Publications

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Schank, J. C., Miller, M. L., and Smaldino, P. E. (Preprint, 2017). The evolution of fair offers with low rejection thresholds in the ultimatum game. doi:10.1101/162313

The ultimatum game (UG) is widely used in economic and anthropological research to investigate fairness by how one player proposes to divide a resource with a second player who can reject the offer. In these contexts, fairness is understood as offers that are more generous than predicted by the subgame perfect Nash equilibrium (SPNE). A surprising and robust result of UG experiments is that proposers offer much more than the SPNE. These results have spawned many models aimed at explaining why players do not conform to the SPNE by showing how Nash equilibrium strategies can evolve far from the SPNE. However, empirical data from UG experiments indicate that players do not use Nash equilibrium strategies, but rather make generous offers while rejecting only very low offers. To better understand why people behave this way, we developed an agent-based model to investigate how generous strategies could evolve in the UG. Using agents with generic biological properties, we found that fair offers can readily evolve in structured populations even while rejection thresholds remain relatively low. We explain the evolution of fairness as a problem of the efficient conversion of resources into the production of offspring at the level of the group.


Miller, M. L., and Ferrer, E. (2017). The effect of sampling-time variation on latent growth curve models. Structural Equation Modeling: A Multidisciplinary Journal, 24, 831-854.

Longitudinal data are often collected in waves in which a participant’s data can be collected at different times within each wave, resulting in sampling-time variation that is unaccounted for when waves are treated as single time points. Little research has been reported on the effects of this temporal imprecision on longitudinal growth-curve modeling. This article describes the results of a simulation study into the effect of sampling-time variation on parameter estimation, model fit, and model comparison with an empirical validation of the model fit and comparison results.


Miller, M. L., Ringelman, K. M., Eadie, J. M., and Schank, J. C. (2017). Time to fly: A comparison of marginal value theorem approximations in an agent-based model of foraging waterfowl. Ecological Modelling, 351, 77-86.

One of the fundamental decisions foragers face is how long an individual should remain in a given foraging location. Typical approaches to modeling this decision are based on the marginal value theorem. However, direct application of this theory would require omniscience regarding food availability. Even with complete knowledge of the environment, foraging with intraspecific competition requires resolution of simultaneous circular dependencies. In response to these issues in application, a number of approximating algorithms have been proposed, but it remains to be seen whether these algorithms are effective given a large number of foragers with realistic characteristics. We implemented several algorithms approximating marginal value foraging in a large-scale avian foraging model and compared the results. We found that a novel reinforcement-learning algorithm that includes cost of travel is the most effective algorithm that most closely approximates marginal value foraging theory and recreates depletion patterns observed in empirical studies.


Schank, J. C., Smaldino, P. E., & Miller, M. L. (2015). Evolution of fairness in the dictator game by multilevel selection. Journal of Theoretical Biology, 382, 64-73.

The most perplexing experimental results on fairness come from the dictator game where one of two players, the dictator, decides how to divide a resource with an anonymous player. The dictator, acting self-interestedly, should offer nothing to the anonymous second player, but in experimental studies, dictators offer much more than nothing. We developed a multilevel selection model to explain why people offer more than nothing in the dictator game. We show that fairness can evolve when population structure emerges from the aggregation and limited dispersal of offspring. We begin with an analytical model that shows how fair behavior can benefit groups by minimizing within-group variance in resources and thereby increasing group fitness. To investigate the generality of this result, we developed an agent-based model with agents that have no information about other agents. We allowed agents to aggregate into groups and evolve different levels of fairness by playing the dictator game for resources to reproduce. This allowed multilevel selection to emerge from the spatiotemporal properties of individual agents. We found that the population structure that emerged under low population densities was most conducive to the evolution of fairness, which is consistent with group selection as a major evolutionary force. We also found that fairness only evolves if resources are not too scarce relative to the lifespan of agents. We conclude that the evolution of fairness could evolve under multilevel selection. Thus, our model provides a novel explanation for the results of dictator game experiments, in which participants often fairly split a resource rather than keeping it all for themselves.


Miller, M. L., Ringelman, K. M., Schank, J. C., and Eadie, J. M. (2014). SWAMP: An agent-based model as a conservation management tool. Simulation, 90, 52-68.

The management of North American waterfowl is widely recognized as a premier example of a successful conservation program. Conservation managers on the wintering grounds typically use simple estimates of food availability and population-wide cumulative energy demand to determine how many birds can be supported on a given landscape. When attempting to plan for future needs due to land reallocation, climate change, and other large-scale environmental changes, simple bioenergetic models may not capture important impacts on individual behavior, such as changes in metabolic costs due to increased travel-time and reduced food accessibility leading to non-linear declines in forager success. We describe the development of an agent-based model of foraging waterfowl that uses explicit individual behavior to generate more detailed and potentially more accurate insights into the impact of environmental changes on forager success and survival. While there is growing recognition of the potential utility of agent-based models in conservation planning, there has yet to be an attempt to formulate, validate, and communicate such a model for use as a decision support tool to guide habitat management conservation for wetlands in North America. Our model seeks to provide the foundational framework for such an effort. We predict that this model will be a useful tool for stakeholders making conservation management decisions.


Payette, N., Bujorianu, M., Ropella, G., Cline, K., Schank, J., Miller, M. … Wei, E. (2013). Future MASON directions: Community Recommendations (Report of the 2013 MASON NSF Workshop) (GMU-CS-TR-2013-9). On the George Mason University, Department of Computer Science, Volgenau School of Engineering website.

Report to the National Science Foundation on future needs and directions for the MASON agent-based modeling library.