Pure strategy nash equilibrium

src/Games.jl

@@ -1,10 +1,21 @@
 module Games
 
+# Packages
+
 # package code goes here
 include("normal_form_game.jl")
+include("nash_equilibrium.jl")
+
+export Player, NormalFormGame,  # Types
 
-export Player, NormalFormGame,
+       # Type aliases
+       Action, MixedAction, PureAction, ActionProfile,
+
+       # Normal form game functions
  	   best_response, best_responses, is_best_response, payoff_vector,
-       is_nash, pure2mixed, num_players, num_actions, num_opponents
+       is_nash, pure2mixed, pure_strategy_NE,
+
+       # General functions
+       num_players, num_actions, num_opponents
 
 end # module

src/nash_equilibrium.jl

@@ -0,0 +1,23 @@
+"""
+Finds all pure strategy Nash equilibrium for a normal form
+game. It returns an empty array if there are no nash
+equilibrium
+"""
+function pure_strategy_NE(nfg::NormalFormGame)
+    # Get number of players and their actions
+    np = num_players(nfg)
+    na = nfg.nums_actions
+
+    # Holder for all NE
+    ne = Array(ActionProfile, 0)
+
+    # For each action profile check whether it is NE
+    as = CartesianRange(na)
+    for a in as
+        _a = a.I::NTuple{np, Int}
+        is_nash(nfg, _a) ? push!(ne, _a) : nothing
+    end
+
+    return ne
+end
+

src/normal_form_game.jl

@@ -594,3 +594,4 @@ function pure2mixed(num_actions::Integer, action::PureAction)
     mixed_action[action] = 1
     return mixed_action
 end
+

test/test_normal_form_game.jl

@@ -167,6 +167,19 @@
         @test_throws ArgumentError g = NormalFormGame(zeros((2, 2, 1)))
     end
 
+    # Pure strategy Nash equilibrium
+    @testset "2x2 Pure strategy Nash equilibrium" begin
+        A = [9.0 1.0
+             10.0 3.0]
+        p1 = Player(A)
+        p2 = Player(A)
+
+        nfg = NormalFormGame(p1, p2)
+        psne = pure_strategy_NE(nfg)
+
+        @test psne == [(2, 2)]
+    end
+
     # Utility functions #
 
     @testset "pure2mixed" begin