Respect thy Neighbor: Actor Incentivization and Equilibria in a Networked Public Goods Model (2014)

Undergraduate: Lauren Friedmann

Faculty Advisor: Peter Mucha
Department: Economics

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Traditionally in a public goods model, individuals decide whether or not to contribute to the good based off of the actions of their neighbors, and a pre-determined payoff parameter that will tend to be uniform for all actors in the network. This decision-making process for an individual actor to contribute to a public good has historically been instrumental in providing the theoretical framework for the conservation of public goods. In this study, an existing popular proposition in the literature claiming that if the absolute value of the minimum eigenvalue of the adjacency matrix is less than the inverse of the payoff parameter, then there is a unique Nash equilibria, is tested. In this process, the condition that one payoff parameter must be utilized for all the agents in the network is relaxed, and is tested on two randomized network models: the Erdős¿R¿nyi and Stochastic Block Models. Then, the existence of both unique and multiple Nash equilibria, and their location as interior solutions are explored in relation to the number and range of the different payoff parameters. While the final analysis is still in progress, it has become apparent that the number of Nash Equilibria notably increases once the payoff parameters in the network rise above a ¿threshold¿ value.