Universal Solvers Game Theory

Please see Appendix Pedagogical Outlook.

First paper in Footnotes on the Foundations of Game Theory. It provides verifiable information of a universal solver g[], for finite pure-strategy Nash Equilibria, without disclosing code. In doing so, theory at work is displayed. In particular, this feat exploits a bridge between static games and Replicator dynamics to show that only predicted symmetric NE are stable fixed points. A theoretical discussion from the perspective of a Machiavellian ruler accompanies this mathematical treatment.

The second part establishes a link between the number of solutions and their character in terms of symmetric (diagonal) solutions and coupled (off-diagonal) in symmetric matrices with heuristics. Data generated with g[] is used to test hypotheses.

Main result is a method to predict the distribution of NE which extends to more general tensors and incentive distributions. A statistical model to predict the distribution of the number of solutions is given as an example. Data supports the model. All results follow from simple or common-knowledge concepts and definitions. More general solvers will be discussed in future work.

Keywords:

Game Theory, Applied Mathematics, Social Science, Evolution.

Please note: This paper is a first draft, revision may result in major updates. Comments, requests or questions are welcome.

You may contact me at manuel.echeverria.q@gmail.com

gametheory-f1-wpress-versionDownload

Note: Date is year of publication, for archive.