Merge 8ee9e73 into 7ffab27

src/Games.jl

@@ -58,6 +58,7 @@ include("pure_nash.jl")
 include("repeated_game.jl")
 include("random.jl")
 include("support_enumeration.jl")
+include("vertex_enumeration.jl")
 
 export
     # Types
@@ -87,6 +88,9 @@ export
     random_game, covariance_game,
 
     # Support Enumeration
-    support_enumeration, support_enumeration_task
+    support_enumeration, support_enumeration_task,
+
+    # Vertex Enumeration
+    vertex_enumeration, vertex_enumeration_task
 
 end # module

src/vertex_enumeration.jl

@@ -0,0 +1,97 @@
+import Polyhedra: hyperplane
+
+function vertex_enumeration(g::NormalFormGame{2};
+                            plib=getlibraryfor(2, Float64))
+
+    c = Channel(0)
+    task = vertex_enumeration_task(c, g, plib)
+    bind(c, task)
+    schedule(task)
+    NEs = Tuple{Vector{Real}, Vector{Real}}[NE for NE in c]
+
+    return NEs
+
+end
+
+function vertex_enumeration_task(c::Channel,
+                                 g::NormalFormGame{2},
+                                 plib)
+
+    task = Task(
+        () -> _vertex_enumeration_producer(c, g, plib)
+    )
+
+    return task
+
+end
+
+function _vertex_enumeration_producer{T}(c::Channel,
+                                         g::NormalFormGame{2, T},
+                                         plib)
+
+    n, m = size(g.players[1].payoff_array)
+
+    # create Representation for player 1
+    H1, V1, H2, V2 = construction_BRP(g, plib)
+
+    ZERO_LABELING_BITS = (1 << (n+m)) - (1 << m)
+    COMPLETE_LABELING_BITS = 1 << (n+m) - 1
+
+    for v1 in vreps(V1)
+        labelings_bits1 = labelings_bits(v1, H1)
+        if labelings_bits1 == ZERO_LABELING_BITS
+            continue
+        end
+        for v2 in vreps(V2)
+            labelings_bits2 = labelings_bits(v2, H2)
+            if xor(labelings_bits1, labelings_bits2) == COMPLETE_LABELING_BITS
+                put!(c, (_get_mixed_action(v1),
+                         _get_mixed_action(v2)))
+            end
+        end
+    end
+
+end
+
+function construction_BRP{T}(g::NormalFormGame{2, T}, plib)
+
+    n, m = size(g.players[1].payoff_array)
+
+    # create Representation for player 1
+    C = Matrix{T}(n+m, n)
+    C[1:m, :] = g.players[2].payoff_array
+    C[m+1:end, :] = -eye(T, n)
+    b1 = Vector{T}(n+m)
+    b1[1:m] = one(T)
+    b1[m+1:end] = zero(T)
+    H1 = SimpleHRepresentation(C, b1)
+    p1 = polyhedron(H1, plib)
+    V1 = SimpleVRepresentation(p1)
+
+    # create Representation for player 2
+    D = Matrix{T}(n+m, m)
+    D[1:m, :] = -eye(T, m)
+    D[m+1:end, :] = g.players[1].payoff_array
+    b2 = Vector{T}(n+m)
+    b2[1:m] = zero(T)
+    b2[m+1:end] = one(T)
+    H2 = SimpleHRepresentation(D, b2)
+    p2 = polyhedron(H2, plib)
+    V2 = SimpleVRepresentation(p2)
+
+    return H1, V1, H2, V2
+end
+
+function labelings_bits(v::VRepElement, p::HRep)
+    b = 0
+    for (i, h) in enumerate(hreps(p))
+        if v in hyperplane(h)
+            b += 1 << (i-1)
+        end
+    end
+    return b
+end
+
+function _get_mixed_action(a::Vector)
+    return a ./ sum(a)
+end