Tag-blindness: An Antidote for Discriminatory Bargaining

Transcript

1. Tag-Blindness
   Modeling Discriminatory Bargaining Practices in Buyer-Seller Transactions:
   Replication and Extension of the Emergence of Classes ABM Bargaining Model
   Griffin Vernor Drutchas
   Temple University, Beasley School of Law
   Philadelphia, PA
   SWARMFEST 2013
   University of Central Florida - Office of Research and Commercialization
   Orlando, FL
   Special thanks to
   Dr. Hosea H. Harvey, Temple University, Beasley School of Law
   Dr. Péter Érdi, Kalamazoo College, Center for Complex Systems Studies
   

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2. How many non-discriminatory sellers does it
   take to eliminate statistical discrimination from
   a bargain-based market?
   

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3. two motivations
   1. the (anonymous?) internet + new car bargaining
   2. prisoner’s dilemma “shoehorn” in legal scholarship
   

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4. Emergence of Classes Model - Axtell/Epstein/Young (2000)
   Nash demand game . . .
   1. Two Players demand a portion of a “pie”
   2. If D1 + D2 <= 100%, both players get their demand
   3. If D1 + D2 > 100%, both get zero (negotiation breakdown)
   Axtell, Epstein, and Young. Emergence of Classes in a Multi-Agent Bargaining Model. Center on Social and Economic Dynamics, Working Paper No. 9 (2000)
   seller reservation price
   (profit = 0 = marginal cost)
   buyer reservation price
   (consumer surplus = 0)
   

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5. Axtell, Epstein, and Young. Emergence of Classes in a Multi-Agent Bargaining Model. Center on Social and Economic Dynamics, Working Paper No. 9 (2000)
   . . . with simplified demands . . .
   H: 70% — M: 50% — L: 30%
   Payoff Matrix
   0,0 0,0 70,30
   0,0 50,50 50,30
   30,70 30,50 30,30
   H
   H
   M
   L
   M L
   . . . in an agent-based model.
   (choosing equilibrium without
   a priori selection)
   

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6. Axtell, Epstein, and Young. Emergence of Classes in a Multi-Agent Bargaining Model. Center on Social and Economic Dynamics, Working Paper No. 9 (2000)
   memory-based demand decision.
   Memory of length, m
   past m opponents’ demands
   benefit-maximizing demand.
   ε: random choice of H, M, or L
   1 - ε: MAX[ E(BL), E(BM), E(BH) ]
   where,
   E(BL) = L * P(L) + M * P(M) + H * P(H)
   E(BM) = L * P(L) + M * P(M)
   E(BH) = L * P(L)
   where,
   P(demand) = frequency in memory
   H H M L L H M H H M
   

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7. Axtell, Epstein, and Young. Emergence of Classes in a Multi-Agent Bargaining Model. Center on Social and Economic Dynamics, Working Paper No. 9 (2000)
   heterogenous agents.
   N agents
   N/2 have “tags"
   tags.
   proxy for any observable characteristic that could
   become “socially salient”, but is here
   “fundamentally irrelevant”
   H H M H H H L H H M
   L L M L L H L L M L
   two memory sets
   tag
   no tag
   

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8. Axtell, Epstein, and Young. Emergence of Classes in a Multi-Agent Bargaining Model. Center on Social and Economic Dynamics, Working Paper No. 9 (2000)
   Baseline Parameters
   H: 70% — M: 50% — L: 30%
   m = 20
   ε = 0.2
   N = 100
   Ntag = N/2
   

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9. Axtell, Epstein, and Young. Emergence of Classes in a Multi-Agent Bargaining Model. Center on Social and Economic Dynamics, Working Paper No. 9 (2000)
   defining a state.
   All agents have at least (1 - ε)*m instances
   of a particular demand in their memory.
   state threshold.
   (1 - 0.2) * 20 = 16.
   simplexes.
   agent position determined by incidences of
   particular demand in each memory type.
   H in m = L benefit
   L in m = H benefit
   equal benefit to
   demand at
   borders
   high stability.
   1. at baseline parameters, state transitions
   from the first center of attraction take
   ~10,000 iterations to occur
   2. transition times increase monotonically
   and exponentially as m increases and ε
   decreases
   “basin of
   attraction”
   

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10. Axtell, Epstein, and Young. Emergence of Classes in a Multi-Agent Bargaining Model. Center on Social and Economic Dynamics, Working Paper No. 9 (2000)
    “equitable equilibrium”
    “fractious state”
    a 70/30 or 30/70 equilibrium
    “no compromise”
    

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11. benefit-max decision not replicated.
    1. using max benefit rule and baseline parameters, only reached equitable state.
    2. fractious states only emerged as first centre of attraction on runs with low N or
    low m parameter values.
    new memory decision rule.
    1. best reply against opponents’ most frequent demand
    2. changes simplex borders
    New Insights Replication - Poza et. al. (2011)
    Poza, Villafanez, Pajares, Lopez-Parades, and Hernandez. New Insights on the Emergence of Classes Model. Discrete Dynamics in Nature and Society (2011)
    flawed state criteria?
    

