From e254e888184c8bfd4bb77dbc0e95029d9691f3ca Mon Sep 17 00:00:00 2001 From: Gautam <1gautamj@gmail.com> Date: Tue, 29 Oct 2024 13:25:34 +0000 Subject: [PATCH 1/6] adds a minimal untested version of polymatrix and the lcp solver --- quantecon/game_theory/polymatrix_game.py | 232 +++++++++++++++++++++++ 1 file changed, 232 insertions(+) create mode 100644 quantecon/game_theory/polymatrix_game.py diff --git a/quantecon/game_theory/polymatrix_game.py b/quantecon/game_theory/polymatrix_game.py new file mode 100644 index 000000000..00035ffa9 --- /dev/null +++ b/quantecon/game_theory/polymatrix_game.py @@ -0,0 +1,232 @@ +from normal_form_game import NormalFormGame, Player +import numpy as np +from itertools import product +from ..optimize.pivoting import _pivoting, _lex_min_ratio_test +from ..optimize.lcp_lemke import _get_solution + + +def hh_payoff_player( + nf: NormalFormGame, + my_player_number, + my_action_number, + is_polymatrix=False +): + """ + hh stands for head-to-head. + Approximates the payoffs to a player when they play + an action with values at the actions of other players + that try to sum to the payoff. + Precise when the game can be represented with a polymatrix. + + Args: + my_player_number (_type_): The number of the player making the action. + my_action_number (_type_): The number of the action. + is_polymatrix : + Is the game represented by this normal form + actually a polymatrix game. + + Returns: + _type_: + Dictionary giving an approximate component + of the payoff at each action for each other player. + """ + action_combinations = product(*( + [range(nf.nums_actions[p]) if p != my_player_number else [my_action_number] + for p in range(nf.N)] + )) + my_player: Player = nf.players[my_player_number] + my_payoffs = my_player.payoff_array + hh_actions_and_payoffs = np.vstack([ + np.hstack( + [ + np.eye(nf.nums_actions[p])[action_combination[p]] + for p in range(nf.N) if p != my_player_number + ] + [ + my_payoffs[ + action_combination[my_player_number:] + + action_combination[:my_player_number] + ] + ] + ) + for action_combination in action_combinations + ]) + hh_actions = hh_actions_and_payoffs[:, :-1] + combined_payoffs = hh_actions_and_payoffs[:, -1] + + # different ways to solve the simultaneous equations + if is_polymatrix: + # this does not go much faster and + # could also be used for games with no actual polymatrix + hh_payoffs_array, residuals, _, _ = np.linalg.lstsq( + hh_actions, combined_payoffs, rcond=None + ) + assert not residuals, "The game is not actually a polymatrix game" + else: + hh_payoffs_array = np.dot(np.linalg.pinv(hh_actions), combined_payoffs) + + payoff_labels = [ + (p, a) + for p in range(nf.N) if p != my_player_number + for a in range(nf.nums_actions[p]) + ] + + payoffs = {label: payoff for label, payoff in zip( + payoff_labels, hh_payoffs_array)} + + return payoffs + + +class PolymatrixGame: + + def __str__(self) -> str: + str_builder = "" + for k, v in self.polymatrix.items(): + str_builder += str(k) + ":\n" + str_builder += str(v) + "\n\n" + return str_builder + + def __init__(self, number_of_players, nums_actions, polymatrix) -> None: + self.N = number_of_players + self.nums_actions = nums_actions + self.polymatrix = polymatrix + + @classmethod + def from_nf(cls, nf: NormalFormGame, is_polymatrix=False): + """ + Creates a Polymatrix approximation to a + Normal Form Game. Precise if possible. + + Args: + nf (NormalFormGame): Normal Form Game to approximate. + is_polymatrix : + Is the game represented by the normal form + actually a polymatrix game. + + Returns: + _type_: New Polymatrix Game. + """ + polymatrix_builder = { + (p1, p2): np.full((nf.nums_actions[p1], nf.nums_actions[p2]), -np.inf) + for p1 in range(nf.N) + for p2 in range(nf.N) + if