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
. . . 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)
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)
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
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
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
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”
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”
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?
............................. 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)
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.
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