NON-SYMMETRIC STABLE SETS IN THE MAJORITY PILLAGE GAME

Open Access
Author:
Pakzad-Hurson, Bobak
Area of Honors:
Economics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • James Schuyler Jordan, Thesis Supervisor
  • David Shapiro, Honors Advisor
Keywords:
  • Pillage games
  • cooperative game theory
  • anarchy
Abstract:
The majority pillage game, introduced by Jordan (2006) is a model of Hobbesian anarchy in which a given number of players fight over a fixed amount of wealth, normalized to unity. Coalitions of varying sizes can form, and the power of coalitions is determined by their size and wealth. Therefore, power is endogenously defined within the game by means of a power function. More powerful coalitions have the ability to pillage, with certainty and without cost, weaker coalitions. Previous work on majority pillage games has focused on the stable set solution concept (von Neumann-Morgenstern solution) as an endogenous balance of power. This paper explores new results on the stable set in the case of four players. A programming model detailed within the paper suggests that stable sets do not exist – in other words, there is no endogenous balance of power for this game. A theoretical approach explores several properties of a stable set, and illustrates the possible areas which prevent the existence of stable sets. Finally, formal results for stable sets are given which can be generalized to the broader class of majority pillage games with more than four players.