p1 != p2 + } + for p1 in range(nf.N): + for a1 in range(nf.nums_actions[p1]): + payoffs = hh_payoff_player( + nf, p1, a1, is_polymatrix=is_polymatrix) + for ((p2, a2), payoff) in payoffs.items(): + polymatrix_builder[(p1, p2)][a1][a2] = payoff + + return cls(nf.N, nf.nums_actions, polymatrix_builder) + + def range_of_payoffs(self): + """ + The lowest and highest components of payoff from + head to head games. + + Returns: + _type_: Tuple of minimum and maximum. + """ + min_p = min([np.min(M) for M in self.polymatrix.values()]) + max_p = max([np.max(M) for M in self.polymatrix.values()]) + return (min_p, max_p) + + +def polym_lcp_solver(polym: PolymatrixGame): + LOW_AVOIDER = 2.0 + # makes all of the costs greater than 0 + positive_cost_maker = polym.range_of_payoffs()[1] + LOW_AVOIDER + # Construct the LCP like Howson: + M = np.vstack([ + np.hstack([ + np.zeros((polym.nums_actions[player], polym.nums_actions[player])) if p2 == player + else (positive_cost_maker - polym.polymatrix[(player, p2)]) + for p2 in range(polym.N) + ] + [ + -np.outer(np.ones(polym.nums_actions[player]), np.eye(polym.N)[player]) + ]) + for player in range(polym.N) + ] + [ + np.hstack([ + np.hstack([ + np.outer(np.eye(polym.N)[player], np.ones( + polym.nums_actions[player])) + for player in range(polym.N) + ] + ), + np.zeros((polym.N, polym.N)) + ]) + ] + ) + total_actions = sum(polym.nums_actions) + q = np.hstack([np.zeros(total_actions), -np.ones(polym.N)]) + + n = np.shape(M)[0] + tableau = np.hstack([ + np.eye(n), + -M, + np.reshape(q, (-1, 1)) + ]) + + basis = np.array(range(n)) + z = np.empty(n) + + starting_player_actions = { + player: 0 + for player in range(polym.N) + } + + for player in range(polym.N): + row = sum(polym.nums_actions) + player + col = n + sum(polym.nums_actions[:player]) + \ + starting_player_actions[player] + _pivoting(tableau, col, row) + basis[row] = col + + # Array to store row indices in lex_min_ratio_test + argmins = np.empty(n + polym.N, dtype=np.int_) + p = 0 + retro = False + while p < polym.N: + finishing_v = sum(polym.nums_actions) + n + p + finishing_x = n + \ + sum(polym.nums_actions[:p]) + starting_player_actions[p] + finishing_y = finishing_x - n + + pivcol = finishing_v if not retro else finishing_x if finishing_y in basis else finishing_y + + retro = False + + while True: + + _, pivrow = _lex_min_ratio_test( + tableau, pivcol, 0, argmins, + ) + + _pivoting(tableau, pivcol, pivrow) + basis[pivrow], leaving_var = pivcol, basis[pivrow] + + if leaving_var == finishing_x or leaving_var == finishing_y: + p += 1 + break + elif leaving_var == finishing_v: + print("entering the backtracking case") + p -= 1 + retro = True + break + elif leaving_var < n: + pivcol = leaving_var + n + else: + pivcol = leaving_var - n + + combined_solution = _get_solution(tableau, basis, z) + + eq_strategies = [ + combined_solution[ + sum(polym.nums_actions[:player]) : sum(polym.nums_actions[:player+1]) + ] + for player in range(polym.N) + ] + + return eq_strategies From 9cf083c3dd6e299a17f38810be33762475af28ec Mon Sep 17 00:00:00 2001 From: Gautam <1gautamj@gmail.com> Date: Tue, 5 Nov 2024 13:58:39 +0000 Subject: [PATCH 2/6] load games from gam files. tests for lcp hoswon lover on polymatrix games. --- quantecon/game_theory/game_converters.py | 33 ++++++ quantecon/game_theory/howson_lcp.py | 102 ++++++++++++++++++ quantecon/game_theory/polymatrix_game.py | 101 +---------------- .../game_theory/tests/gam_files/big_polym.gam | 8 ++ .../tests/gam_files/triggers_back_case.gam | 8 ++ .../game_theory/tests/test_howson_lcp.py | 25 +++++ 6 files changed, 177 insertions(+), 100 deletions(-) create mode 100644 quantecon/game_theory/game_converters.py create mode 100644 quantecon/game_theory/howson_lcp.py create mode 