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12. Current Replication
    +
    Extension
    Axtell-Epstein-Young Framework
    +
    Baseline Parameters
    +
    Poza Memory Decision Rule
    Python 3.3
    +
    Buyers & Sellers
    +
    Tag-blind Sellers
    +
    =
    

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13. N/2 Buyers, N/2 Sellers
    N/4 tag, N/4 no tag no tag
    

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14. new graphical representation
    (yes, I skipped a step)
    “equitable equilibrium” or dual equilibrium
    imperfect state according to AEY/Poza criterion
    all after 400 iterations
    

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15. new metric: benefit
    dual equilibrium
    Benefit Graph Legend
    Seller --------------------------------- Blue-Dashed
    Tagged-Buyer ............................. Red-Dotted
    Untagged-Buyer .-.-.-.-.-. Green-Dash-Dotted
    Overall ______________________ Solid Black
    additional perk: seeing the state convergence
    

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16. intra-equilibrium
    +
    inter-low
    high bids in memory,
    low benefit from
    perspective of tagged
    buyer, worse off than
    untagged buyer.
    

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17. intra-equilibrium + inter-low
    Benefit Graph Legend
    Seller --------------------------------- Blue-Dashed
    Tagged-Buyer ............................. Red-Dotted
    Untagged-Buyer .-.-.-.-.-. Green-Dash-Dotted
    Overall ______________________ Solid Black
    pardon the color confusion
    sellers have highest avg benefit =
    1/2 *(M demand to untagged buyers
    + H demand to tagged buyers)
    

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18. intra-equilibrium
    +
    inter-high
    low bids in memory,
    high benefit from
    perspective of tagged
    buyer
    opposite situation, but
    still discriminatory:
    buyers treated
    unequally.
    

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19. intra-low
    [intra-high]
    +
    inter-equilibrium
    high bids in memory,
    low benefit from
    perspective of untagged
    buyer
    opposite situation
    occurs too, but
    still discriminatory:
    buyers treated
    unequally.
    this part of state doesn’t exist
    in extension. No intra-dealings
    for tagged buyers.
    

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20. intra-high
    [intra-low]
    +
    inter-low
    [inter-high]
    opposite situation
    occurs too, but
    still discriminatory:
    buyers treated
    unequally.
    this part of state doesn’t exist
    in extension. No intra-dealings
    for tagged buyers.
    

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21. that’s all the AEY-Poza
    scenarios.
    Now for two new ones!
    

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22. Sellers’ Market
    NON-DISCRIMINATORY
    

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23. Sellers’ Market
    Benefit Graph Legend
    Seller --------------------------------- Blue-Dashed
    Tagged-Buyer ............................. Red-Dotted
    Untagged-Buyer .-.-.-.-.-. Green-Dash-Dotted
    Overall ______________________ Solid Black
    

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24. NON-DISCRIMINATORY
    Buyers’ Market
    

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25. Buyers’ Market
    Benefit Graph Legend
    Seller --------------------------------- Blue-Dashed
    Tagged-Buyer ............................. Red-Dotted
    Untagged-Buyer .-.-.-.-.-. Green-Dash-Dotted
    Overall ______________________ Solid Black
    

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26. stability analysis: new state criterion.
    average frequency of most frequent demand >= 1 - ε
    ~95% of simulations reach one of the equilibrium states.
    

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27. tag-blind extension.
    eliminating discriminatory scenarios
    preserving non-discriminatory scenarios
    tag-blind sellers.
    only one memory set
    

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28. tag-blind experiments.
    30 “means” x 100 runs x 400 iterations
    measuring occurrence of states
    

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29. number of tag-blind sellers
    number of tag-blind sellers
    occurrences of state
    non-occurrences of state
    likely linear, but missing runs
    at every tag-blind value.
    32 18 42 29 30 26 14 51 20 33 35
    discriminatory scenarios gradually
    disappear as tag-blindness increases
    

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30. no efficiency tradeoff!? (i think).
    overall benefit for non-discriminatory states holds with increased blindness,
    but discriminatory scenarios are worse overall when they do occur.
    (average overall benefit for last 100 iterations)
    

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31. next steps
    

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32. key assumptions.
    equal proportion of tag/untagged buyers
    sellers are all untagged
    agents all have equal bargaining ability/style
    agents all have zero costs
    zero competition
    

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33. next.
    introduce blindness to transition to other state
    remove buyer/seller distinction - generalize tag-blind
    is there a competitive advantage to discrimination?
    other salient bargaining features (h, multi-step offers)
    

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34. 
    

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