On the Duration and Intensity of Competitions in Nonlinear Pólya Urn Processes with Fitness
Abstract
Cumulative advantage (CA) refers to the notion that accumulated resources foster the accumulation of further resources in competitions, a phenomenon that has been empirically observed in various contexts. The oldest and arguably simplest mathematical model that embodies this general principle is the Pólya urn process, which finds applications in a myriad of problems. The original model captures the dynamics of competitions between two equally fit agents under linear CA effects, which can be readily generalized to incorporate different fitnesses and nonlinear CA effects. We study two statistics of competitions under the generalized model, namely duration (i.e., time of the last tie) and intensity (i.e., number of ties). We give rigorous mathematical characterizations of the tail distributions of both duration and intensity under the various regimes for fitness and nonlinearity, which reveal very interesting behaviors. For example, fitness superiority induces much shorter competitions in the sublinear regime while much longer competitions in the superlinear regime. Our findings can shed light on the application of Pólya urn processes in more general contexts where fitness and nonlinearity may be present.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 14, 2016
- Source ID
- 10.1145/2964791.2901475
Entities
People
- Bo Jiang
- Bruno Ribeiro
- Daniel R. Figueiredo
- Don Towsley
Organizations
- Army Research Office
- Coordenação de Aperfeicoamento de Pessoal de Nível Superior
- Federal University of Rio de Janeiro
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- National Council for Scientific and Technological Development
- Purdue University
- United States Army Research Laboratory
- University of Massachusetts