University of Illinois Urbana-Champaign

Cellular Games

Levine, Lenore E.

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Description

Title
Cellular Games
Author(s)
Levine, Lenore E.
Issue Date
1994
Doctoral Committee Chair(s)
Palmore, Julian
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Abstract
  • A cellular game is a dynamical system in which cells, placed in some discrete structure, are regarded as playing a game with their immediate neighbors. Individual strategies may be either deterministic or stochastic. Strategy success is measured according to some universal and unchanging criterion. Successful strategies persist and spread; unsuccessful ones disappear.
  • In this thesis, two cellular game models are formally defined, and are compared to cellular automata. Computer simulations of these models are presented.
  • Conditions providing maximal average cell success, on one and two-dimensional lattices, are examined. It is shown that these conditions are not necessarily stable; and an example of such instability is analyzed. It is also shown that Nash equilibrium strategies are not necessarily stable.
  • Finally, a particular kind of zero-depth, two-strategy cellular game is discussed; such a game is called a simple cellular game. It is shown that if a simple cellular game is left/right symmetric, and if there are initially only finitely many cells using one strategy, the zone in which this strategy occurs has probability 0 of expanding arbitrarily far in one direction only. With probability 1, it will either expand in both directions or disappear.
  • Computer simulations of such games are presented. These experiments suggest the existence of two different kinds of asymptotic behavior.
Graduation Semester
1994
Type of Resource
text
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http://hdl.handle.net/2142/72547

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