100644 quantecon/game_theory/tests/gam_files/big_polym.gam create mode 100644 quantecon/game_theory/tests/gam_files/triggers_back_case.gam create mode 100644 quantecon/game_theory/tests/test_howson_lcp.py diff --git a/quantecon/game_theory/game_converters.py b/quantecon/game_theory/game_converters.py new file mode 100644 index 000000000..d289d1ebf --- /dev/null +++ b/quantecon/game_theory/game_converters.py @@ -0,0 +1,33 @@ +from .normal_form_game import NormalFormGame +from itertools import product + +def qe_nfg_from_gam_file(filename): + + with open(filename, 'r') as file: + lines = file.readlines() + combined = [ + token + for line in lines + for token in line.split() + ] + + i = iter(combined) + players = int(next(i)) + actions = [int(next(i)) for _ in range(players)] + + nfg = NormalFormGame(actions) + + entries = [ + { + tuple(reversed(action_combination)): float(next(i)) + for action_combination in product(*[range(a) for a in actions]) + } + for _ in range(players) + ] + + for action_combination in product(*[range(a) for a in actions]): + nfg[tuple(reversed(action_combination))] = [ + entries[p][action_combination] for p in range(players) + ] + + return nfg \ No newline at end of file diff --git a/quantecon/game_theory/howson_lcp.py b/quantecon/game_theory/howson_lcp.py new file mode 100644 index 000000000..84a639448 --- /dev/null +++ b/quantecon/game_theory/howson_lcp.py @@ -0,0 +1,102 @@ +import numpy as np +from .polymatrix_game import PolymatrixGame +from ..optimize.pivoting import _pivoting, _lex_min_ratio_test +from ..optimize.lcp_lemke import _get_solution + +def polym_lcp_solver(polym: PolymatrixGame): + LOW_AVOIDER = 2.0 + # makes all of the costs greater than 0 + positive_cost_maker = polym.range_of_payoffs()[1] + LOW_AVOIDER + # Construct the LCP like Howson: + M = np.vstack([ + np.hstack([ + np.zeros((polym.nums_actions[player], polym.nums_actions[player])) if p2 == player + else (positive_cost_maker - polym.polymatrix[(player, p2)]) + for p2 in range(polym.N) + ] + [ + -np.outer(np.ones(polym.nums_actions[player]), np.eye(polym.N)[player]) + ]) + for player in range(polym.N) + ] + [ + np.hstack([ + np.hstack([ + np.outer(np.eye(polym.N)[player], np.ones( + polym.nums_actions[player])) + for player in range(polym.N) + ] + ), + np.zeros((polym.N, polym.N)) + ]) + ] + ) + total_actions = sum(polym.nums_actions) + q = np.hstack([np.zeros(total_actions), -np.ones(polym.N)]) + + n = np.shape(M)[0] + tableau = np.hstack([ + np.eye(n), + -M, + np.reshape(q, (-1, 1)) + ]) + + basis = np.array(range(n)) + z = np.empty(n) + + starting_player_actions = { + player: 0 + for player in range(polym.N) + } + + for player in range(polym.N): + row = sum(polym.nums_actions) + player + col = n + sum(polym.nums_actions[:player]) + \ + starting_player_actions[player] + _pivoting(tableau, col, row) + basis[row] = col + + # Array to store row indices in lex_min_ratio_test + argmins = np.empty(n + polym.N, dtype=np.int_) + p = 0 + retro = False + while p < polym.N: + finishing_v = sum(polym.nums_actions) + n + p + finishing_x = n + \ + sum(polym.nums_actions[:p]) + starting_player_actions[p] + finishing_y = finishing_x - n + + pivcol = finishing_v if not retro else finishing_x if finishing_y in basis else finishing_y + + retro = False + + while True: + + _, pivrow = _lex_min_ratio_test( + tableau, pivcol, 0, argmins, + ) + + _pivoting(tableau, pivcol, pivrow) + basis[pivrow], leaving_var = pivcol, basis[pivrow] + + if leaving_var == finishing_x or leaving_var == finishing_y: + p += 1 + break + elif leaving_var == finishing_v: + print("entering the backtracking case") + p -= 1 + retro = True + break + elif leaving_var < n: + pivcol = leaving_var + n + else: + pivcol = leaving_var - n + + combined_solution = _get_solution(tableau, basis, z) + + eq_strategies = [ + combined_solution[ + sum(polym.nums_actions[:player]) : sum(polym.nums_actions[:player+1]) + ] + for player in range(polym.N) + ] + + return eq_strategies \ No newline at end of file diff --git a/quantecon/game_theory/polymatrix_game.py b/quantecon/game_theory/polymatrix_game.py index 00035ffa9..d6c4aa676 100644 --- a/quantecon/game_theory/polymatrix_game.py +++ b/quantecon/game_theory/polymatrix_game.py @@ -1,6 +1,6 @@ -from normal_form_game import NormalFormGame, Player import numpy as np from itertools import product +from .normal_form_game import NormalFormGame, Player from ..optimize.pivoting import _pivoting, _lex_min_ratio_test from ..optimize.lcp_lemke import _get_solution @@ -131,102 +131,3 @@ def range_of_payoffs(self): min_p = min([np.min(M) for M in self.polymatrix.values()]) max_p = max([np.max(M) for M in self.polymatrix.values()]) return (min_p, max_p) - - -def polym_lcp_solver(polym: PolymatrixGame): - LOW_AVOIDER = 2.0 - # makes all of the costs greater than 0 - positive_cost_maker = polym.range_of_payoffs()[1] + LOW_AVOIDER - # Construct the LCP like Howson: - M = np.vstack([ - np.hstack([ - np.zeros((polym.nums_actions[player], polym.nums_actions[player])) if p2 == player - else (positive_cost_maker - polym.polymatrix[(player, p2)]) - for p2 in range(polym.N) - ] + [ - -np.outer(np.ones(polym.nums_actions[player]), np.eye(polym.N)[player]) - ]) - for player in range(polym.N) - ] + [ - np.hstack([ - np.hstack([ - np.outer(np.eye(polym.N)[player], np.ones( - polym.nums_actions[player])) - for player in range(polym.N) - ] - ), - np.zeros((polym.N, polym.N)) - ]) - ] - ) - total_actions = sum(polym.nums_actions) - q = np.hstack([np.zeros(total_actions), -np.ones(polym.N)]) - - n = np.shape(M)[0] - tableau = np.hstack([ - np.eye(n), - -M, - np.reshape(q, (-1, 1)) - ]) - - basis = np.array(range(n)) - z = np.empty(n) - - starting_player_actions = { - player: 0 - for player in range(polym.N) - } - - for player in range(polym.N): - row = sum(polym.nums_actions) + player - col = n + sum(polym.nums_actions[:player]) + \ - starting_player_actions[player] - _pivoting(tableau, col, row) - basis[row] = col - - # Array to store row indices in lex_min_ratio_test - argmins = np.empty(n + polym.N, dtype=np.int_) - p = 0 - retro = False - while p < polym.N: - finishing_v = sum(polym.nums_actions) + n + p - finishing_x = n + \ - sum(polym.nums_actions[:p]) + starting_player_actions[p] - finishing_y = finishing_x - n - - pivcol = finishing_v if not retro else finishing_x if finishing_y in basis else finishing_y - - retro = False - - while True: - - _, pivrow = _lex_min_ratio_test( - tableau, pivcol, 0, argmins, - ) - - _pivoting(tableau, pivcol, pivrow) - basis[pivrow], leaving_var = pivcol, basis[pivrow] - - if leaving_var == finishing_x or leaving_var == finishing_y: - p += 1 - break - elif leaving_var == finishing_v: - print("entering the backtracking case") - p -= 1 - retro = True - break - elif leaving_var < n: - pivcol = leaving_var + n - else: - pivcol = leaving_var - n - - combined_solution = _get_solution(tableau, basis, z) - - eq_strategies = [ - combined_solution[ - sum(polym.nums_actions[:player]) : sum(polym.nums_actions[:player+1]) - ] - for player in range(polym.N) - ] - - return eq_strategies diff --git a/quantecon/game_theory/tests/gam_files/big_polym.gam b/quantecon/game_theory/tests/gam_files/big_polym.gam new file mode 100644 index 000000000..52e276b96 --- /dev/null +++ b/quantecon/game_theory/tests/gam_files/big_polym.gam @@ -0,0 +1,8 @@ +5 +4 4 4 4 4 + +1.6001086679228855 8.704046769731992 -6.659273078581798 -10.582083017931385 0.9546087155533698 8.494228670896629 -4.158320360377914 -8.402281441779948 -1.7711953760298762 