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The solvers I know so far are designed only to allow payoffs as given numbers. But is there a solver allowing users to type payoffs as variables?

Rita Tseng
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  • Question too imprecise and vague. What do you mean by "type payoffs as variables" ? – dohmatob Aug 15 '15 at 16:59
  • Yes. Since the solvers I found so far only accept given numbers as payoff inputs, I wonder if there is a solver that can type variables as payoff inputs to see how Nash equilibria perform. – Rita Tseng Aug 16 '15 at 03:08

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Not that I am aware of. You could always write a script that generates instances of a parametrically defined game for an existing solver and then do a parameter sweep. For more than two players, even describing the set of equilibria for a given game (with all payoffs specified as actual numbers) is highly non-trivial, and given the state-of-the-art what you are asking for is rather unrealistic (except maybe for very small games).

Rahul Savani
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  • Oh yes, that is what I am doing now. It seems python is a better choice to apply than matlab if I use Gambit as the solver. Thank you for your information. It is good to know the computational aspect of Nash equilibrium. – Rita Tseng Aug 17 '15 at 14:32
  • Python is certainly a good choice, especially with Gambit. How many players do your games have? – Rahul Savani Aug 17 '15 at 16:37
  • Just two. So I guess it is simpler than the general case in which n players are involved. – Rita Tseng Aug 18 '15 at 03:40
  • Then you can and should use exact arithmetic. Gambit should be fine. Gambit can use lrslis with the -L flag, but I am not sure who widely tested this is. Any problems, then you could also use lrs directly, see http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html#nash and this other answer here: http://math.stackexchange.com/questions/881906/computer-software-for-solving-mixed-strategy-nash-equilibrium – Rahul Savani Aug 18 '15 at 06:31