Add vertex enumeration.

Author: shizejin

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 +1,74 @@
+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(c::Channel,
+                                      g::NormalFormGame{2},
+                                      plib)
+
+    n, m = size(g.players[1].payoff_array)
+    BRSv = [_BRS_vertices(g, opp_idx, plib) for opp_idx in 1:2]
+    ZERO_LABELING = BitArray(vcat(zeros(m), ones(n)))
+    COMPLETE_LABELING = trues(n+m)
+
+    for i in 1:size(BRSv[1][3])[1]
+        v1 = BRSv[1][3][i, :]
+        labeling1 = *(BRSv[1][1], v1) .≈ BRSv[1][2]
+
+        if labeling1 == ZERO_LABELING
+            continue
+        end
+
+        for j in 1:size(BRSv[2][3])[1]
+            v2 = BRSv[2][3][j, :]
+            labeling2 = *(BRSv[2][1], v2) .≈ BRSv[2][2]
+
+            if xor.(labeling1, labeling2) == COMPLETE_LABELING
+                put!(c, (_get_mixed_action(v1),
+                         _get_mixed_action(v2)))
+            end
+        end
+    end
+end
+
+function _BRS_vertices(g::NormalFormGame, idx::Integer, plib)
+
+    opp_idx = idx % 2 + 1
+    B = g.players[opp_idx].payoff_array
+    n, m = size(B)
+
+    arr = [B, -eye(m)]
+    D = vcat(arr[idx], arr[opp_idx])
+    vec = [ones(Float64, n), zeros(Float64, m)]
+    b = vcat(vec[idx], vec[opp_idx])
+
+    hrep = SimpleHRepresentation(D, b)
+    p = polyhedron(hrep, plib)
+    vertices = SimpleVRepresentation(p).V
+
+    return D, b, vertices
+end
+
+function _get_mixed_action(a)
+    return a ./ sum(a)
+end