3.8942993804901214 -2.1580876038754795 -6.896657105462536 -6.386494303489018 5.655422883708059 -3.004948581137473 -17.5494734198317 -1.1376957537841221 14.03148280243252 -9.781950711880455 -4.739897227422116 -1.7831957061536414 13.821664703597165 -7.280997993676571 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1.760937971067463 3.862301671888215 -1.6373947738570074 5.009261181843655 4.491505067728134 6.5928687685488825 3.9108679103190376 10.557523866019697 10.039767751904176 12.141131452724927 1.9959402591142386 8.642596214814901 8.12484010069938 10.226203801520128 -4.57555084504857 2.0711051106520912 1.5533489965365703 3.654712697357322 -1.8449837483879001 4.801672207312755 4.283916093197238 6.38527979401799 diff --git a/quantecon/game_theory/tests/test_howson_lcp.py b/quantecon/game_theory/tests/test_howson_lcp.py new file mode 100644 index 000000000..2c0a068f7 --- /dev/null +++ b/quantecon/game_theory/tests/test_howson_lcp.py @@ -0,0 +1,25 @@ +""" +Tests for howson_lcp.py +""" +import numpy as np +from numpy.testing import assert_allclose, assert_, assert_raises +from quantecon.game_theory.game_converters import qe_nfg_from_gam_file +from quantecon.game_theory.howson_lcp import polym_lcp_solver +from quantecon.game_theory.polymatrix_game import PolymatrixGame + + +def test_polym_lcp_solver_where_solution_is_pure_NE(): + filename = "gam_files/big_polym.gam" + nfg = qe_nfg_from_gam_file(filename) + polym = PolymatrixGame.from_nf(nfg) + ne = polym_lcp_solver(polym) + worked = nfg.is_nash(ne) + assert_(worked) + +def test_polym_lcp_solver_where_lcp_solver_must_backtrack(): + filename = "gam_files/triggers_back_case.gam" + nfg = qe_nfg_from_gam_file(filename) + polym = PolymatrixGame.from_nf(nfg) + ne = polym_lcp_solver(polym) + worked = nfg.is_nash(ne) + assert_(worked) From 1e5b94df994512fe8a6f811131d42b0084ed5b46 Mon Sep 17 00:00:00 2001 From: Gautam <1gautamj@gmail.com> Date: Tue, 5 Nov 2024 15:08:36 +0000 Subject: [PATCH 3/6] describes the functions and adds links to Howson's paper and GameTracer --- quantecon/game_theory/game_converters.py | 18 ++++++++++++- quantecon/game_theory/howson_lcp.py | 13 ++++++++++ quantecon/game_theory/polymatrix_game.py | 25 ++++++++++--------- .../game_theory/tests/test_howson_lcp.py | 4 +-- 4 files changed, 45 insertions(+), 15 deletions(-) diff --git a/quantecon/game_theory/game_converters.py b/quantecon/game_theory/game_converters.py index d289d1ebf..83a392779 100644 --- a/quantecon/game_theory/game_converters.py +++ b/quantecon/game_theory/game_converters.py @@ -1,8 +1,24 @@ +""" +Functions for converting between ways of storing games. +""" + from .normal_form_game import NormalFormGame from itertools import product def qe_nfg_from_gam_file(filename): - + """ + Makes a QuantEcon Normal Form Game from a gam file. + Gam files are described by GameTracer. + http://dags.stanford.edu/Games/gametracer.html + + Args: + filename: path to gam file. + + Returns: + NormalFormGame: + The QuantEcon Normal Form Game + described by the gam file. + """ with open(filename, 'r') as file: lines = file.readlines() combined = [ diff --git a/quantecon/game_theory/howson_lcp.py b/quantecon/game_theory/howson_lcp.py index 84a639448..d7be37a04 100644 --- a/quantecon/game_theory/howson_lcp.py +++ b/quantecon/game_theory/howson_lcp.py @@ -4,6 +4,19 @@ from ..optimize.lcp_lemke import _get_solution def polym_lcp_solver(polym: PolymatrixGame): + """ + Finds the Nash Equilbrium of a polymatrix game + using Howson's algorithm described in + https://www.jstor.org/stable/2634798 + which utilises linear complimentarity. + + Args: + polym (PolymatrixGame): Polymatrix game to solve. + + Returns: + Probability distribution across actions for each player + at Nash Equilibrium. + """ LOW_AVOIDER = 2.0 # makes all of the costs greater than 0 positive_cost_maker = polym.range_of_payoffs()[1] + LOW_AVOIDER diff --git a/quantecon/game_theory/polymatrix_game.py b/quantecon/game_theory/polymatrix_game.py index d6c4aa676..5a7879d0b 100644 --- a/quantecon/game_theory/polymatrix_game.py +++ b/quantecon/game_theory/polymatrix_game.py @@ -1,9 +1,6 @@ import numpy as np from itertools import product from .normal_form_game import NormalFormGame, Player -from ..optimize.pivoting import _pivoting, _lex_min_ratio_test -from ..optimize.lcp_lemke import _get_solution - def hh_payoff_player( nf: NormalFormGame, @@ -19,16 +16,15 @@ def hh_payoff_player( Precise when the game can be represented with a polymatrix. Args: - my_player_number (_type_): The number of the player making the action. - my_action_number (_type_): The number of the action. - is_polymatrix : + my_player_number: The number of the player making the action. + my_action_number: The number of the action. + is_polymatrix: Is the game represented by this normal form actually a polymatrix game. Returns: - _type_: - Dictionary giving an approximate component - of the payoff at each action for each other player. + Dictionary giving an approximate component + of the payoff at each action for each other player. """ action_combinations = product(*( [range(nf.nums_actions[p]) if p != my_player_number else [my_action_number] @@ -77,7 +73,12 @@ def hh_payoff_player( class PolymatrixGame: - + """ + In a polymatrix game, the payoff to a player is the sum + of their payoffs from bimatrix games against each player. + i.e. If two opponents deviate, the change in payoff + is the sum of the changes in payoff of each deviation. + """ def __str__(self) -> str: str_builder = "" for k, v in self.polymatrix.items(): @@ -103,7 +104,7 @@ def from_nf(cls, nf: NormalFormGame, is_polymatrix=False): actually a polymatrix game. Returns: - _type_: New Polymatrix Game. + New Polymatrix Game. """ polymatrix_builder = { (p1, p2): np.full((nf.nums_actions[p1], nf.nums_actions[p2]), -np.inf) @@ -126,7 +127,7 @@ def range_of_payoffs(self): head to head games. Returns: - _type_: Tuple of minimum and maximum. + Tuple of minimum and maximum. """ min_p = min([np.min(M) for M in self.polymatrix.values()]) max_p = max([np.max(M) for M in self.polymatrix.values()]) diff --git a/quantecon/game_theory/tests/test_howson_lcp.py b/quantecon/game_theory/tests/test_howson_lcp.py index 2c0a068f7..b2ccb9f42 100644 --- a/quantecon/game_theory/tests/test_howson_lcp.py +++ b/quantecon/game_theory/tests/test_howson_lcp.py @@ -1,8 +1,8 @@ """ Tests for howson_lcp.py """ -import numpy as np -from numpy.testing import assert_allclose, assert_, assert_raises + +from numpy.testing import assert_ from quantecon.game_theory.game_converters import qe_nfg_from_gam_file from quantecon.game_theory.howson_lcp import polym_lcp_solver from quantecon.game_theory.polymatrix_game import PolymatrixGame From 72447236f0b915b0ecabedbb25a0616ff21cfdde Mon Sep 17 00:00:00 2001 From: Gautam <1gautamj@gmail.com> Date: Tue, 5 Nov 2024 15:46:31 +0000 Subject: [PATCH 4/6] make PEP8 changes --- quantecon/game_theory/game_converters.py | 14 ++++++----- quantecon/game_theory/howson_lcp.py | 23 +++++++++++++------ quantecon/game_theory/polymatrix_game.py | 8 +++++-- .../game_theory/tests/test_howson_lcp.py | 1 + 4 files changed, 31 insertions(+), 15 deletions(-) diff --git a/quantecon/game_theory/game_converters.py b/quantecon/game_theory/game_converters.py index 83a392779..f558094db 100644 --- a/quantecon/game_theory/game_converters.py +++ b/quantecon/game_theory/game_converters.py @@ -1,10 +1,11 @@ """ -Functions for converting between ways of storing games. +Functions for converting between ways of storing