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Social Choice and Welfare

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03.04.2018 | Original Paper

Cost asymmetry and incomplete information in a volunteer’s dilemma experiment

verfasst von: Andrew J. Healy, Jennifer G. Pate

Erschienen in: Social Choice and Welfare | Ausgabe 3/2018

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Abstract

We utilize a laboratory experiment to examine the effect of asymmetric costs in the volunteer’s dilemma, a public goods game where all players receive a benefit if at least one person volunteers and nothing otherwise, which presents a social dilemma where the optimal action for the individual differs from that for the group. Additionally, we introduce uncertainty to explore the role of information and find that individual behavior aligns most closely with the more intuitive Nash equilibrium strategies under full information and to a lesser extent with incomplete information. Although uncertainty about fellow group members’ costs incentivizes greater volunteering and thus has the potential to improve efficiency, we find that the inability to coordinate prevents groups from experiencing welfare gains as a result.

Vorheriger Artikel Working time regulation, unequal lifetimes and fairness

Nächster Artikel A concept of sincerity for combinatorial voting

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Diekmann applied this reasoning to the case of Kitty Genovese, a New Yorker who was stabbed to death in from of a building block where a significant number of people allegedly witnessed the attack. No one supposedly came to her rescue or even called the police. This situation demonstrates a volunteer’s dilemma; everyone likely would have benefitted if at least one person called the police, yet there was a diffusion of responsibility where everyone apparently believed that someone else would make the call. This resulted in the non-optimal outcome where the public good, in this case the arrival of the police, was not provided.

There is also a coordinated volunteer’s dilemma where, if more than one person volunteers, only one player is randomly selected to serve as the volunteer so there is no redundant volunteering. The coordinated game models scenarios where a maximum of one volunteer may bear the cost, resulting in a different set of strategies and potential outcomes. See Bergstrom et al. (2015) for theory and experimental findings on coordinated volunteer’s dilemma games.

In Darley and Latane (1968), the experiment involved recruiting college students under the ruse that they were taking part in a conversation with another student about college life over an intercom system. Then, one of the students would have a, “very serious nervous seizure similar to epilepsy.” The dependent variable in the experiment was how long each subject took to report the emergency to the experimenter.

Meaning, if N = 6, in individual that draws a $0.60 cost knows that either all six group members have $0.60 or that half of the group (3 other members) face a cost of $0.20, with equal probability. The costs were randomly drawn across rounds in advance and set in the design to ensure consistency in the variation and order of cost draws experienced across experimental sessions.

The goal is not to encourage or support learning across the experiment, but rather to make each round independent from one another in order to test how the likelihood of volunteering may vary across costs and information specifications. Thus, we provided the minimum amount of information between rounds, which is strictly whether or not there was at least one volunteer (which subjects could infer from their earnings in each round).

There are also asymmetric equilibria where one person volunteers and other group member (or members, when N = 6) do not, even when costs are identical. The random re-matching function of the experimental design would make this equilibrium challenging for coordination, but it is worthwhile to note.

There is also a mixed strategy Nash equilibrium that is similarly counter-intuitive. For N = 2, the probability that the low-cost player contributes is 2/5 and the high-cost player contributes with probability 4/5.

There is no purely mixed strategy equilibrium when N = 6 with 3 of each type of player (low cost or high cost), as noted in Diekmann (1993). For N = 6, this means that players may be constrained to an equilibrium where one type (the high-cost player) does not mix, which is supported by the experimental data.

For N = 2, the expected rate of return to volunteering is always positive when the cost draw is low, while the expected return with a high-cost draw is always negative, so there are no mixed-strategy equilibria with N = 2 with incomplete information.

It is straightforward to show that there is an asymmetric pure strategy equilibrium where the low cost players volunteer with probability p = 1 and the high cost players do not volunteer if and only if N ≤ 3. The payoff to the low-cost volunteers is 0.8. If we assume the high-cost players do not volunteer, the expected return to a low-cost player who does not volunteer is 1 − $ (1/2)^{N - 1} . $ There will be a pure strategy of this type only if 1 − c > 1 − $ (1/2)^{N - 1} , $ which is only true for N ≤ 3.

Although we use the more-intuitive predictions to make comparisons to the experimental data, it is worthwhile to note that the many other asymmetric and mixed-strategy Nash equilibria are still possible regardless of whether or not they are intuitive.

Although subjects in this experiment could not communicate, other experiments with repeated games have found successful instances of turn-taking. For example, in common-pool resources games (Cason et al. 2013), or in repeated allocation games (Kuzmics et al. 2014), or theoretically (in Leo 2017).

Hillenbrand and Winter (2018) find that lower costs to volunteer do not increase a player’s likelihood of volunteering, but there are two critical experimental differences: (1) they use a one-shot version of the game so subjects only experience one cost specification and thus there is no opportunity to observe how an individual subject would change strategies in response to differing costs, and (2) the cost variations in that study were quite small, with a “low” cost of 4€ or a “high” cost of 5€, both with a benefit of 10€, which also likely contributed to the non-finding.

Another unintuitive result may be the lack of a significant gender effect. Vesterlund et al. (2015) find evidence from a coordinated volunteer’s dilemma that people believe that women are more likely to volunteer, but there is no evidence in our data to suggest a gender effect in any of the cost specifications or overall rate of volunteering. We revisit player behavior by gender again in Sect. 5.4.

When costs are high, subjects volunteer approximately 11.1% of the time under incomplete information versus 13.7% with full information, which are not significantly different (p value of two-sided t-test = 0.39).

If we include an individual fixed effect in the regression in column 1 of Table 4, the coefficient for free-riding in the previous period is − 0.072, with a standard error of 0.021. The coefficients for all the variables that vary within-subjects remain essentially equivalent to those in column 1.

We found no significant gender effects in this experiment, either in rates of volunteering (p-value of a two-sided t-test = 0.905) or in preference types. Regarding the latter, is interesting to note that although those with the highest and lowest volunteer rates were men, women were the second and third next-highest volunteers in the sample, and women were also the next two lowest volunteers at the low side, right before the three pure free-riding males.

A successful free-rider with cost c = 0.20 has relative earnings of $1.00 compared to $0.80 if they volunteered (a 20% return on free-riding), while a successful free-rider with cost c = 0.60 has relative earnings of $1.00 compared to $0.40 if they volunteered (a 40% return on free-riding).

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Titel: Cost asymmetry and incomplete information in a volunteer’s dilemma experiment
verfasst von: Andrew J. Healy
Jennifer G. Pate
Publikationsdatum: 03.04.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2018
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-018-1124-6

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