Work in Progress 

Beliefs in Beauty Contests  with Simon Gächter & Diego Marino Fages (draft in preparation)

Beauty contests are frequently used to infer the strategic sophistication of individuals. However, it is uncertain how much can be inferred about participants' beliefs simply by observing their choices. Previous studies have treated the chosen numbers as estimates of beliefs about average choices and the choices of others, leading to conclusions that are based on choices rather than actual beliefs or they estimated beliefs imprecisely which makes it hard to arrive at general conclusions. 

We propose a new method to elicit beliefs about the behaviour of other players. Our method adds to the literature by allowing us to estimate a distribution of individual beliefs. Using this method, we can examine whether there are similar focal points in beliefs as in decisions and investigate whether people internalize the level k thinking of others. To do this we follow Schlag (2015) and test the consistency of elicited beliefs with behaviour, their correspondence with individual beliefs and we investigate whether behaviour changes in the expected direction when we induce different beliefs. The goal of the paper is to not only understand how well beliefs predict behaviour, but also to examine whether this relationship is significantly different between individuals with high and low CRT scores.

Our experiment consists of four parts. In the first part, subjects participate in a cognitive reflection test. In the second part, subjects participate in a standard Beauty Contest game in which players are asked to select an integer between 0 and 100 and the winner is the player whose number is closest to the mean of all chosen numbers multiplied by a parameter p. In the third part, the subjects participate in the 'battleship game'. For each of the participants we randomly select 25 answers of other players from the beauty contest game. The task of the subjects is to guess as many of them as possible which gives us an estimate about their beliefs of the whole distribution. Finally, the subjects participate in a modified version of the battle ship game. In the modified version, we manipulate beliefs such that the subjects have to guess the answers of the half of participants that performed better in the CRT test. Between treatments, we exogenously manipulate the order of the tasks, the parameter 'p' and whether the battleship game is incentivized or not. 

We conducted the experiment with two subject different subject pools, one from the United Kingdom and one form Argentina, and find qualitatively similar results. We find the behaviour in the beauty contests similar to the behavior reported in other experimental studies. As in previous experiments, the results indicate that subjects follow an iteration process starting from their initial reference point. Interestingly, we can observe this not only for the behaviour in the beauty contest game but we see a very similar pattern when we elicit the individual belief distributions. We further find that subjects who seem to follow an iteration process in the beauty contest game are more likely to guess that other players arrive at one of the outcomes of the same iteration process. When manipulating the beliefs in the modified dictator game, a large fraction of the subjects change their beliefs in the expected direction (i.e., they respond with lower numbers when they know they play with subjects with higher CRT). We also examine the connection between the CRT and the beliefs in the beauty contest game. In contrast to our expectations, the CRT does not seem to be significantly correlated with the belief distribution.

Peer earnings and giving (draft in preparation)

We investigate the effect of peer earnings on giving in a controlled experiment. We presented subjects with an opportunity to donate to an external charity while exogenously varying peer earnings. By randomizing peer earnings but by keeping the decision environment constant, we differentiate our research from related studies of social pressures and giving behavior (DellaVigna et al., 2012; Andreoni et al., 2017; List, 2011). By introducing a real donation decision to an outside charity, we abstract away from within-lab re-distributive concerns (Côté et al., 2015; Sheremeta and Uler,2021).

In the social version of our experiment, two subjects participate in each session. Each subject is assigned one of the two roles, decision maker or peer, by a publicly observed coin toss. The peer receives a fixed payment, whereas the decision makers face a real donation situation. Peer earnings, hence, serve as a natural source of comparison for decision-makers. In a between subject design, the peer earnings were exogenously varied between £5 (High Treatment) and £2 (Low Treatment). In our experiment, each decision maker was endowed with £6.

As the donation task, we gave the subjects the possibility to allocate money from their initial endowment of to WWF’s Climate Relief Fund. Consequently, any difference in the average level of giving to the charity by the decision makers between treatments can be traced back to social reference points in form of peer earnings.

In the non-social treatments, the social nature of peer earnings and, hence, donation incentives based on social comparisons were removed, whereas potential effects based of regret, experimenter demand, anchoring, and reference points based on counterfactual information remained untouched. In the non-social version of the experiment, only one subject participated. A coin toss assigned each single subject per session to make a donation decision or leave with pre-determined earnings. The donation decision was the same as in the social treatments. In a between-subject design, active subjects were exposed to the amount of money they would have earned if their coin toss had assigned them to the role of a peer before making a decision. Consequently, the donation decision differs between the social and non-social treatments only in the fact that exposure to counterfactual earnings referred to peer earnings in the social treatments and not obtained earnings in the non-social treatments.