games. """ from .normal_form_game import NormalFormGame from itertools import product + def qe_nfg_from_gam_file(filename): """ Makes a QuantEcon Normal Form Game from a gam file. @@ -17,8 +18,8 @@ def qe_nfg_from_gam_file(filename): Returns: NormalFormGame: The QuantEcon Normal Form Game - described by the gam file. - """ + described by the gam file. + """ with open(filename, 'r') as file: lines = file.readlines() combined = [ @@ -30,13 +31,14 @@ def qe_nfg_from_gam_file(filename): i = iter(combined) players = int(next(i)) actions = [int(next(i)) for _ in range(players)] - + nfg = NormalFormGame(actions) entries = [ { tuple(reversed(action_combination)): float(next(i)) - for action_combination in product(*[range(a) for a in actions]) + for action_combination in product( + *[range(a) for a in actions]) } for _ in range(players) ] @@ -46,4 +48,4 @@ def qe_nfg_from_gam_file(filename): entries[p][action_combination] for p in range(players) ] - return nfg \ No newline at end of file + return nfg diff --git a/quantecon/game_theory/howson_lcp.py b/quantecon/game_theory/howson_lcp.py index d7be37a04..3a3272c48 100644 --- a/quantecon/game_theory/howson_lcp.py +++ b/quantecon/game_theory/howson_lcp.py @@ -3,31 +3,35 @@ from ..optimize.pivoting import _pivoting, _lex_min_ratio_test from ..optimize.lcp_lemke import _get_solution + def polym_lcp_solver(polym: PolymatrixGame): """ Finds the Nash Equilbrium of a polymatrix game using Howson's algorithm described in https://www.jstor.org/stable/2634798 which utilises linear complimentarity. - + Args: polym (PolymatrixGame): Polymatrix game to solve. Returns: Probability distribution across actions for each player at Nash Equilibrium. - """ + """ LOW_AVOIDER = 2.0 # makes all of the costs greater than 0 positive_cost_maker = polym.range_of_payoffs()[1] + LOW_AVOIDER # Construct the LCP like Howson: M = np.vstack([ np.hstack([ - np.zeros((polym.nums_actions[player], polym.nums_actions[player])) if p2 == player + np.zeros( + (polym.nums_actions[player], polym.nums_actions[player]) + ) if p2 == player else (positive_cost_maker - polym.polymatrix[(player, p2)]) for p2 in range(polym.N) ] + [ - -np.outer(np.ones(polym.nums_actions[player]), np.eye(polym.N)[player]) + -np.outer(np.ones( + polym.nums_actions[player]), np.eye(polym.N)[player]) ]) for player in range(polym.N) ] + [ @@ -77,7 +81,11 @@ def polym_lcp_solver(polym: PolymatrixGame): sum(polym.nums_actions[:p]) + starting_player_actions[p] finishing_y = finishing_x - n - pivcol = finishing_v if not retro else finishing_x if finishing_y in basis else finishing_y + pivcol = ( + finishing_v if not retro + else finishing_x if finishing_y in basis + else finishing_y + ) retro = False @@ -107,9 +115,10 @@ def polym_lcp_solver(polym: PolymatrixGame): eq_strategies = [ combined_solution[ - sum(polym.nums_actions[:player]) : sum(polym.nums_actions[:player+1]) + sum(polym.nums_actions[:player]): + sum(polym.nums_actions[:player+1]) ] for player in range(polym.N) ] - return eq_strategies \ No newline at end of file + return eq_strategies diff --git a/quantecon/game_theory/polymatrix_game.py b/quantecon/game_theory/polymatrix_game.py index 5a7879d0b..c659eb3ca 100644 --- a/quantecon/game_theory/polymatrix_game.py +++ b/quantecon/game_theory/polymatrix_game.py @@ -2,6 +2,7 @@ from itertools import product from .normal_form_game import NormalFormGame, Player + def hh_payoff_player( nf: NormalFormGame, my_player_number, @@ -27,7 +28,9 @@ def hh_payoff_player( of the payoff at each action for each other player. """ action_combinations = product(*( - [range(nf.nums_actions[p]) if p != my_player_number else [my_action_number] + [ + range(nf.nums_actions[p]) if p != my_player_number + else [my_action_number] for p in