Simplified three player Kuhn pokerTools Billingham, John (2017) Simplified three player Kuhn poker. Working Paper. Arxiv. (Unpublished)
AbstractWe study a very small three player poker game (onethird street Kuhn poker), and a simplified version of the game that is interesting because it has three distinct equilibrium solutions. For onethird street Kuhn poker, we are able to find all of the equilibrium solutions analytically. For large enough pot size, P, there is a degree of freedom in the solution that allows one player to transfer profit between the other two players without changing their own profit. This has potentially interesting consequences in repeated play of the game. We also show that in a simplified version of the game with P>5, there is one equilibrium solution if 5<P<P∗≡(5+sqrt(73))/2, and three distinct equilibrium solutions if P>P∗. This may be the simplest nontrivial multiplayer poker game with more than one distinct equilibrium solution and provides us with a test case for theories of dynamic strategy adjustment over multiple realisations of the game.
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