Graduation Year
2012
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Francis Edward Su
Reader 2
Stephen Adolph
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
Rights Information
© August Guang
Abstract
Roughgarden et al. (2006) proposed a theory called social selection as a behavioral game theoretic model for sexual reproduction that incorporates both competition and cooperation in 2006. Players oscillate between playing competitively to maximize their individual fitness, leading to a Nash Competitive Equilibrium, and playing cooperatively to maximize a team fitness function, leading to a Nash Bargaining Solution. Roughgarden et al. (2006) gives rates of change for both the competitive state and the cooperative state, but does not explain her rates or how to switch between the states in sufficient detail.
We test and rederive the rates, critiquing an assumption that the derivation of such a rate must make, as well as create a probabilistic model that switches between the two states. We test our model on the reproductive behaviors of Symphodus tinca, the peacock wrasse. The results follow the trajectory of the reproductive strategies for the wrasse throughout the breeding system, suggesting that cooperation could be a mechanism through which wrasse change their reproductive behaviors. However, the inputs to the model need to be analyzed more critically. Future work could include deriving rates for competitive play and cooperative play that do not rely on assumptions of being able to quantify strategy allocation proportion and refining the model and drawing generalized conclusions about it.
Recommended Citation
Guang, August, "Switching Between Cooperation and Competition in Social Selection" (2012). HMC Senior Theses. 40.
https://scholarship.claremont.edu/hmc_theses/40
