Source-linked AI summary
Cooperation and Contagion in Web-Based, Networked Public Goods Experiments
Siddharth Suri, Duncan J. Watts
TL;DR
The paper tests whether network structure reinforces cooperation through conditional responses and contagion. Across web-based public goods experiments with 24 players on five topologies, topology had no significant effect on average contributions, while conditional responses were bidirectional and positive influence reached only direct neighbors. The authors also report that web-based experiments enabled 113 experiments at low cost, though the contagion design limited conclusions about influence at different distances.
Problem
Prior theoretical, simulation, and experimental findings were ambiguous about whether network structure affects cooperation through reinforcement and contagion.
Method
The study conducted web-based local public goods experiments with 24 players arranged on five network topologies, then introduced artificial cooperative or defecting seed players to test conditional cooperation and contagion.
Results
Network topology had no significant effect on average contributions; conditional responses included both increases and decreases, and positive cooperation effects were contagious only to direct neighbors.
Takeaways & Limitations
Highly clustered networks need not improve cooperation because conditional cooperation can reinforce defection as well as cooperation, while positive influence may remain local.
Takeaways & Limitations
The seed arrangement subjected human players to the same potential direct and indirect influence, limiting conclusions about contagion at different distances.
Abstract
from arXiv · showhide
A longstanding idea in the literature on human cooperation is that cooperation should be reinforced when conditional cooperators are more likely to interact. In the context of social networks, this idea implies that cooperation should fare better in highly clustered networks such as cliques than in networks with low clustering such as random networks. To test this hypothesis, we conducted a series of web-based experiments, in which 24 individuals played a local public goods game arranged on one of five network topologies that varied between disconnected cliques and a random regular graph. In contrast with previous theoretical work, we found that network topology had no significant effect on average contributions. This result implies either that individuals are not conditional cooperators, or else that cooperation does not benefit from positive reinforcement between connected neighbors. We then tested both of these possibilities in two subsequent series of experiments in which artificial seed players were introduced, making either full or zero contributions. First, we found that although players did generally behave like conditional cooperators, they were as likely to decrease their contributions in response to low contributing neighbors as they were to increase their contributions in response to high contributing neighbors. Second, we found that positive effects of cooperation were contagious only to direct neighbors in the network. In total we report on 113 human subjects experiments, highlighting the speed, flexibility, and cost-effectiveness of web-based experiments over those conducted in physical labs.
Introduction
The paper addresses conflicting evidence about whether network structure shapes cooperation, focusing on conditional cooperation and contagion as possible mechanisms. It motivates clarifying web-based experiments testing how network topology relates to cooperation.
- Conditional-cooperation models predict that highly clustered networks should sustain higher aggregate cooperation because neighbors reinforce one another.
- A second proposed mechanism is contagion, whereby increased cooperation can spread through direct and indirect network connections.
- Conditional cooperation can also reinforce defection, so clustering may amplify negative as well as positive effects.
- Prior simulations and experiments produced mixed or inconclusive conclusions, motivating clarifying experimental evidence.
- The paper investigates whether network structure affects cooperation in networked public goods experiments.
Results
The study uses a networked public goods game in which players contribute to a common pool and receive redistributed benefits. The game preserves a social dilemma because collective welfare favors contribution while individual incentives favor free riding.
- 113 experiments used a public goods or common pool resource game in which participants made voluntary contributions to a common pool.
- Players’ payoffs combine their endowment, voluntary contribution, and a multiplied share of contributions within the relevant interaction group.
Experimental Design
The experiment places 24 players with degree 5 on network topologies ranging from disconnected cliques to a regular random graph. Payoffs are calculated from each player’s local network neighborhood rather than the entire population.
- Players’ payoffs sum contributions over Γ(i), the neighborhood of player i including i itself, rather than over the entire group.
- All networks contain n = 24 players with constant degree k = 5, while varying in clustering, average path length, and diameter.
- In the experiment screenshot, players interact with a local network of five others.
