Fairness Preferences in a Bilateral Trade Experiment

Abstract

Is the willingness to make trades influenced by how the total gains from trade are split between the trading partners? We present results from a bilateral trade game (n = 128) where all participants were price-takers and trading pairs faced one of three exogenously imposed trading prices. The fixed prices divided the gains either symmetrically in the reference treatment or asymmetrically in treatments favoring either the buyer or seller. Price treatments generating asymmetric gains from trade reduced desired transaction levels on both sides of the market, but more strongly by the disfavored party. The data weakly indicated a larger reduction when the disfavored party was a seller.

1. Introduction

Public concern with fairness in consumer and labor markets has been widely documented by surveys [1,2,3], boycotts or by increased demand for “fair trade” and charity-linked products [4,5,6,7]. These phenomena suggest that perceptions of fairness in terms of trade may influence the desire to trade. Some people may feel “exploited” by low wages or high prices; they may feel that they would exploit others if they bought products involving unfair trade with developing countries [8] (or, conversely, being willing to pay extra money for products made in ethical ways Elliott and Freeman [7]); or they may want to disassociate themselves from markets seen as legitimizing unfair actions. This latter concern has been for example used by opposers of emission quota trade systems [9].

In this article, we assess whether “unfair” imposed terms-of-trade in a quasi-market setting affects willingness to participate in trade that is Pareto-improving in monetary payoffs. While many experimental studies of other-regarding preference have involved institutions where strategic considerations play an important role [10], we reduce opportunities for strategic behavior to isolate the effect of other-regarding preferences1. Such preferences have previously been found in dictator games (where many individuals split the payoff with their co-player even in one-stage games, see e.g., Kahneman et al. [1] and Forsythe et al. [11].), but in these cases an increase in payoff to one player always comes at the expense of a decreased payoff for the other player. In our game, by contrast, both players maximize their own payoff as well as the other player’s by trading to the maximum extent possible—but in two of the three treatments trading the maximum amount also maximize the inequality in the earnings distribution.

Previous research has found that buyers in posted-offer experiments withhold Pareto-improving trade when posted prices implied an uneven distribution of the gains, but also that this effect decreased substantially in the final rounds. This suggests that the early restrictions were strategically motivated to force fairer offers in later rounds [12,13,14], indicating a smaller role for other-regarding preferences. Similarly, players are typically far more generous in the ultimatum game—where there are strategic motives—than in the dictator game—where there are none [11]. The importance of distinguishing between strategic and other-regarding preferences has also been highlighted in the literature on inequality aversion, where some theories highlight other-regarding preferences [15,16,17], while others focus on strategic motives [18,19,20].

We contribute to the literature by designing a stylised bilateral trade game that isolates other-regarding preferences. Strategic incentives or retaliation motives are largely absent: the terms of trade are fixed by the experimenters and no communication between partners in a trading pair is allowed. Our experimental design allows us to study how asymmetric splits of the gains from trade influence willingness to make trades that are Pareto improving in monetary payoffs, where the highest payoff for both participants is achieved by maximizing trade in each period.

Participants were randomly paired into buyer-seller pairs and randomized across three treatments defined by varying exogenously fixed trading prices. Sellers had high resource endowments in each period, but low productivity: they received a small payoff per resource held at the end of each period. Buyers had low resource endowments in each period, but high productivity: they received a high payoff from each resource held at the end of each period. The productivity difference generates a potential gain-from-trade, where the distribution of the gains depends on the transaction price per unit. Only the realized trade in each period, determined by the constraining partner(s) in the pair, was made known to both participants.

Prices were exogenously given, both parties were price-takers, and all possible trades were Pareto improving in monetary outcomes. Both participants chose a desired transaction volume, and the lowest choice determined actual trade in the round. The game lasted ten rounds, and cumulative payoffs were updated between each round and displayed to participants both numerically and with bar-charts (see instructions in Supporting information Appendix B). In any round, participants were given the opportunity to test how these payoffs would change conditional on different trading volumes in the ongoing round.

