Persistence Of Dynamic Fairness And Altruism In The Ultimatum Game

Open Access
Author:
Easton, Matthew Daniel
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Andrew Leonard Belmonte, Thesis Supervisor
  • Aissa Wade, Honors Advisor
Keywords:
  • game theory
  • mathematics
  • economics
Abstract:
In this paper, we explore a dynamic version of the Ultimatum Game and study its results with regards to population dynamics, stability, and preference set construction. The Ultimatum Game is a famous economic experiment that studies human belief structures and behaviors, such as equal- ity, fairness, and cooperation. Previous studies of the game have shown that theoretical results for the game are not often mirrored experimentally. While many models were produced to take account of such differences, emphasis was put on explaining decision-making through individual optimization of strategies alone. Our treatment addresses how populations of players with different preferences form offers, accept or reject proposals, and rationalize interactions over time. We pro- pose that belief systems for fairness and unfairness can be understood by establishing dependence between how players assign utility to offers received and offers made to others. We then analyze the dynamics of a population of players who adapt their trading behaviors based upon population size. We find that a model where groups in a population interact with population dynamics in mind will exhibit tendencies to approach proportional equilibria and that the growth and stability of the overall population of players depends upon a delicate balance between the preferences of the group and the individual.