- The design keeps partners fixed while changing the connectivity among each player’s partners across network structures.
- The five topologies span four disconnected cliques, connected and near-clique structures, a small-world network, and a random regular graph.
Recruiting and Retention.
The researchers used Amazon Mechanical Turk to recruit participants for simultaneous web-based network experiments. Because filling 24-player networks was difficult, they built a standing panel and used a virtual waiting room to coordinate participants.
- Amazon Mechanical Turk workers were recruited through paid human intelligence tasks.
- A virtual waiting room held participants until all positions in the network were filled and the game could begin.
- Preliminary four-player experiments helped create a standing panel of 152 returning players who understood the instructions.
- The researchers used automated contribution entry and other rules to handle missed turns, departures, and nonparticipation.
Calibrating the AMT population
The study first addressed whether web-based AMT experiments produce results comparable to physical-lab studies and whether compensation levels affect contributions.
- The authors conducted 24 preliminary experiments to replicate conditions from a previous lab-based study.
Testing for Effects of Network Structure
Across five network topologies, network structure did not produce noticeable differences in contributions at aggregate, group, or individual levels. Initial contribution differences persisted over time, and removing them further reduced the already small topology differences.
- 23 experiments compared average contributions across five network topologies, finding no significant differences by round.The smallest Kruskal-Wallis test result was H=6.43, df=4, P=0.17 in round 8.
- Initial contribution curves that began higher generally remained higher throughout the experiments, although first-round contributions were unrelated to topology.
- Vertically shifting contribution curves to equalize their initial values further diminished the already small differences between topologies.
- The fraction of groups contributing at least X and the distributions of individual contributions were similar across all topologies.Individual contribution distributions changed over the ten rounds, reflecting an average decline, but those changes were similar across topologies.
- The study concludes that topology did not noticeably affect contributions at aggregate, group, or individual levels.
Testing for Conditional Cooperation.
Seed-player experiments showed that participants responded conditionally to cooperating and defecting neighbors, but higher clustering did not consistently amplify seed effects. Triangles increased coordination in both directions rather than increasing contributions overall.
- In 30 experiments, four computer-controlled seed players contributed either 10 or 0 in every round.
- The cover arrangement exposed human players to equivalent direct and indirect seed influence across the network.
- Cooperating seeds increased aggregate contributions, whereas defecting seeds decreased them across all topologies.These responses indicate that subjects behaved as conditional cooperators.
- Seed effects were not consistently larger in highly clustered graphs: Cliques produced effects similar to Random Regular networks with fewer than one-tenth as many triangles.
- Adding edges or completing triangles increased similarity between human players’ contributions, but raised contributions near cooperating seeds and lowered them near defecting seeds.Thus, triangle-based coordination was bidirectional and did not correspond to higher contribution levels overall.
Testing for Contagion.
The concentrated-seed experiments tested whether cooperation spreads beyond seed neighbors. Human responses were positive near cooperating seeds but did not produce positive effects at two network steps.
- Limitations: The cover-seed experiment could not isolate contagion by distance because all human players experienced the same potential direct and indirect influence.
- Experimental design: The concentrated condition placed four cooperating seeds into two adjacent pairs, exposing some players to two direct seeds and others only indirectly.The clique topology was excluded because it could not accommodate this arrangement.
- Experimental design: The experiment predicted higher contributions from two-step neighbors than corresponding positions in all-human networks and higher direct-neighbor contributions than in the cover-seed condition.
- Results: Direct neighbors of two cooperating seeds contributed more than players with no seed neighbors but less than players attached to one seed.This pattern suggests that too many unconditional cooperators can invite free riding.
- Results: Immediate neighbors of cooperating seeds contributed more than in the no-seed condition, but two-step neighbors contributed slightly less than corresponding nodes in all-human experiments.
- Testing for learning effects: Additional all-human experiments found no systematic decline from learning, experience, or selection effects that could explain the reduced two-step contributions.Average contributions had, if anything, increased slightly in the later all-human experiments, and players with up to 40 games did not contribute more or less on average.