Since all trades under all price regimes were Pareto-improving in monetary payoffs, both minimax, efficiency and strategic theories of inequality aversion would predict full trade, while the inequality aversion theory of Fehr and Schmidt [15] would predict trade restriction. This allows us to study whether “pure” inequality aversion influences willingness to trade in a trade setting where these potential confounds are removed by design.

Our hypothesis, in line with the theory of inequality aversion by Fehr and Schmidt [15], is that strongly asymmetric payoffs would reduce trade - particularly from the low-benefiting side. In an earlier pilot experiment conducted in Oslo, Norway, we also assessed whether low-gain sellers reduced trade more than low-gain buyers2. This hypothesis, for which we do not have a theoretical justification, seemed psychologically plausible to us based on introspection, in that having to sell something you own for a price far below its value would feel more unjust than having to buy something for a price close to its actual value.

The results show clear evidence of trade-restriction from both sides in treatments with asymmetric price, but a substantially stronger reduction from the low-benefit partner. The hypothesis that low-benefit sellers reduce more than a low-benefit buyer finds weaker support. Estimates are similar when based on data from the last five rounds (to avoid potential learning effects), but weaker for the seller/buyer distinction.

The paper is organized as follows: Section 2 presents the game and gives a detailed description of the experimental design. Section 3 describes the data and reports the results. Finally we conclude by discussing the findings and their implications.

2. Experimental Design

A total of 128 students from Columbia University were recruited with the Online Recruitment System for Economic Experiments (ORSEE) and divided in six sessions over different days. The participant group is diverse in terms of gender, discipline of study and country of origin, although a majority of participants are from the United States (see

Table 1. Summary Statistics.

Variable	Mean	Std. Dev	Percent
Female			55%
Age	24	3.9
Field of study:
Economics & Business			15%
Other social sciences			30%
Engineering			11%
Humanities			9%
Natural Sciences			12%
Other			23%
Nationality:
North America			48%
South America			5%
Asia			30%
Europe			7%
Other			11%

Number of Observations: 128.

). The experiment was programmed with z-tree software [21] and was run in April 2014 at Columbia Experimental Laboratory in the Social Sciences. The experiment used a fixed-partner and between-subjects design. Take home earnings ranged from USD 5.4 to USD 45.6 with an average of USD 24.3, plus a flat show up fee of 5 USD. The payment was made in cash immediately after the experiment as the students left the lab. Subjects were asked to answer a short survey immediately after playing the game. The experiment lasted in total about one hour. At the beginning of each experimental session, a written set of instructions was handed out to the participants and read aloud (reported in Supporting information Appendix B).

2.1. The Trade Game

Participants were randomly assigned to be buyers or sellers and then randomly matched into trading pairs that remained fixed for ten identical trading rounds. Subjects were told that they would face a trading price that was given and constant across all rounds, and that this price would determine how the gains of trade were split between the two parties. Players were also given a fixed number of resources as endowment every round, and a productivity parameter that translated resources into the Experimental Currency Unit (ECU). The ECU had a fixed and known exchange rate to US dollars, with 50 ECU = 1 USD.

Buyers converted resources to monetary payoffs with a high productivity, but were given a low initial resource endowment. In each round, they received one resource and at the end of each round they earned 20 ECU for each held resource. Sellers faced the opposite situation, with low productivity and high resource endowments: in each round, they received 20 resources and they earned 1 ECU per resource held at the end of the round. Note that the no-trade payoffs were identical (20 ECU per round) for both buyers and sellers. The total gain from trading was determined by the difference in productivity, in that each resource held at the end of a round was worth 19 ECU more for the buyer than for the seller. Price, resource endowments and productivity for both types was common knowledge.

During the experiment, the buyer-seller pairs were free to trade resources at a fixed and given price to increase their payoffs. The instructions specifically reminded them that they could trade resources with their partner “to increase earnings”. Trade in each round took place as follows: both players simultaneously stated their desired trading level (ranging from zero to ten units per round). Since trade was voluntary, actual trade was determined by the lowest offer. Before making their choice, both parties were visually informed, with bar graphs and numbers, of their own and their co-player’s (1) secured incomes in the present round (i.e., the players’ earnings in the absence of trade); (2) possible gains from different levels of trade in that round; and (3), from the second round onwards, cumulative payoffs from all previous trading rounds. For players in all treatment groups, this visualization made one aspect of trade particularly relevant to the experiment clear, that is, that trade increased both parties’ payoff. The visualization received by players under the asymmetric treatment also made it clear that trade made outcomes highly unequal.

