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
2. How many non-discriminatory sellers does it take to eliminate statistical discrimination from a bargain-based market?
3. two motivations 1. the (anonymous?) internet + new car bargaining 2. prisoner’s dilemma “shoehorn” in legal scholarship
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)
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)
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
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
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
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”
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”
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?
12. Current Replication + Extension Axtell-Epstein-Young Framework + Baseline Parameters + Poza Memory Decision Rule Python 3.3 + Buyers & Sellers + Tag-blind Sellers + =
13. N/2 Buyers, N/2 Sellers N/4 tag, N/4 no tag no tag
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
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
16. intra-equilibrium + inter-low high bids in memory, low benefit from perspective of tagged buyer, worse off than untagged buyer.
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)
18. intra-equilibrium + inter-high low bids in memory, high benefit from perspective of tagged buyer opposite situation, but still discriminatory: buyers treated unequally.
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.
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.
21. that’s all the AEY-Poza scenarios. Now for two new ones!
22. Sellers’ Market NON-DISCRIMINATORY
23. Sellers’ Market Benefit Graph Legend Seller --------------------------------- Blue-Dashed Tagged-Buyer ............................. Red-Dotted Untagged-Buyer .-.-.-.-.-. Green-Dash-Dotted Overall ______________________ Solid Black
24. NON-DISCRIMINATORY Buyers’ Market
25. Buyers’ Market Benefit Graph Legend Seller --------------------------------- Blue-Dashed Tagged-Buyer ............................. Red-Dotted Untagged-Buyer .-.-.-.-.-. Green-Dash-Dotted Overall ______________________ Solid Black
26. stability analysis: new state criterion. average frequency of most frequent demand >= 1 - ε ~95% of simulations reach one of the equilibrium states.
27. tag-blind extension. eliminating discriminatory scenarios preserving non-discriminatory scenarios tag-blind sellers. only one memory set
28. tag-blind experiments. 30 “means” x 100 runs x 400 iterations measuring occurrence of states
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
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)
31. next steps
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
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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