Using Gambit as a standalone package#
This file contains some information and tests for the use of Gambit as a stand alone package.
To install gambit as an optional package run (from root of Sage):
$ sage -i gambit
The python API documentation for gambit shows various examples that can be run easily in IPython. To run the IPython packaged with Sage run (from root of Sage):
$ ./sage --ipython
Here is an example that constructs the Prisoner’s Dilemma:
In [1]: import gambit
In [2]: g = gambit.Game.new_table([2,2])
In [3]: g.title = "A prisoner's dilemma game"
In [4]: g.players[0].label = "Alphonse"
In [5]: g.players[1].label = "Gaston"
In [6]: g
Out[6]:
NFG 1 R "A prisoner's dilemma game" { "Alphonse" "Gaston" }
{ { "1" "2" }
{ "1" "2" }
}
""
{
{ "" 0, 0 }
{ "" 0, 0 }
{ "" 0, 0 }
{ "" 0, 0 }
}
1 2 3 4
In [7]: g.players[0].strategies
Out[7]: [<Strategy [0] '1' for player 'Alphonse' in game 'A
prisoner's dilemma game'>,
<Strategy [1] '2' for player 'Alphonse' in game 'A prisoner's dilemma game'>]
In [8]: len(g.players[0].strategies)
Out[8]: 2
In [9]: g.players[0].strategies[0].label = "Cooperate"
In [10]: g.players[0].strategies[1].label = "Defect"
In [11]: g.players[0].strategies
Out[11]: [<Strategy [0] 'Cooperate' for player 'Alphonse' in game 'A
prisoner's dilemma game'>,
<Strategy [1] 'Defect' for player 'Alphonse' in game 'A prisoner's dilemma game'>]
In [12]: g[0,0][0] = 8
In [13]: g[0,0][1] = 8
In [14]: g[0,1][0] = 2
In [15]: g[0,1][1] = 10
In [16]: g[1,0][0] = 10
In [17]: g[1,1][1] = 2
In [18]: g[1,0][1] = 2
In [19]: g[1,1][0] = 5
In [20]: g[1,1][1] = 5
Here is a list of the various solvers available in gambit:
ExternalEnumPureSolver
ExternalEnumMixedSolver
ExternalLPSolver
ExternalLCPSolver
ExternalSimpdivSolver
ExternalGlobalNewtonSolver
ExternalEnumPolySolver
ExternalLyapunovSolver
ExternalIteratedPolymatrixSolver
ExternalLogitSolver
Here is how to use the ExternalEnumPureSolver:
In [21]: solver = gambit.nash.ExternalEnumPureSolver()
In [22]: solver.solve(g)
Out[22]: [<NashProfile for 'A prisoner's dilemma game': [Fraction(0, 1), Fraction(1, 1), Fraction(0, 1), Fraction(1, 1)]>]
Note that the above finds the equilibria by investigating all potential pure pure strategy pairs. This will fail to find all Nash equilibria in certain games. For example here is an implementation of Matching Pennies:
In [1]: import gambit
In [2]: g = gambit.Game.new_table([2,2])
In [3]: g[0, 0][0] = 1
In [4]: g[0, 0][1] = -1
In [5]: g[0, 1][0] = -1
In [6]: g[0, 1][1] = 1
In [7]: g[1, 0][0] = -1
In [8]: g[1, 0][1] = 1
In [9]: g[1, 1][0] = 1
In [10]: g[1, 1][1] = -1
In [11]: solver = gambit.nash.ExternalEnumPureSolver()
In [12]: solver.solve(g)
Out[12]: []
If we solve this with the LCP solver we get the expected Nash equilibrium:
In [13]: solver = gambit.nash.ExternalLCPSolver()
In [14]: solver.solve(g)
Out[14]: [<NashProfile for '': [0.5, 0.5, 0.5, 0.5]>]
Note that the above examples only show how to build and find equilibria for two player strategic form games. Gambit supports multiple player games as well as extensive form games: for more details see http://www.gambit-project.org/.
If one really wants to use gambit directly in Sage (without using the
NormalFormGame class as a wrapper) then integers must first be
converted to Python integers (due to the preparser). Here is an example
showing the Battle of the Sexes:
sage: # optional - gambit
sage: import gambit
sage: g = gambit.Game.new_table([2,2])
sage: g[int(0), int(0)][int(0)] = int(2)
sage: g[int(0), int(0)][int(1)] = int(1)
sage: g[int(0), int(1)][int(0)] = int(0)
sage: g[int(0), int(1)][int(1)] = int(0)
sage: g[int(1), int(0)][int(0)] = int(0)
sage: g[int(1), int(0)][int(1)] = int(0)
sage: g[int(1), int(1)][int(0)] = int(1)
sage: g[int(1), int(1)][int(1)] = int(2)
sage: solver = gambit.nash.ExternalLCPSolver()
sage: solver.solve(g)
[<NashProfile for '': [[1.0, 0.0], [1.0, 0.0]]>,
<NashProfile for '': [[0.6666666667, 0.3333333333], [0.3333333333, 0.6666666667]]>,
<NashProfile for '': [[0.0, 1.0], [0.0, 1.0]]>]
AUTHOR:
Vince Knight (11-2014): Original version