Prices were known, exogenously given, and constant over all rounds within each buyer-seller pair. Each pair faced one of three price treatments. The buyer treatment favors the buyer, with a fixed price of 3 ECU. For each unit sold, the seller made a 2 ECU profit relative to keeping the unit and producing ECUs with a low productivity, while the buyer made a 17 ECU profit by receiving 20 ECU from production minus the purchasing price of 3 ECU. The seller treatment, benefits the seller with a price of 18 ECU. Each unit traded in this treatment gave the seller a profit of 17 ECU (18 in sales price minus 1 in foregone production income), while the buyer netted a profit of 2 ECU. Finally, the symmetric treatment is equally beneficial to both with a price of 10.5 ECU. They both earned a profit of 9.5 for each resource traded (the seller earned the sales price 10.5 minus 1 in foregone production and the buyer earned the production “revenue” of 20 minus a purchasing price of 10.5 ECU). Payoffs are shown in

Table 2. Payoffs for Buyers and Sellers by Treatments.

	Buyer T		Seller T		Symmetric T
	Price: 3		Price: 18		Price: 10.5
Resources	Buyer	Seller	Buyer	Seller	Buyer	Seller
0	20	20	20	20	20	20
1	37	22	22	37	29.5	29.5
2	54	24	24	54	39	39
3	71	26	26	71	48.5	48.5
4	88	28	28	88	58	58
5	105	30	30	105	67.5	67.5
6	122	32	32	122	77	77
7	139	34	34	139	86.5	86.5
8	156	36	36	156	96	96
9	173	38	38	173	105.5	105.5
10	190	40	40	190	115	115

. For instance, in the buyer treatment, if the buyer suggested full trade while the seller offered to trade only 8 resources, the actual number of resources traded would be 8 and the final payoffs would be 156 ECU for the buyer and 36 ECU for the seller.

3. Results

This section analyses trading behavior of 126 students from Columbia University who participated in six experimental sessions run at similar times during a two-week period in April 2014.3 There was a total of three treatments: 22 pairs took part in the buyer favoring treatment, 20 pairs in the seller favoring treatment, and 21 pairs in the symmetric treatment.

3.1. Statistical Model

Each participant faced constant trading terms within the experiment, and had to decide how many of 100 potential transactions they wanted to accept on these terms. Assuming that the probability of rejecting any single transaction is constant at the individual level conditional on an individual’s position in the market (buyer/seller) and treatment (exogenous price), the number of rejected transactions will be a binomial draw with an individual-specific rejection probability.

The individual-specific rejection probability may differ systematically with treatment, in addition to differing “non-systematically” due to heterogeneity in the baseline trading preferences of the participants. If the underlying heterogeneity in baseline trading preferences can be captured using the flexible beta-distribution, this implies that the number of rejected transactions will follow a beta-binomial distribution. Note that this imposes no strong structure on the preference distribution: It allows for a bi-modal distribution where people are either trading fully or not at all, as well as distributions where people are concentrated around a specific region of trade-rejection probabilities.

An intuitive illustration of the beta-binomial distribution is that we face a large number of jars that have different shares of red and white balls. The distribution of red-ball shares across the different jars is given by a beta-distribution. Each observation (i.e., total trades rejected by an individual across 10 rounds) consists of 100 balls drawn from a single randomly drawn jar.

The beta-distribution is parametrized in terms of an “average” probability and a dispersion parameter that captures the heterogeneity in baseline trading preferences. We assume that the treatment effects influence the average probability, and model the average probability using a logit formulation with additive coefficients capturing the systematic influences from market position and treatment:

• Inequality—Individuals in the symmetric payoff treatment are the reference category—all others have this parameter capturing the effect of being in an asymmetric payoff treatment. We hypothesize that asymmetric price treatments would reduce trade.
• Relative loser—In one of the two asymmetric payoff treatments the price benefits the seller, in the other the buyer. We expecte that the “relative loser” would restrict trade to a larger extent.
• Seller side—Based on an earlier pilot experiment in Oslo, Norway, we suspected that sellers might restrict trade to a larger extent than buyers when on the “losing side” of an asymmetric payoff treatment. We speculate that this might reflect a feeling that “your” resource is being “exploited” by someone else.

