Public Good Provision in Overlapping Neighborhoods

2023-09-26

2024-01-20

• Closed neighborhoods (T1, T2) to resemble existing literature findings on linear public
goods (investments positive, but declining in both T1, T2); high endowment types investing larger absolute, but smaller relative share of endowment than low endowment players; potentially detrimental total effect of heterogeneity (T2 vs. T1) on investments and payoff.
• Overlapping neighborhoods (T3, T4, T5): players payoff depends not only on level, but
location of investments, players predicted to invest only in their own neighborhood.
• We explore if individual investments are governed by efficiency/equity/equality concerns.
Old: Whereas equity and equality can be reached simultaneously in the homogeneous settings (T1 and T3), these are competing hypotheses in the heterogeneous settings (T2, T4 and T5)./
New: By analyzing where people invest, we can differentiate the competing motivations which cannot be differentiated in normal public good settings. For instance, people can be equality, equity or efficiency oriented and thereby change their investment location. If this is the case we might observe larger total investment levels in T4 and T5.
• T5,T4 vs. T2: the spatial setting allows to address equity concerns by changing the location and not necessarily the level of total investments. Thus: rich players expected to contribute more in T4 /T5 than in T2 resulting in larger total payoffs, potentially also less inequality In T4, but larger inequality in T5 where rich players are clustered. Players predicted to invest in location(s) of own neighborhood which neighbors the largest number of neighboring high endowment players.
• Adjustment of investments over time: size and location of investments respond to type and investment decisions of neighbor as well as neighbor’s neighbor. Thus, we expect an
investment into the neighborhoods of rich players as more likely, with dynamic changes of investment locations in response to relative “kindness” of left vs. right neighbors.
• T3 vs. T1: larger provision levels over time than in T1 as change of location of own
investments allows for implicit punishment of underperforming neighbor.

• Dynamic adjustments of investment decisions
Also, further control variables from a short questionnaire at the end of the experiment:
• Demographics: Sex, age, field of study.
• Social preferences: risk-taking, prosociality.
• Task-related opinions: satisfaction with their own/their groupmembers’ decisions, perceived
generosity of their own/their groupmembers’ decisions.
• Task comprehension

We introduce a spatial public good game with overlapping neighborhoods. Six subjects interact and are located on a circle. Subjects are identified with their respective location (i ∈ {A,B,C,D,E,F}. For each subject, we define a neighborhood Ni. We consider closed and overlapping neighborhoods. The former serves as a baseline and forms a variant of a typical three-player public good game, NA = NB = NC = {A,B,C} and ND = NE = NF = {D,E, F}. In the latter, the neighborhood of a player is given by her location and her two direct neighbors. That is, NA = {A,B, F}, NB = {A,B,C}, NC = {B,C,D}, . . . ,NF = {E, F,A}. Here, each experimental subject benefits from public good investments in his location as well as the location of her two neighbors. Conversely, investments in any location benefit three players. The experimental treatments vary the endowments the individual players receive. We compare homogenous endowments of all players with heterogenous settings where three players receive a large, and three players receive a small endowment. In such heterogenous settings, the spatial distribution matters: we compare clustered endowment settings where three direct neighbors are rich (A, B,C) while the other three are poos (D,E,F) and alternating endowment settings where rich and poor alternate (A, C, E rich; B,D,F poor). We consider
this experimental setting as both novel and empirically relevant. Our experiment consists of five treatments. As a baseline, we reconsider “closed” neighborhood settings where groups of three individuals play a standard public good game. The only variant to the typical public good setup is the simultaneous presence (and information about) another group as well as the option to invest in any location. In this closed neighborhood setting, we consider a homogeneous income treatment, CNhom, where all agents have an endowment of 30, and a heterogenous setting, CNhet, where in one group two players are endowed with 20 and one player with 40, while in the other group two players are endowed with 40 and one player with 20 tokens. The other treatments introduce the overlapping neighborhoods as described above. Again, we consider homogenous endowments, ONhom, and two heterogenous settings, ONhetCL and ONhetAL, in which endowments are clustered or alternate, respectively. We otherwise stick to a linear public good setting. That is, each player can invest in any location. The payoff from investments to a player then is proportional to the total sum of investments in her neighborhood. The experimental sessions are scheduled to begin by the end of September 2023. They will be conducted by the experimental laboratory of the University of Vienna (Austria) in an in-person lab setting.
The University of Hamburg with which all researchers of this project are affiliated, does not issue IRBs but instead they have an internal ethical approval process in which a 'Declaration of compliance with Terms of Use and Ethical Standards' (DoC) needs to be signed and submitted. The details of the experiment are hereby approved by the dean of the faculty. The DoC has been submitted and approval has been received.

Note on previous data collection: During January and July 2023, we have collected data for this research project at the experimental laboratory of the University of Hamburg. As the capacity of the student pool for this in-person experiment was exhausted after about 200 data points, we decided to re-collect the whole required sample of 450 participants at the University of Vienna. The design was not changed and we intend to primarily use the data collected in Vienna and potentially make some exploratory comparisons with the data collected in Hamburg.

Randomization done in office by a computer.

Individual.
Randomization into treatments as well as locations and roles within the experiment done by
computer.

No

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The experiment will involve 90 participants, i.e. 15 independent observations of groups of six people, per treatment. Given the five treatments, we plan to recruit a total of 450 participants.

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