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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Entropy-Based Measure of Statistical Complexity of a Game Strategy.

Fryderyk Falniowski1

  • 1Department of Mathematics, Cracow University of Economics, Rakowicka 27, 31-510 Kraków, Poland.

Entropy (Basel, Switzerland)
|December 8, 2020
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Summary

We introduce excess strategic entropy, a new measure for quantifying strategy complexity and predictability. This entropy-based approach offers insights into player behavior in game theory and strategic decision-making.

Keywords:
complexity of a strategyentropy-based measurepredictability of a strategy

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Area of Science:

  • Game Theory
  • Information Theory
  • Decision Science

Background:

  • Understanding strategy complexity is crucial in game theory.
  • Existing measures may not fully capture the nuances of strategic decision-making.
  • Quantifying predictability in mixed strategies is an ongoing challenge.

Purpose of the Study:

  • Introduce excess strategic entropy as a novel measure.
  • Quantify the complexity and predictability of a player's mixed strategy.
  • Explore the properties and potential applications of this new measure.

Main Methods:

  • Developed an entropy-based mathematical framework.
  • Defined excess strategic entropy based on information theory principles.
  • Analyzed the theoretical properties of the proposed measure.

Main Results:

  • Excess strategic entropy quantifies strategy complexity and predictability.
  • Demonstrated the measure's ability to differentiate between strategies.
  • Identified potential applications in analyzing player behavior.

Conclusions:

  • Excess strategic entropy provides a valuable tool for strategy analysis.
  • The measure enhances understanding of complexity and predictability in game theory.
  • Further research can explore its application in various strategic contexts.