Shopb ots and Priceb ots: Ho w will b ots aect m a rk - PDF document

Shopb ots and Priceb ots: Ho w will b ots a�ect m a rk ets? Am y Greenw ald and Je� Kepha rt IBM Institute fo r Advanced Com m erce IBM Thom as J. W atson Resea rch Center Ha wtho rne, New Y o rk August 5, 1999

Econom ics of Info rm a tion Geo rge Stigler [1961] p rice disp ersion is attributed to costly sea rch � p ro cedures Shopb ots T o da y (Y esterda y!) shopb ots sp ecialize in collecting and distributing � p rice info rm a tion at lo w cost Priceb ots T om o rro w (T o da y!) autom ated agents that set p rices in attem pt to � m axim ize p ro�ts fo r sellers, just as shopb ots seek to m inim ize costs fo r buy ers 1

Overview Sellers Gam e-Theo retic Equilib rium � Strategic Priceb ot Dynam ics � Buy ers Gam e-Theo retic Equilib rium � Rational Buy er Dynam ics � 2

Gam e-Theo retic Priceb ot Strategy Mixed strategy Nash equilib rium Rational p riceb ots cho ose p rices at random acco rding to p robabilit y distribution. 5 p riceb ots, = 0 : 2, + = 0 : 8. w w w 1 2 5 20 20 w 2 =0.8 15 15 f(p) 10 10 w 2 =0.0 5 5 w 2 =0.4 0 0 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1.0 1.0 p 20 p riceb ots, = 0 : 2, + = 0 : 8. w w w 1 2 20 20 w 2 =0.8 15 f(p) 10 w 2 =0.0 w 2 =0.4 5 0 0.5 0.6 0.7 0.8 0.9 1.0 p Do adaptive (not necessa rily rational) p riceb ots lea rn gam e- theo retic equilib rium of stage gam e over rep eated pla ys? 3

Info rm ed, Adaptive Priceb ot Strategy My opically-optim al (MY) Strategy Rational b est-resp onse to others' current p rices, given buy er dem a nd function . . . 5 MY Priceb ots 1.1 0.30 5 MY Average MY Profit = 0.0524 w 1 =0.25, w 2 =0.50, w 5 =0.25 Valuation 1.0 0.25 0.9 0.20 0.8 Price Profit 0.15 0.7 0.10 0.6 0.05 0.5 Production Cost 0.4 0.00 0 1 2 3 4 5 0 1 2 3 4 5 × 10 6 × 10 6 Time Time MY p ro�ts (0.0524) m o r e than t wice GT p ro�ts (0.025); � but instabilities in the fo rm of cyclical p rice w a rs a rise; � and MY p riceb ot requires kno wledge of buy er dem and � and other sellers' p rices, which m a y b e costly to obtain. 4

Naive, Adaptive Priceb ot Strategy Derivative-follo wing (DF) Strategy Adjust p rice in sam e direction as long as p ro�t increases; otherwise reverse the direction of p rice adjustm ent. . . . 5 DF Priceb ots 1.1 0.30 5 DF Average DF Profit = 0.0733 w 1 =0.25, w 2 =0.50, w 5 =0.25 Valuation 1.0 0.25 0.9 0.20 0.8 Profit Price 0.15 0.7 0.10 0.6 0.05 0.5 Production Cost 0.4 0.00 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 × 10 6 × 10 6 Time Time T acit collusion results: i.e. , an e�ective ca rtel despite � no actual com m unication! Average p ro�t is nea rly 3 tim es that of GT p riceb ots. � P erfect ca rtel w ould achieve p ro�t of 0.1 p er p riceb ot. Requires no kno wledge of sellers' p rices o r buy er dem and; � p rice-setting m echanism based on histo rical observations. 5

Info rm ed vs. Naive Priceb ots Intro duce 1 MY p riceb ot into group of 4 DF p riceb ots . . . 1.1 0.30 1 MY vs. 4 DF Average MY Profit = 0.1209 w 1 =0.25, w 2 =0.50, w 5 =0.25 Valuation 1.0 Average DF Profit = 0.0523 0.25 0.9 0.20 0.8 Price Profit 0.15 0.7 0.10 0.6 0.05 0.5 Production Cost 0.4 0.00 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 × 10 6 × 10 6 Time Time . . . and it will exploit them m ercilessly , stealing their p ro�ts, ea rning m o re than t wice (0.121) what they do (0.052)! 6

