empty = [""]
singletons = list(items)
pairs = preferences.pairs(items)
triplets = preferences.triplets(items)
quartets = preferences.quartets(items)
prefs_of_Alice = quartets + triplets + [
"wx", "wy", "wz", "xy", "w", "xz", "yz", "x", "y", "z"
] + empty
prefs_of_Bob = quartets + triplets + pairs + ["w", "z", "x", "y"] + empty
prefs_of_Carl = quartets + triplets + pairs + ["x", "y", "w", "z"] + empty
prefs_of_Dana = quartets + triplets + pairs + singletons + empty
prefs = [prefs_of_Alice, prefs_of_Bob, prefs_of_Carl, prefs_of_Dana]
budgets = [160, 130, 90, 66]
print(
"\nWith the preferences in the paper, there are no competitive equilibria:"
)
ce.display(ce.find_equilibrium(items, prefs, budgets))
print(
"\nAs a control, with only the three highest-income agents, a competitive equilibrium exists:"
)
ce.display(ce.find_equilibrium(items, prefs[0:3], budgets[0:3]))
print(
"\nWith the preferences in the paper, even a *personalized* equilibrium does not exist:"
)
ce.display(ce.find_personalized_equilibrium(items, prefs, budgets))
by exhaustively checking all allocations.
See Appendix D, Example 4
AUTHOR: Erel Segal-Halevi
SINCE: 2019-08
"""
import preferences
import competitive_equilibrium as ce
import sys, logging
if len(sys.argv)<2 or sys.argv[1]!="quiet":
ce.logger.setLevel(logging.INFO)
items = "xyz"
prefs_of_Alice = ["xyz", "xy","yz","xz", "x","y","z", ""]
prefs_of_Bob = ["xyz", "xy","xz","yz", "y","x","z", ""]
prefs_of_Carl = preferences.triplets(items) + preferences.pairs(items) + list(items) + [""]
budget_of_Alice = budget_of_Bob = 4; budget_of_Carl = 2 # or any other a,b,c such that a=b > c
print("\nWith only Alice and Bob, no competitive equilibria exists:")
ce.display(ce.find_equilibrium(items, [prefs_of_Alice, prefs_of_Bob], [budget_of_Alice, budget_of_Bob]))
print("\nWith all three agents, a competitive equilibrium exists:")
ce.display(ce.find_equilibrium(items, [prefs_of_Alice, prefs_of_Bob, prefs_of_Carl],
[budget_of_Alice, budget_of_Bob, budget_of_Carl]))
print("\nWith only Alice and Bob, even a *personalized* competitive equilibrium does not exist:")
ce.display(ce.find_personalized_equilibrium(items, [prefs_of_Alice, prefs_of_Bob], [budget_of_Alice, budget_of_Bob]))
import preferences
import competitive_equilibrium as ce
import sys, logging
if len(sys.argv)<2 or sys.argv[1]!="quiet":
ce.logger.setLevel(logging.INFO)
items = "wxyz"
empty = [""]
singletons = list(items)
pairs = preferences.pairs(items)
triplets = preferences.triplets(items)
quartets = preferences.quartets(items)
prefs_of_Alice = quartets + triplets + ["wx", "wy", "wz", "xy", "w", "xz", "yz", "x", "y", "z"] + empty
prefs_of_Bob = quartets + triplets + pairs + ["w", "z", "x", "y"] + empty
prefs_of_Carl = quartets + triplets + pairs + ["x", "y", "w", "z"] + empty
prefs_of_Others = quartets + triplets + pairs + singletons + empty
prefs = [prefs_of_Alice, prefs_of_Bob, prefs_of_Carl, prefs_of_Others, prefs_of_Others]
budgets = [160, 130, 90, 66, 55]
print("\nWith the preferences in the paper, there are no competitive equilibria:")
ce.display(ce.find_equilibrium(items, prefs, budgets))
print("\nAs a control, if we change the budgets, there is a competitive equilibrium:")
alternative_budgets = [18, 11, 9, 6, 5]
ce.display(ce.find_equilibrium(items, prefs, alternative_budgets))
print("\nWith the preferences in the paper, even a *personalized* equilibrium does not exist:")
ce.display(ce.find_personalized_equilibrium(items, prefs, budgets))
prefs_of_Alice = quintuplets + quartets + [
