the public good in repeated voluntary contribution mechanism games is that subjects do not understand the game the first time they encounter it, but come to understand it better over time and gradually converge to the Nash equilibrium prediction of free-riding.” How far do you agree? Justify your answer.
Note that the word limit was 1500 words.
Below we provide two sample answers for you to consider.
In preparation for the tutorial please do the following:
1. Consider the question above and, consulting relevant lectures, tutorials and reading, formulate your own view of what would constitute a good answer. (To do this, you may wish to construct an essay plan that you would follow, if you were answering this question).
2. Read the two example essays below and consider what grade you would give to each one based on its strengths and weaknesses. Consider points like the following. Does the answer cover all key points? Is it well-structured and clearly written? Are explanations and arguments clear and compelling? Does the answer show a good understanding of the relevant material? Does it avoid errors and inaccuracies? Is it suitably substantial and detailed? Does it show evidence of reflection/private study? Does it make a good use of the word limit? Is there anything else that you would consider? As you go through them, you may wish to note down aspects of the essay that strike you as good or bad.
3. After reading each essay, decide on the grade you would give it if you were the marker and write a brief summary (no more than 100 words each) to explain your mark for each essay. You are encouraged to consider the School’s grading guidelines before deciding on your proposed grades.
4. Come to the tutorial prepared to discuss your evaluation of the two sample essays.
Sample Essay 1
Voluntary contribution mechanism games (VCM) are public goods game in which players receive an endowment of tokens ‘E’ and face a contribution decision to a public account, which yields a return ‘m’ per token for all players regardless of contributions, and a private account which yields a return of 1 per token only for that player. The game assumes that all players are attempting to maximise their own payoff according to the self-interest theory, further incentivised by the fact that tokens have monetary value at the end of the experiment. The Nash equilibrium for such games is where individuals maximise their payoff given the strategy of all other players and therefore have no incentive to deviate from this decision. Assuming m<1, the Nash equilibrium of this game is zero contribution into the public account i.e., every player becomes a free rider. Given that every other player has an incentive to invest in their private account, this is assumed to be their strategy and therefore the payoff maximising decision for player i is to invest zero in the public account. However, this is not observed in repeated VCM games. Many VCM experiments start with relatively low levels of free riding and in most cases, this percentage tends to rise over time (Fischbacher & Gächter, 2010, FG2010 hereafter; Fischbacher, Gächter & Fehr, 2001, FGF2001 hereafter). A prevailing theory of why this decay in contributions occurs is the learning hypothesis, which suggests that players do not fully understand the game initially but learn how to maximise their payoff over time and therefore converge to the Nash equilibrium of free riding (Andreoni, 1988). It follows that if the game were to be repeated for a high number of rounds, we would expect a ubiquitous free riding outcome from even the highest early contributors.
However, various experiments have added treatments to the base VCM game to add increased realism. Before we can evaluate the role of the learning hypothesis in this decay of contributions, we must first confirm that these variations of the VCM game also have a free riding Nash equilibrium and as such, that contributions ought to decay over time.
The base VCM game from FG2010 provides us with some stylised facts. We learn for instance that conditional contributors want to undercut the public contributions of other players and therefore play the strategy hypothesis mentioned in Andreoni (1988), where players contribute in early rounds to encourage other players do the same, only to later reduce their own contribution and benefit from others’ contributions. We also learn that the proportion of free riders in the group has a positive effect on the rate of decay of contributions i.e., free riders speed up the decay of contributions as they reduce the average contribution. When paired with conditional contributors, this can lead to a rapid downwards spiral in contributions. Subsequently, FG2010 conclude that this signals to unconditional and perfect conditional contributors that the proportion of non-contributors is high and they therefore lose the belief that cooperation will yield them utility, and they too reduce their contributions. Here, it is also plausible that some contributors learn that their incentive is to free ride having seen other players do the same and observing their own payoff fall as the proportion of free riders increases.
