Combinatorics Seminar 2018

Speaker: Xinran Zhu (朱欣然), Shanghai Jiao Tong University

Date: Wed, Jun 27, 2018

Time: 14:00 - 15:00

Venue: 3323A

Title: Dynamics and equilibria of iterated prisoner's dilemma


Iterated prisoner's dilemma (IPD) has long been a metaphor for the evolution of cooperation in biological societies and sociology. For a prisoner's game of one single round, a simple and obvious Nash equilibrium is mutual defection instead of cooperation. However, in an iterated prisoner's game, where the game is repeated forever, cooperation becomes a promising option, and thus dynamics and equilibrium of the evolution become more complicated. In this work, we study dynamic patterns and stability of equilibria of the iterated prisoner's dilemma using the discrete replicator equation. As for the stability of equilibrium, we characterize the external stability in the sense of invasion as well as the asymptotic stability and prove the internal relationship between different kinds of stability. As for the dynamical pattern of the evolution, we characterize the dynamics pattern under certain strategy spaces and find conditions where such the dynamic pattern occurs.

This is joint work with David Bindel.

Slides: View slides