Ergodicity and entropy in sequence spaces

WCU Author/Contributor (non-WCU co-authors, if there are any, appear on document)
Christopher Miglino (Creator)
Western Carolina University (WCU )
Web Site:
Julia Barnes

Abstract: The infi nite permutations of possible moves in a game, or positions on a game board, form a one-sided sequence space. We are working with a probability measure on the space of measurable subsets of the sequence space. We are studying a shift transformation on this space, which is measure preserving. We explore conditions under which the shift transformation is ergodic and calculate the entropy of the shift that is associated with the steady state of the game where applicable. These concepts are exemplifi ed by the games Rock, Paper, Scissors and Monopoly. We then create new games and study how the properties of ergodicity and entropy change with respect to diff erent aspects of the games.

Additional Information

Language: English
Date: 2013
Ergodic Theory, Games, Markov, Probability
Measure-preserving transformations
Sequence spaces
Ergodic theory
Entropy (Information theory)

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