Fehr & Gächter (2000) introduce a second stage to the VCM game in which players are told the contributions of others (their identity remains anonymous as to avoid a feud) and then have the opportunity to level a punishment. It costs the punisher one of their ten assigned punishment points and reduces the payoff of the punished by 10% per punishment levelled on them per round. In a partners, strangers treatment, FG2010 finds that punishment increases contributions in both treatments, although to greater effect in the partners treatment, where the same players continue to play the game together rather than against strangers after each round as they do in the strangers treatment. Other literature also finds that as the intensity of punishment increases, contributions tend to rise (Herman, Thoni & Gächter, 2008). In the absence of punishment, contributions decay and the difference between the treatments becomes almost negligible by the final round. It seems then, that the introduction of punishment has led to a change in decision making. Contributions no
longer decay. In a game where there are at least some players willing to punish under-contribution either due to reciprocity or having Fehr-Schmidt inequality-averse preferences, the payoffs of free riders will fall. The exact new equilibrium of a game with punishment would depend on the number of punishment points available, the damage they can do relative to payoffs and the number of social players, among other things. This lends weight to the learning hypothesis as contributions rise over time once players observe free riders being punished and receiving reduced payoffs as a result. Nikiforakis (2008) introduces a third stage in which a costly counter-punishment can be exacted against players’ stage 2 punishers. This threat of revenge reduces the number and intensity of stage 2 punishments, particularly antisocial punishments by free riders on contributors, and therefore depresses contributions, although they remain higher in both the partner and stranger treatments than the base VCM game as shown by figures 1 and 2. This supports the learning hypothesis as the equilibrium for such a game would be to lower contributions although, again, the exact equilibrium would depend on a variety of factors.
Given that these VCM games have only the potential for one type of error, players would over- contribute where the Nash equilibrium was zero contribution, Keser (1996) proposed to redesign the VCM game so that there was a possibility for under-contribution as well and that this would help to determine what proportion of contributions are intended and made in error. This was done by adjusting the payoffs into a quadratic form, so that there would be an optimum contribution greater than zero. Keser (1996) found that only 27% of players contributed the optimum amount, with 13% of players under-contributing. This signifies that the ‘error’ is two-way and as such, we cannot fully rely on the base VCM game to explain the direction of ‘error’ .
However, this finding does not help us determine whether or not the learning hypothesis is responsible, as it is plausible that both strategic players and players who misunderstand their incentives contribute sub-optimally. Andreoni (1988) attempts to untangle these two effects more directly by introducing a sudden restart treatment in which the subjects are told at the end of 10 rounds that another 10 will be played. In actuality, only 3 rounds were played. This deception allowed the experimenters to observe the trend of the restart, in which players should have gained an understanding of the game, without the strategic effect of the conditional contributors – they would raise their contributions in order to set up the conditions to free ride but will not get the chance to do the latter. The restart saw contributions increase, much more in the partners treatment than the strangers. This increase cannot be explained by the learning hypothesis as players would understand the free riding Nash equilibrium having played 10 rounds. It seems to be evidence of conditional contributors setting up the conditions to free ride later on in the game. Due to some irregularities in the matching protocol, where strangers contributed higher than partners, the robustness of the results were called into question. Croson (1996) replicated the larger uptick in contributions in the partners case post-restart, while also recording the expected matching protocol. These findings suggest that the learning hypothesis cannot fully explain the sub-optimal contributions made by players, but also does not rule it out as an explanatory factor for the initial decline of contributions.
In the base VCM game, it is clear that the Nash equilibrium is to free ride. The fact contributions fall over time does little to separate the strategy and learning hypotheses as explanations for this trend. The introduction of VCM games with punishment and counter-punishment show us a different version of the VCM game in which the equilibrium may not be to free ride. Nonetheless, in these games, we observe some evidence for the learning hypothesis as contributions rise in the punishment treatment and fall in the punishment-counter-punishment treatment as the net payoff dynamics change. Andreoni (1988) and Croson (1996) manage to separate out these two hypotheses through the sudden restart treatment and show that there is definitely a strong strategy effect alongside the learning effect. This hypothesis is consistent with other findings within behavioural
economics such as the findings of Braga et. al (2009), who suggest that feedback for lottery games reduce overweighting for small probabilities and experienced players bring greater stability, likely due to a better understanding of the game and their incentives. Therefore, it is likely that a combination of the two effects leads to the trends we observe in VCM games.
