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Evolutionary Games in Natural, Social, and Virtual Worlds$
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Daniel Friedman and Barry Sinervo

Print publication date: 2016

Print ISBN-13: 9780199981151

Published to Oxford Scholarship Online: August 2016

DOI: 10.1093/acprof:oso/9780199981151.001.0001

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Dynamics in n-Dimensional Games

Dynamics in n-Dimensional Games

Chapter:
(p.64) 3 Dynamics in n-Dimensional Games
Source:
Evolutionary Games in Natural, Social, and Virtual Worlds
Author(s):

Daniel Friedman

Barry Sinervo

Daniel Friedman

Barry Sinervo

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199981151.003.0003

This chapter analyzes more complex forms of interaction. Using the rock-paper-scissors game of the European common lizard as an example, it introduces helpful geometric techniques for analyzing 3 × 3 and higher dimensional games and shows how to extend them to nonlinear games. The authors then consider two-population games, both the usual “asymmetric” analysis and own-population effects. The chapter also introduces more general dynamics than replicator, including several forms of monotone dynamics. Finally, it explains how to estimate the payoff matrix from time-series data on the side-blotched lizard using maximum likelihood techniques and state-of-the-art multinomial logit and Dirichlet models.

Keywords:   rock-paper-scissors, buyer-seller, two-population games, own-population effects, between-population effects, simplex sectoring, maximum likelihood, Dirichlet

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