Use mvn sampler (#40)

* FEAT: Add rng::AbstractRNG option to random_game and covariance_game

FIX: Use MVNSampler instead of MvNormal

* TEST: Add test for corner values of rho

* FIX: Removing dependency on Distributions.jl

* FIX: Change the notation to keep consistent with MVNSampler

* FIX: Correct a typo

* FIX: Correct a typo

* FIX: Correct another typo

src/Games.jl

@@ -4,7 +4,6 @@ module Games
 using Clp
 using MathProgBase
 using QuantEcon
-using Distributions
 
 # Geometry packages
 using Polyhedra

src/random.jl

@@ -8,39 +8,44 @@ Authors: Daisuke Oyama, Zejin Shi
 # Random Games Generating
 #
 """
- random_game{N}(nums_actions::NTuple{N,Int})
+ random_game{N}([rng::AbstractRNG], nums_actions::NTuple{N,Int})
 
 Return a random N-player NormalFormGame instance where the
 payoffs are drawn independently from the uniform distribution
 on [0, 1).
 
 # Arguements
 
+* `rng::AbstractRNG=GLOBAL_RNG`: Random number generator used.
 * `nums_actions::NTuple{N,Int}`: Tuple of the numbers of actions,
  one for each player.
 
 # Returns
 
 * `::NormalFormGame`: The generated random N-player NormalFormGame.
 """
-function random_game{N}(nums_actions::NTuple{N,Int})
+function random_game{N}(rng::AbstractRNG, nums_actions::NTuple{N,Int})
  if N == 0
  throw(ArgumentError("nums_actions must be non-empty"))
  end
 
  players::NTuple{N,Player{N,Float64}} =
- ntuple(i -> Player(rand(tuple(nums_actions[i:end]...,
+ ntuple(i -> Player(rand(rng, tuple(nums_actions[i:end]...,
  nums_actions[1:i-1]...))),
  N)
 
  return NormalFormGame(players)
 end
 
+random_game{N}(nums_actions::NTuple{N,Int}) = 
+ random_game(Base.GLOBAL_RNG, nums_actions)
+
 #
 # Covariance Games Generating
 #
 """
- covariance_game{N}(nums_actions::NTuple{N,Int}, rho::Real)
+ covariance_game{N}([rng::AbstractRNG], nums_actions::NTuple{N,Int}, 
+ rho::Real)
 
 Return a random N-player NormalFormGame instance with N>=2 where
 the payoff profiles are drawn independently from the standard
@@ -49,6 +54,7 @@ multi-normal with the covariance of any pair of payoffs equal to
 
 # Arguements
 
+* `rng::AbstractRNG=GLOBAL_RNG`: Random number generator used.
 * `nums_actions::NTuple{N,Int}`: Tuple of the numbers of actions, 
  one for each　player.
 * `rho::T`: Covariance of a pair of payoff values. Must be in
@@ -64,25 +70,29 @@ multi-normal with the covariance of any pair of payoffs equal to
  Nash Equilibria in Random Games," Games and Economic Behavior
  (2000), 274-293.
 """
-function covariance_game{N}(nums_actions::NTuple{N,Int}, rho::Real)
+function covariance_game{N}(rng::AbstractRNG, nums_actions::NTuple{N,Int},
+ rho::Real)
  if N <= 1
  throw(ArgumentError("length of nums_actions must be at least 2"))
  end
 
- if !(-1 / (N - 1) < rho < 1)
+ if !(-1 / (N - 1) <= rho <= 1)
  lb = (N == 2) ? "-1" : "-1/$(N-1)"
- throw(ArgumentError("rho must be in ($lb, 1)"))
+ throw(ArgumentError("rho must be in [$lb, 1]"))
  end
 
  mu = zeros(N)
- C = fill(rho, (N, N))
- C[diagind(C)] = ones(N)
+ Sigma = fill(rho, (N, N))
+ Sigma[diagind(Sigma)] = ones(N)
 
- d = MvNormal(mu, C)
- x = rand(d, prod(nums_actions))
+ d = MVNSampler(mu, Sigma)
+ x = rand(rng, d, prod(nums_actions))
 
  payoff_profile_array =
  reshape(transpose(x), (nums_actions..., N))
 
  return NormalFormGame(payoff_profile_array)
 end
+
+covariance_game{N}(nums_actions::NTuple{N,Int}, rho::Real) =
+ covariance_game(Base.GLOBAL_RNG, nums_actions, rho)

test/test_random.jl

@@ -9,11 +9,28 @@
 
  @testset "test covariance game" begin
  nums_actions = (2, 3, 4)
+ N = length(nums_actions)
 
  rho = 0.5
  g = covariance_game(nums_actions, rho)
  @test g.nums_actions == nums_actions
 
+ rho = 1
+ g = covariance_game(nums_actions, rho)
+ for a in CartesianRange(nums_actions)
+ payoff_profile = g[a]
+ for i in 1:(N-1)
+ @test payoff_profile[i] ≈ payoff_profile[end]
+ end
+ end
+
+ rho = -1/(N-1)
+ g = covariance_game(nums_actions, rho)
+ for a in CartesianRange(nums_actions)
+ payoff_profile = g[a]
+ @test sum(payoff_profile) ≈ 0 atol=1e-10
+ end
+
  end
 
  @testset "test random game value error" begin