Sample Essay 2
In a voluntary contribution mechanism (VCM) game the dominant strategy is to free-ride, yet players often initially contribute to the public account and only converge to the Nash equilibrium of zero contributions gradually. One explanation for this is that players initially do not understand the game and hence do not play optimally. Only with experience and learning from others do they make optimal decisions. I argue this hypothesis fails to explain various aspects of observed behaviour using evidence from several papers, before using a series of papers by Fischbacher & Gächter to argue disappointed expectations amongst conditional co-operators best explains such observations. I also briefly mention the strategy hypothesis as a weak alternative to the learning hypothesis, due to its strength in supporting the disappointed expectations hypothesis.
In a VCM game each player has an endowment which they can keep (private account) or contribute to a public account shared by all players. Funds in the public account generate a return greater than funds in private accounts, but they are split equally amongst all players. As such, even though all players contributing their whole endowment to the public account is socially optimal, each player’s dominant strategy is to contribute nothing, assuming the experimenter sets the game’s parameters to create a n-person prisoner’s dilemma.
Chaudhuri (2009) surveys the literature and finds that initial contributions are consistently between 40% and 60% of the possible maximum, though each individual player’s contribution varies beyond this. Repeated play of the game, however, reduces contributions. For example, in one of his own studies (p.127), by round 10 contributions have fallen from around 50% to around 10% of the possible maximum.
One possible explanation for this decay is players not initially understanding the game. Specifically, faced with an unfamiliar situation, players do not work out what is best for themselves immediately and only after a few rounds, perhaps by observing others who have ‘worked it out’ quicker, do they realise their best option is to free ride. This is labelled the learning hypothesis.
Three studies offer evidence that this is a weak explanation. Firstly, Keser (1996) allows for these ‘errors’ to occur as under-contributions as well as the usual over-contributions by making the dominant strategy an interior solution rather than a corner solution (contributing zero). This is done by giving contributions to the private account a diminishing return to create a point where the marginal returns from the private and public accounts are equal. If the learning hypothesis were correct, we would expect players to erroneously over and under-contribute at equal rates. She instead finds players, on average, over-contribute in all 25 rounds, suggesting over-contribution in VCM games with corner solutions is not caused by errors being limited to one direction, but rather there is a different factor causing systematic over-contributions. Andreoni (1998) includes a surprise restart after an initially planned ten rounds which sees contributions jump in the unexpected round 11. This is inconsistent with the learning hypothesis: if the contribution decay were caused by players learning how to play optimally, they would not forget these lessons for the extra round. Finally, Yamakawa, et. al. (2016) run pairwise VCM games with three treatments: the other player in the pair is either a human (H), a computer with pre-determined contributions (C), or a computer playing on behalf of a human (HC). They find essentially no contributions with the computer
treatment, again contradicting the learning hypothesis which would have expected some initial erroneous contributions.
Overall, the learning hypothesis does not withstand these experiments and can be ruled out as the primary explanation for contribution decay. Whilst in any individual game it might play a part, for example the dominant strategy in Keser (1996) will not be immediately obvious, errors do not have a systematic effect in causing over-contribution.
Instead, Andreoni (1998) proposes a strategy hypothesis where sophisticated players contribute to the public account in early rounds to encourage others (perhaps unsophisticated players) to contribute more in future rounds. They will then contribute less in latter rounds to maximise their own outcomes, hence explaining the contributions decay. To support this, he runs two types of VCM games, one in which the players in each group are randomised each round (‘strangers’), and another where groups stay the same in all rounds (‘partners’). After the restart there is a marked jump in round 11 followed by a new, higher path in rounds 12 and 13 for partners, whilst an insignificant jump in strangers is followed by a return to the previous path, supporting the strategy hypothesis. Yamakawa, et. al. (2016) find contributions in their H treatment are significantly higher (until the final round), which they argue is because players can influence the other player’s contributions with their own contributions. However, the strategic hypothesis does not offer a perfect explanation. Andreoni (1998) also predicts that partners will contribute more than strangers in the early rounds, as repeated play with the same players allows for strategic play. This is not the case, however, and whilst some replications have found partners to contribute more, Chaudhuri (2009) notes that results are mixed with no consistent answer.