"vwx", "vwy", "vwz", "vw", "xyz"
] + triplets + pairs + singletons + empty
prefs_of_Bob = quintuplets + quartets + triplets_except_xyz + [
"vx", "vy", "vz", "wx", "wy", "wz", "xyz", "vw", "w", "v", "xy", "xz",
"yz", "x", "y", "z"
] + empty
prefs_of_Carl = quintuplets + quartets + triplets + pairs + singletons + empty
prefs = [prefs_of_Alice, prefs_of_Bob, prefs_of_Carl]
budgets = [12, 10, 1] # or any other a,b,c such that a > b+c and > 3(a+c)/4
print(
"\nWith the preferences in the paper, there are no competitive equilibria:"
)
ce.display(ce.find_equilibrium(items, prefs, budgets))
print(
"\nAs a control, if we slightly change the preferences of Alice, there is a competitive equilibrium:"
)
alternative_prefs_of_Alice = quintuplets + quartets + [
"vwx", "vwy", "vwz", "vw"
] + triplets + pairs + singletons
alternative_prefs_of_Bob = prefs_of_Bob
ce.display(
ce.find_equilibrium(
items,
[alternative_prefs_of_Alice, alternative_prefs_of_Bob, prefs_of_Carl],
budgets))
print(
SINCE: 2019-08
"""
import competitive_equilibrium as ce
import sys, logging
if len(sys.argv) < 2 or sys.argv[1] != "quiet":
ce.logger.setLevel(logging.INFO)
items = "xyz"
prefs_of_any_agent = ["", "x", "y", "xy", "z", "zx", "zy", "zxy"]
prefs = [prefs_of_any_agent, prefs_of_any_agent, prefs_of_any_agent]
budgets = [-7, -8, -9]
print("\nWith budgets as in the paper, there are no competitive equilibria:")
ce.display(ce.find_equilibrium(items, prefs, budgets, negative_prices=True))
print(
"\nAs a control, if we change the budgets, there is a competitive equilibrium:"
)
alternative_budgets = [-3, -7, -15]
ce.display(
ce.find_equilibrium(items,
prefs,
alternative_budgets,
negative_prices=True))
print("\nEven a *personalized* competitive equilibrium does not exist:")
ce.display(
ce.find_personalized_equilibrium(items,
prefs,
ce.logger.setLevel(logging.INFO)
items = "vwxyz"
empty = [""]
singletons = list(items)
pairs = preferences.pairs(items)
triplets = preferences.triplets(items)
quartets = preferences.quartets(items)
quintuplets = [items]
triplets_except_xyz = preferences.list_difference(triplets, ["xyz"])
triplets_except_vwx_vwy_vwz_xyz = preferences.list_difference(triplets, ["vwx","vwy","vwz","xyz"])
pairs_except_vw = preferences.list_difference(pairs, ["vw"])
prefs_of_Alice = preferences.goods_to_chores(items, quintuplets + quartets + ["vwx","vwy","vwz","vw","xyz"] + triplets_except_vwx_vwy_vwz_xyz + pairs_except_vw + singletons + empty)
prefs_of_Bob = preferences.goods_to_chores(items, quintuplets + quartets + triplets_except_xyz + ["vx","vy","vz","wx","wy","wz","xyz","vw","w","v","xy","xz","yz","x","y","z"] + empty)
budgets = [-10,-12]
print("\nWith the preferences in the paper, there are no competitive equilibria:")
ce.display(ce.find_equilibrium(items, [prefs_of_Alice, prefs_of_Bob], budgets, negative_prices=True))
print("\nAs a control, if we slightly change the preferences of Alice, there is a competitive equilibrium:")
alternative_prefs_of_Alice = preferences.goods_to_chores(items, quintuplets + quartets + ["vwx","vwy","vwz","xyz"] + triplets_except_vwx_vwy_vwz_xyz + pairs + singletons + [""])
alternative_prefs_of_Bob = prefs_of_Bob
ce.display(
ce.find_equilibrium(items, [alternative_prefs_of_Alice, alternative_prefs_of_Bob], budgets, negative_prices=True))
print("\nWith the original preferences, even a *personalized* competitive equilibrium does not exist.")
ce.display(ce.find_personalized_equilibrium(items, [prefs_of_Alice, prefs_of_Bob], budgets, negative_prices=True))
