Research

My research aims at understanding factors that play a role in the emergence and maintenance of cooperation in social groups. I study this question using mathematical models and computer simulations. Current and past research includes the following:

Matching theory and mutual mate choice

The award of the 2012 Nobel Prize in Economic Sciences to the two main founders of matching theory, Alvin E. Roth and Lloyd S. Shapley, establishes the fundamental importance and specificity of matching theory. In collaboration with Oscar Puebla and Georg Nöldeke we are applying economic matching theory to evolutionary biology in order to explore the role played by mutual mate choice in sexual selection and speciation.

Multi-player binary-action games

Symmetric games with multiple players and two available actions (e.g., “cooperate” and “defect”; “volunteer” and “ignore”; “vote” and “abstain”) are often found in the theoretical literature of the evolution of cooperation and altruism (biology), the voluntary provision of collective goods (economics), and voting participation (political science). However, a systematic mathematical framework to analyze these games is lacking. I have been developing a theoretical framework, based on the shape-preserving properties of polynomials in Bernstein form, which greatly simplifies the analysis of binary-action games (with Laurent Lehmann and Georg Nöldeke). Our approach also makes it easy to incorporate family and spatial structure, and to connect these models with inclusive fitness theory (with L. Lehmann and G. Nöldeke). In addition to this, we have recently proved a conjecture concerning the existence, multiplicity, and comparative statics of the symmetric Nash equilibria of a classic model of voter turnout (with G. Nöldeke).

(Peña et al., 2014, JTBPeña et al., 2015, JTB; Nöldeke and Peña, In revision at GEB)

Group-size effects in collective action problems

Group size is an important factor in social evolution. I have explored the impact of variable group sizes in the evolution of collective action; this is of particular relevance in behavioral ecology as group size distributions of animal aggregations can be highly skewed (with G. Nöldeke). Currently, I am investigating the more classical “group-size effect” (or “group-size paradox”) of collective action theory (with G. Nöldeke) and the consequences of endogenous group formation (with G. Nöldeke and Arne Traulsen) in threshold public goods games.

(Peña, 2012, Evolution; Peña and Nöldeke, 2016, JTB; Nöldeke and Peña, In preparation; Peña et al., In preparation)

Evolutionary game dynamics in graphs and social networks

Relying mostly on computer simulations, I have investigated the effects of network structure (e.g., degree distribution, clustering coefficient) and imitation rules (e.g., conformity biases) on the evolutionary dynamics of social dilemmas (with Marco Tomassini and colleagues from the University of Lausanne). More recently, I worked on an analytical approach to compare different models of spatial structure (including graphs and social networks as examples) with respect to their potential to promote the evolution of cooperation (with A. Traulsen and colleagues at the Max Planck Institute).

(Peña et al., 2009, PRE; Peña et al., 2011, JTB; Buesser et al., 2011, Phys. A; Peña and Rochat, 2012, PLoS ONE; Peña et al., 2016, JRSI; Peña et al., In revision at PLOS CB)

Swarm intelligence (computer science)

I have done research in computer science on the simplification, mathematical analysis, and hardware implementation (in field programmable gate arrays) of particle swarm optimizers. Particle swarm optimization is a metaheuristic akin to genetic algorithms used to find solutions to problems by an iterative method. In particle swarm optimization, particles (individuals) update their candidate solutions by a process of individual search combined with social imitation. In this topic, I collaborated (among others) with Marco Dorigo and researchers from his lab at the Université Libre de Bruxelles.

Other

Currently I am working on a variety of topics including demographic assumptions in models of the evolution of eusociality (with Mauricio González-Forero), optimal life cycle strategies in the evolution of multicellularity (with Yuriy Pichugin and A. Traulsen), and models of many-to-many mutualisms (with Chaitanya Gokhale).