A different approach considers players having different preferences and suggest that learning about, and adapting to, other players’ preferences explain contribution decay. Fischbacher, Gächter & Fehr (2001, FGF) provides a method for identifying heterogenous groups of players. They use a strategy method to reveal what players’ contribution levels would be, given the contributions of other players. This allows the experimenters to view their strategies when faced with the full range of contribution levels, and so allows them to group players by their preferences, which are assumed to be fixed. They classify 50% of players as conditional co-operators (CCs) who contribute only if other players contribute, and contribute more as other players do so too (this includes a mix of perfect co- operators who match others’ contributions and imperfect co-operators who undercut others’ contributions), and 30% as free-riders who never contribute. They argue that contribution decay happens as CCs’ beliefs adjust to the behaviour of other players. In the presence of free-riders their belief about others’ contributions will be adjusted downwards, creating a vicious cycle as CCs will then contribute less and further lower their beliefs again. Further, Fischbacher & Gächter (2010) show that the presence of free-riders is not necessary to cause the cycle. Instead, imperfect CCs who track but look to undercut other players’ contributions will cause this cycle by competing amongst themselves.
This theory explains the initial over-contribution (as CCs believe others will also contribute), the differences in players’ contributions at the start of the game (heterogenous strategies), and the decay (downwards, insufficient adjustment of CCs’ beliefs). Experimental evidence for it comes from Fischbacher, Gächter & Quercia (2012, FGQ) who predict players’ contributions in a repeated VCM game (‘C-experiment’) based off their preferences, revealed by FGF’s strategy method (‘P- experiment’), and their beliefs about how other players will play in the round. In both experiments players are incentivised to give honest answers.
Their P-experiment results are similar to the initial FGF classifications, with CCs being the most common, followed by free-riders. At an aggregate level, the C-experiment results show the usual
decay in contributions, and this is also matched by a decay in players’ beliefs about what other players will contribute. Importantly, in any given round, players believe there will be higher contributions than there actually are, hence they revise their expectations, and so contributions, downwards next round. Individual-level predictions perform well overall. For free-riders in rounds 6- 10, predictions are accurate 80% of the time and for CCs that figure is 38%. Allowing an error of ± 2 tokens (10% of the endowment) gives an accuracy of 88% and 65% respectively. This evidence supports the theory that disappointed expectations amongst CCs cause them to lower their beliefs and thus their contributions, causing the decay which is observed at an aggregate level.
A final consideration is the relative weakness of the predictions for rounds 1-5, in comparison with those for rounds 6-10. The accuracy falls to 60% and 26% (63% and 52% allowing for error margin) for free-riders and CCs respectively. This suggests the disappointed expectations theory does not wholly explain contribution decay in public goods games. A supplementary explanation could involve the aforementioned strategy hypothesis. Whilst it performed weakly in the partners/strangers set- up, it may still explain some behaviour in VCM games. For example, the stark difference in free- riders’ behaviour in early and latter rounds suggest free-riders try to raise CCs’ beliefs in the early rounds to slow/prevent decay in latter rounds.
In conclusion, not only do I disagree with the claim that contribution decay in VCM games is best explained by players not initially understanding the game, but I do not believe it explains this decay at all, at least in a systematic manner. Several experiments provide convincing evidence against the learning hypothesis. Instead, disappointed expectations amongst conditional co-operators provides the theory which best captures the initial contributions and subsequent decay, perhaps supported by an element of strategic behaviour in early rounds
2022-04-19