Abstract
The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory.
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Notes
The axiom names used above are ours.
As long as the same secret can not appear simultaneously on the left and right hand side of the independence symbol. Otherwise, one more axiom should be added to achieve completeness.
It is important to keep in mind that \(-1\equiv 1\pmod 2\).
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Acknowledgments
Brittany Nicholls have been supported by National Science Foundation through a CREU award given by Computing Research Association Committee on the Status Of Women in Computing Research in conjunction with the Coalition to Diversify Computing.
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Naumov, P., Nicholls, B. On interchangeability of Nash equilibria in multi-player strategic games. Synthese 190 (Suppl 1), 57–78 (2013). https://doi.org/10.1007/s11229-013-0277-1
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DOI: https://doi.org/10.1007/s11229-013-0277-1