The model is estimated using Bayesian Maximum Likelihood (ML). To reduce overfitting to stochastic noise, the model is specified using a normal distribution for the effect priors. The effect priors are centered on 0 with a standard deviation of 0.5 standard deviation. This is a conservative prior that, roughly stated, asserts that effect sizes are unlikely to alter an individual’s “baseline” probability of rejecting a transaction by more than +/− 65%. By comparison, a “frequentist” (non-Bayesian) maximum likelihood model would be equivalent to Bayesian model with a prior assigning equal prior probability to any coefficient value from minus to plus infinity.

Analysing the data within this model has the benefit that we estimate all effects simultaneously using a statistical model that explicitly accounts for between-participant heterogeneity in trading preferences. In addition, the Bayesian priors help shrink effect estimates towards zero and reduce the risk of statistical overfitting to random noise. For robustness we analyze the data using non-parametric tests, and the results are in line with the ones reported below (see Supporting information Appendix C).

3.2. Estimation

The actual distribution of “total rejected transactions” within each treatment is shown in Figure 1, separately for each side of the market (see supporting materials for further plots of raw data).

The model is specified in the Stan language for probabilistic models (see supporting info for code in Supporting information Appendix A) and estimated using Hamiltonian Markov Chain Monte Carlo and a No U-Turn Sampler [22]. Four chains were run for 10,000 iterations, with the first half used for warm up and discarded from analysis.

3.3. Results

The estimation returns a sample of parameter values drawn from the posterior distribution of the model parameters. The model converges well, as shown by the Rhat values in the estimate table (

Table 3. Estimation output.

	Mean	SE_Mean	SD	2.5%	25%	50%	75%	97.5%	n_eff	Rhat
${\varphi }_{raw}$	−3.28	0.00	0.30	−3.88	$-3.48$	−3.27	−3.07	−2.70	12,773	1
${\lambda }_{raw}$	0.66	0.00	0.21	0.23	0.52	0.67	0.81	1.06	15,810	1
$selle{r}_{coef}$	0.26	0.00	0.31	−0.36	0.05	0.26	0.47	0.87	16,425	1
$losing\_sid{e}_{coef}$	0.75	0.00	0.30	0.16	0.55	0.75	0.95	1.32	15,518	1
$inequalit{y}_{coef}$	0.56	0.00	0.30	−0.03	0.36	0.56	0.77	1.17	13,942	1
lp	−2262.79	0.02	1.60	−2266.80	−2263.60	−2262.47	−2261.61	−2260.69	8841	1

). These assess how similar the posterior estimates are in different chains and in different sections of the same chain, and should be close to 1, as they are.

To assess the results, we compare the prior distribution imposed on the effect coefficients to the posterior distribution. This tells us how informative the data is - the extent to which it updates and shifts the prior. As seen in Figure 2, all effect distributions are updated in the expected direction. Given the model and the prior, the probability that the effect coefficients are positive has increased from 50% to 99.3% (the “relative loser” parameter), 96.9% (the “asymmetric price” parameter) and 80.1% (the “seller” coefficient)—with average effect parameter values across the posterior of 0.75, 0.56 and 0.26 respectively.

To interpret the parameters, we note that these influence the average transaction rejection probability through an additive term in a logit specification. Exponentiated parameters will express the odds-ratios of rejecting transactions when the effect represented by a given parameter is present relative to when it is not. These odds-ratios can in turn be interpreted as relative risks, since the baseline rejection probability is very low.

We can thus calculate the relative risk of rejecting a transaction for the three possible combinations of effect parameters. Using the average parameter values under the posterior:

• Being in an asymmetric treatment on the benefiting side increases your probability of rejecting a transaction by a factor of 1.75
• A buyer with an asymmetric price that does not favor him/her has a rejection probability increased by a factor of 1.75 × 2.12 = 3.71
• A seller with an asymmetric price that does not favor him/her has a rejection probability increased by a factor of 1.75 × 2.12 × 1.30 = 4.823

Note that these are relative risks, which means that the increase in absolute risk will be small for most participants given the low baseline trade-rejection probabilities (see Figure 3).