Discussion
The experiments found no significant effect of network topology on contributions, despite strong conditional cooperation. Positive influence did not propagate through multiple network steps, although targeted cooperative seeding could increase contributions cost-effectively.
- Network topology had no significant effect on contribution levels in the standard public goods game.
- Players showed strong conditional cooperation, increasing contributions near cooperative neighbors and decreasing them near defecting neighbors.
- Positive cooperation effects did not spread through multiple steps along fixed network ties.
- Highly clustered networks provide opportunities for both positive and negative reinforcement, while random graphs largely block propagation in either direction.
- The findings leave open which theoretical conditions produce contagion in dynamic games with fixed neighbors.
- Cooperative seeding or subsidies can stimulate network contributions without adding punishment, rewards, or sanctioning actions to the game.
- Positive seeding was cost-effective in four of five topologies, with seed costs below the marginal contribution increase among other players.
- The web-based design supported 113 experiments at roughly $1.50 per subject per experiment and could scale beyond networks of n = 24.
Materials and Methods
Participants were recruited through Amazon Mechanical Turk for a web-based Investment Game, with human-subjects review and anonymized data handling.
- Participants were recruited on Amazon Mechanical Turk through a HIT titled “The Investment Game.”
Ethics Statement
The terms required informed consent and governed participation, payment, confidentiality, indemnity, warranties, liability, and public statements.
- Participants had to read and acknowledge a terms-of-use agreement equivalent to informed consent before participating.
- The project was offered to workers registered with Amazon Mechanical Turk and governed by additional Mechanical Turk conditions.
- Yahoo! owned work produced through participation and paid $0.50 plus a skill-dependent bonus through Mechanical Turk.
- Participants could leave at any time, while Yahoo! could suspend or terminate the project and pay for completed tasks.
- Participants were required to keep project, terms, policy, and technical information confidential.
- Participants agreed to indemnify Yahoo! for claims arising from their activities, including legal, privacy, and intellectual-property violations.
- The project was provided “as is,” without guarantees of uninterrupted or error-free operation or earnings.
- Yahoo! disclaimed liability for indirect damages and capped direct damages at amounts already paid; dissatisfied participants’ remedy was discontinuation.
Participant Instructions
Participants played a fixed-neighbor, ten-round local public goods game in a network of 24 Turkers, choosing contributions from a 10-point endowment and receiving neighborhood-based payoffs.
- Participant Instructions: The experiment collected data on how well people played the Investment Game after participants accepted the HIT and completed a comprehension quiz.
- Overview: Each participant interacted with 23 other Turkers but observed only directly connected neighbors, with network ties fixed throughout.
- Overview: The game lasted 10 rounds, and each round’s project payoff was split equally among a player and direct neighbors.
- Overview: Points were converted to dollars at 2 cents per point, while the base HIT payment was 50 cents for passing the quiz.
- How the game works: Players received a 10-point endowment each round and chose an irreversible contribution between 0 and 10 points.
- How the game works: Round decisions had 45-second limits initially and 30-second limits thereafter; missed decisions earned no points for that round.
- How the game works: Round income combined retained points with project income equal to 0.4 times total contributions from the player and neighbors.
- Four Examples of Payoffs: The payoff examples illustrate outcomes when everyone contributes equally, when neighbors contribute more, and when the focal player contributes more.
Participant Quiz
Participants completed a comprehension quiz before playing, answering public-goods-game income questions under specified contribution scenarios. Incorrect answers allowed a second attempt, but two failures prevented participation and payment.
- Participants had to pass a quiz demonstrating that they understood the game instructions.
- Participants received a second chance after an incorrect answer; two failed attempts barred them from playing and receiving HIT payment.
- Questions 1–4 assumed five neighbors and an endowment of 10 points each.
- The quiz asked participants to calculate total income when nobody or everyone contributed to the project.
- Additional questions varied the participant’s contribution and neighbors’ combined contributions to assess resulting income.