range(nf.N)] )) my_player: Player = nf.players[my_player_number] @@ -107,7 +110,8 @@ def from_nf(cls, nf: NormalFormGame, is_polymatrix=False): New Polymatrix Game. """ polymatrix_builder = { - (p1, p2): np.full((nf.nums_actions[p1], nf.nums_actions[p2]), -np.inf) + (p1, p2): np.full( + (nf.nums_actions[p1], nf.nums_actions[p2]), -np.inf) for p1 in range(nf.N) for p2 in range(nf.N) if p1 != p2 diff --git a/quantecon/game_theory/tests/test_howson_lcp.py b/quantecon/game_theory/tests/test_howson_lcp.py index b2ccb9f42..223c33494 100644 --- a/quantecon/game_theory/tests/test_howson_lcp.py +++ b/quantecon/game_theory/tests/test_howson_lcp.py @@ -16,6 +16,7 @@ def test_polym_lcp_solver_where_solution_is_pure_NE(): worked = nfg.is_nash(ne) assert_(worked) + def test_polym_lcp_solver_where_lcp_solver_must_backtrack(): filename = "gam_files/triggers_back_case.gam" nfg = qe_nfg_from_gam_file(filename) From 61d102bc96ca27b39c73db14cba4b8679a8418ed Mon Sep 17 00:00:00 2001 From: Daisuke Oyama Date: Wed, 6 Nov 2024 14:58:46 +0900 Subject: [PATCH 5/6] Register functions to be exported in `game_theory/__init__.py` --- quantecon/game_theory/__init__.py | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/quantecon/game_theory/__init__.py b/quantecon/game_theory/__init__.py index 003a95b25..fd3279903 100644 --- a/quantecon/game_theory/__init__.py +++ b/quantecon/game_theory/__init__.py @@ -4,6 +4,8 @@ """ from .normal_form_game import Player, NormalFormGame +from .polymatrix_game import PolymatrixGame + from .normal_form_game import pure2mixed, best_response_2p from .random import ( random_game, covariance_game, random_pure_actions, random_mixed_actions @@ -13,6 +15,8 @@ from .lemke_howson import lemke_howson from .mclennan_tourky import mclennan_tourky from .vertex_enumeration import vertex_enumeration, vertex_enumeration_gen +from .howson_lcp import polym_lcp_solver + from .game_generators import ( blotto_game, ranking_game, sgc_game, tournament_game, unit_vector_game ) @@ -21,3 +25,5 @@ from .localint import LocalInteraction from .brd import BRD, KMR, SamplingBRD from .logitdyn import LogitDynamics + +from .game_converters import qe_nfg_from_gam_file From 82e4ebac7ed0c24665f44b5b1be1618bf10d3677 Mon Sep 17 00:00:00 2001 From: Daisuke Oyama Date: Wed, 6 Nov 2024 18:08:08 +0900 Subject: [PATCH 6/6] Get data dir in game_theory/tests --- quantecon/game_theory/tests/test_howson_lcp.py | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) diff --git a/quantecon/game_theory/tests/test_howson_lcp.py b/quantecon/game_theory/tests/test_howson_lcp.py index 223c33494..553fd826b 100644 --- a/quantecon/game_theory/tests/test_howson_lcp.py +++ b/quantecon/game_theory/tests/test_howson_lcp.py @@ -7,10 +7,18 @@ from quantecon.game_theory.howson_lcp import polym_lcp_solver from quantecon.game_theory.polymatrix_game import PolymatrixGame +import os + + +# Mimicing quantecon.tests.util.get_data_dir +data_dir_name = "gam_files" +this_dir = os.path.dirname(__file__) +data_dir = os.path.join(this_dir, data_dir_name) + def test_polym_lcp_solver_where_solution_is_pure_NE(): - filename = "gam_files/big_polym.gam" - nfg = qe_nfg_from_gam_file(filename) + filename = "big_polym.gam" + nfg = qe_nfg_from_gam_file(os.path.join(data_dir, filename)) polym = PolymatrixGame.from_nf(nfg) ne = polym_lcp_solver(polym) worked = nfg.is_nash(ne) @@ -18,8 +26,8 @@ def test_polym_lcp_solver_where_solution_is_pure_NE(): def test_polym_lcp_solver_where_lcp_solver_must_backtrack(): - filename = "gam_files/triggers_back_case.gam" - nfg = qe_nfg_from_gam_file(filename) + filename = "triggers_back_case.gam" + nfg = qe_nfg_from_gam_file(os.path.join(data_dir, filename)) polym = PolymatrixGame.from_nf(nfg) ne = polym_lcp_solver(polym) worked = nfg.is_nash(ne)