Why (Not) Having Social Capital? A Coevolving Network Model of Public Goods Game

• In Event: Poster Session: Political Methodology

Abstract

Two distinct features characterizing high productivity organizations are high levels of cooperation and strong connections between individuals. Because individual-level effort provisions are hard to observe in large, densely connected organizations, Public Goods Games (PGGs) are often used to study the micro-level incentive to free ride in this context. Yet, existing studies limit the analysis of this microfoundation to spatially and temporally restricted two-person network or computer-based experiments without allowing agents to interact with non-immediate neighbors and update their strategies over time.

Recent contributions by Roca and Helbing (2011) and Pichler and Shapiro (2016) study coevolving network models with PGGs application in complex networks, in which a node may choose to cooperate or defect with any arbitrary nodes in a non-planar network according to a satisfaction function that maximizes its aggregate payoffs per period: a node can either alter its current strategy or change its local network topology by adding or severing links with another other nodes. The dynamics of this complex system was then parametrized by a synergy factor to account for the non-zero-sum benefits of cooperation and a greediness factor measuring the adverse effect of free-riding on public goods provision. These models capture the emergence of social cohesion (and the lack thereof) based on self-interest where little assumptions on neighbors’ payoffs and degree distribution are made.

We build on this analytical framework to study social capital, a type of network in which links are formed on the basis of their “usefulness” and incur some sort of cost to maintain without which public goods are not provided. In this study, we develop an adaptive coevolving network model of PGGs with connection cost and preferential attachment to explore the dynamics behind the emergence and stability of cooperation. The model treat links as a form of social capital whose usefulness lies in producing public goods to be shared equally among connected nodes, nodes are thereby expected to connect with (or rewire from) any other nodes in the network only when the expected share of benefits from cooperation outweigh (below) the cost of maintaining the links. Secondly and due largely to this reason, nodes may prefer forming links with well-connected nodes to exploit the potentially larger aggregate payoffs from the networks of their high-degree partners, leading to power law-distributed networks that more closely represent the structure of real-life social networks.

Our adaptive model therefore maintains the low-information assumption of recent coevolving PGGs models, allowing agents to optimize their strategies intertemporally using easily observed structural and individual attributes – the topology of local network, degree distribution, and levels of greediness – without information on their partners’ actual payoffs prior to strategy choice at each time point. Through the imposition of connection cost and preferential attachment, our model also puts a bound on the maximum number of links that can be formed in a given network, thus clarifying why not all kinds of links are equally appreciated in public goods provision as well as the variances in observed inter-group heterogeneity often found in the vast literature of social capital (e.g., Putnam et al. 1993; Tsai 2007). The Monte Carlo simulation identifies the set of parameter values most likely to foster higher levels and longer duration of overall cooperation in the network even in the presence of adverse incentive to free ride.

The model has theoretical implications for a range of low-information social and organizational behaviors, such as shirking in work space where the incentives to connect to more co-workers and free ride on their productivity are both enormous. The model can plausibly be extended to theory of pre-electoral multi-party coalition in which partially observed individual electoral strength creates the incentives for parties to collaborate as well as exploit each other’s campaign effort. We analyze empirical data of work space projects participation and European electoral campaign data to provide further empirical support to the validity of our model.

Authors

• Hsuan-Wei Lee, University of North Carolina at Chapel Hill

• Huan-Kai Tseng, George Washington University