In the social treatments, we find that decision-makers donate more to charity when the peer earnings are relatively low compared to when they are high. Decision makers donated on average £2.29 when peer earnings were low and £1.91 when peer earnings were high. The treatment effect is substantial in size and statistically significant. In the non-social treatments, we find that decision-makers chose fairly donations on average. While decision-makers chose slightly higher donations, when the reference earnings were low (£2.10) compared to high (£2.17), this effect is not statistically significant.

Further, the pairwise comparison of the High and Low Treatment between the social and the non-social treatments indicates that reference earnings of a peer might be more relevant when they are unfavourable compared to when they are favourable. We can corroborate this by showing that the willingness to donate is significantly higher in the social version of the experiment than in the non-social version when peer earnings are high, but not when peer earnings are low. Together, this suggests that people care about income differences and change behaviour accordingly but more so if they are to their disadvantage. Finally, when checking for heterogeneous treatment effects, our results are entirely driven by the behavioural changes of men while women behave similarly across the four decision situations.

Compromise Effects in Ultimatum Games: Experimental Evidence (draft in preparation)

In this paper, we explore the compromise effect in a structured bargaining situation. The experiment is designed to create an environment as in Galeotti et al. (2019) and Galeotti et al. (2021) where we can exogenously manipulate the menu of contracts and observe how this influences bargaining outcomes. By using a structured bargaining protocol we are able to gain further insights into the underlying behaviour. For example, we are able to observe whether changing the menu of contracts makes a given contract more or less acceptable (relative to the acceptance rate in the base scenario), or whether it makes a given contract more likely to be proposed. Specifically, we use ultimatum games as they have a particular simple structure, where a proposer makes a take-it-or-leave-it proposal about how to split a pie and a receiver can either accept or reject the proposal.

In this experiment, we explore two base scenarios where we vary whether the Fair contract is exactly equal or just less unequal than the Greedy contract and whether the Decoy makes the Fair or the Greedy contract a compromise and measure if, by adding a decoy contract making one of the base contracts a compromise has a significant effect on the observed distribution of agreements. There are two feasible contracts, a Greedy contract that gives 80% of the pie to the proposer, and a Fair contract. In one base scenario the Fair contract gives 50% to the proposer and in the other it gives 60% to the proposer. In four decoy scenarios, we then examine the effect of adding a third contract. In two of these scenarios the third contract is very selfish, giving the proposer 90% of the pie. The compromise effect is that this makes the Greedy contract more likely to be implemented compared to the base scenario. In two other decoy scenarios the third contract is a Generous contract, giving the proposer 20% of the pie. The compromise effect is that this makes the Fair contract more likely to be implemented compared to the base scenario.

In all we examine six scenarios using an ultimatum bargaining protocol. For more detailed information on the acceptability of contracts, receivers indicate whether they would accept or reject each feasible contract (i.e. we use a strategy method, see Brandts and Charness (2011)). In addition, we examine each scenario using two more, even simpler, protocols. Using Dictator games, where the receiver cannot reject a proposal, we are able to observe whether proposer preferences are affected by adding a menu option. Finally, we use Random Proposal games, in which the receivers indicate the acceptability of proposals when the proposal is chosen by Nature. This allows us to observe whether the acceptability of contracts is subject to ’pure’ menu effects, independent of the intentions of proposers.

In our experiment, we do not find compromise effects in the ultimatum game - the addition of a third contract does not increase the absolute frequency of any of the pre-existing contracts. Looking at behaviour of proposers and responders separately, we can see that payoff focality seems to matter. For responders in the unequal split base scenario, we observe lower rejection rates for the greedy contract once we add an even greedier proposal. For the equal split base scenario, we can not observe the same effect. For proposers we can not observe a compromise effect per se. However, our design allows us to investigate how each proposer changes their behaviour individually between two scenarios. For the unequal split base scenario, Proposers switch more frequently from offering the fair contract to offering the greedy contract once the selfish decoy is added to the menu of contracts compared to when the selfish decoy is removed from the menu of contracts. For the equal split base scenario, we can not observe the same effect.