The model assumes that the individual-level rejection probabilities of the participants are fixed throughout the experiment. This may not hold. In particular, we did not have practice rounds and may suspect that data from the initial rounds reflects learning and “noise”. Such noise would be common to all treatments and should not substantively influence the effect estimates, but would tend to increase the estimated dispersion of the baseline trade preferences.

To assess this, we re-estimate the model using only data from the last five rounds of the experiment. The effect coefficients remain similar (see Figure 4). We can also visualize the distribution of the baseline “non-trading preferences” in our sample. These are given by the parameters ${\varphi }_{raw}$ and ${\lambda }_{raw}$ in Table 3, and are the logged values of the expectation and dispersion parameters from our beta distribution for non-trade preference heterogeneity 4. In the main analysis, for instance, the median value for this parameter across the posterior implies a probability of not trading a single unit equal to exp(−3.48) = 3.1%. Plotting the preference distribution estimated from the full dataset and from the last five periods shows that the estimated heterogeneity of the baseline trading preferences is substantially reduced in the last five periods (Figure 3). This suggests that some of the non-trades chosen in the earlier periods can be viewed as learning, experimentation or “noise”.

Finally, we teste the inference procedure by re-estimating the model on scrambled data, created by randomly assigning treatment group labels to the observations. In this data there will be no systematic difference between the observations grouped under each treatment. In line with this, the posterior distributions for the effect parameters tends to remain centered on zero, with a reduced variance relative to the prior (not shown). Essentially, in data with no treatment effect the model correctly infers that we should be more certain that the treatment effects were close to zero.

4. Conclusions

In line with predictions from the Fehr and Schmidt model [15] we report evidence of substantial reductions in desired trade when the terms of trade generate substantial inequality. At the individual level, however, trade reductions were typically partial, while the linear utility formulation of the Fehr and Schmidt model would predict that any single participant would trade fully or not at all. While both parties to the trade reject more transactions when trade generates substantial inequality, the reduction is roughly twice as large for the party that benefits the least. While the prior shifts in the expected direction also for the “seller coefficient”, indicating that a non-benefiting seller reduces transactions more than a non-benefiting buyer, the evidence of such role-asymetric effects is weaker.

We note that all trades are Pareto improving in monetary outcomes, such that models of inequality aversion focusing on maximin payoffs or efficiency [16,17,23] would have predicted full trade. We also note that there are no obvious strategic motives for reducing trade in the experiment. In fact, the only way to increase the payoffs of both yourself and your co-player is to increase trade volume, and trading terms are fixed across all rounds for any participant. Only a minimal “signal”, concerning the desired trade relative to the co-player, passed between players during the game. The lack of direct strategic motives in the experimental design supports an interpretation of the findings as aversion to an unequal distribution of trade outcomes.

The strong effect of “unfair” trading terms on the willingness to trade goes against the rather strong claim in Charness and Rabin [16] that “few subjects sacrifice money to reduce inequality by lowering another subjects’ payoff, and only a minority do so even when this is free”. The results imply that such factors may have an influence in some real world markets. We would not, however, claim that the current results are sufficient to establish a substantial role for such influences in real world markets. The experiment made the distribution of gains-from-trade highly salient to participants, whereas such information may often be missing in real world markets. Fair trade products, however, may be viewed as providing such information about the gain distribution in order to attract consumers who care about outcome inequality, arguably raising consumer welfare by facilitating product differentiation [4]. Also, we note that our experiment imposes an exogenous trading price, whereas real world markets have endogenous prices. In theory, this will allow trading parties to agree on an acceptable distribution of the gains from trade and realize all Pareto-improving trades. In practice, however, workers in large companies and consumers in grocery stores may be unlikely to believe that they can enter into bilateral negotiations over wages and prices. As a result, markets may be perceived by participants at different ends of the value-chain as having "exogenously fixed" terms of trade, and the decision to participate in the market or not may then be influenced by perceived "fairness" of the current terms-of-trade.