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Full street simplified three player Kuhn poker

Billingham, John

Authors

JOHN BILLINGHAM john.billingham@nottingham.ac.uk
Professor of Theoretical Mechanics



Abstract

We study a simplified version of full street, three player Kuhn poker, in which the weakest card, J, must be checked and/or folded by a player who holds it. The number of nontrivial betting frequencies that must be calculated is thereby reduced from 23 to 11, and all equilibrium solutions can be found analytically. In particular, there are three ranges of values of the pot size, P, for which there are three distinct, coexisting equilibrium solutions. We also study an ordinary differential equation model of repeated play of the game, which we expect to be at least qualitatively accurate when all players both adjust their betting frequencies sufficiently slowly and have sufficiently short memories. We find that none of the equilibrium solutions of the game is asymptotically stable as a solution of the ordinary differential equations. Depending on the pot size, the solution may be periodic, close to periodic or have long chaotic transients. In each case, the rates at which the players accumulate profit closely match those associated with one of the equilibrium solutions of the game.

Citation

Billingham, J. (2017). Full street simplified three player Kuhn poker. ArXiv

Book Type Monograph
Acceptance Date Jul 5, 2017
Publication Date Jul 5, 2017
Deposit Date Jul 11, 2017
Publicly Available Date Jul 11, 2017
Journal arXiv
Peer Reviewed Not Peer Reviewed
Public URL http://eprints.nottingham.ac.uk/id/eprint/44079
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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1707.01392.pdf (1.6 Mb)
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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