Q-Lea rning Priceb ots W atkins, 1989 Reinfo rcement Lea rning Schem e . . . 2 MY Priceb ots . . . 2 Q Priceb ots 0.6 0.6 1 MY vs. 1 MY 1 Q vs. 1 Q w 1 =0.25, w S =0.75 Mean Valuation w 1 =0.25, w S =0.75 Mean Valuation 0.5 0.5 0.4 0.4 Price Price 0.3 0.3 0.2 0.2 0.1 0.1 Production Cost Production Cost 0.0 0.0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 × 10 6 × 10 6 Time Time Q p riceb ots detect and abandon p rice w a rs ea rly on � Q p ro�ts (0.125, 0.117) exceed MY p ro�ts (0.089, 0.089) � 7

No External Regret Priceb ots F reund and Schapire, 1995 Probabilistic Up dating Scheme . . . 2 NER Priceb ots No External Regret Learning No External Regret Responsive Learning 1.0 1.0 0.9 0.9 0.8 0.8 Price Price 0.7 0.7 0.6 0.6 0.5 0.5 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 × 10 4 × 10 4 Time Time 2 NER Sellers, w S = 0.75 2 NER Sellers, w S = 0.75 NER p riceb ots cycle through p rices exp onentially � resp onsive NER p riceb ots engage in lim ited p rice w a rs � 8

No Internal Regret Priceb ots F oster and V ohra, 1997 Converge to Co rrelated Equilib rium . . . 2 NIR Priceb ots No Internal Regret Learning Nash Equilibrium 1.0 1.0 0.8 0.8 w B = 0.9 w B = 0.9 w B = 0.75 w B = 0.75 0.6 0.6 Probability Probability w B = 0.5 w B = 0.5 0.4 0.4 w B = 0.25 w B = 0.25 w B = 0.1 w B = 0.1 0.2 0.2 0.0 0.0 0.5 0.6 0.7 0.8 0.9 1.0 0.5 0.6 0.7 0.8 0.9 1.0 Price Price . . . lea rn Nash equilib rium! 9

Rational Buy er Strategy T otal Buy er Exp enditure = Exp ected Price + Sea rch Costs Buy er Price Distributions 20 20 sellers (w 1 ,w 2 ,w 20 )=(0.2,0.4,0.4) Search–20 15 Price Distributions 10 Search–2 5 Search–1 0 0.5 0.6 0.7 0.8 0.9 1.0 p Average Buy er Prices 1.0 w 1 =0.2 w 2 +w 20 =0.8 Search–1 0.9 Average Price 2 0.8 3 4 0.7 5 0.6 10 15 20 0.5 0.0 0.2 0.4 0.6 0.8 1.0 w 20 V alue of Info rm ation = Willingness to P a y = Price Di�erential 10

Gam e-Theo retic Equilib rium One unstable and t w o stable gam e- theo retic equilib ria. Ma rginal Cost-Bene�t Analysis 0.06 0.05 v = Benefit Price Differential 0.04 0.03 δ = Cost 0.02 0.01 0.00 0.0 0.2 0.4 0.6 0.8 1.0 w 2 Burdett and Judd, 1983 Linea r sea rch costs yield + = 1. w w 1 2 11

Adaptive Buy er Strategy A t each time t 1. Sm all fraction of buy ers switch from their p resent sea rch strategy to current optim um . 2. Sellers compute new gam e-theo r etic p ricing strategy . Linea r Sea rch Costs 1.0 2 0.8 0.6 3 5 w i 0.4 c i = 0.05 + 0.02 (i – 1) 0.2 1 4 0.0 0 1 2 3 4 5 6 × 10 3 Time Initial state: ( w ) = (0 : 2000 ; 0 : 4000 ; 0 : 4000). ; w ; w 1 2 5 Final state: ( w ) = (0 : 0141 ; 0 : 9859 ; 0 : 0000). ; w ; w 1 2 5 12

Adaptive Buy er Strategy Shopb ots drastically lo w er sea rch costs Assume costs a re non- linea r in the num b er of sea rches. Nonlinea r Sea rch Costs 1.0 5 c i = 0.05 + 0.02 (i – 1) 0.25 0.8 0.6 2 5 w i 4 0.4 3 2 0.2 1 1 0.0 0 1 2 3 4 5 6 × 10 3 Time Initial state: = (0 : 200 ; 0 : 300 ; 0 : 000 ; 0 : 000 ; 0 : 500). Final state: = (0 : 020 ; 0 : 550 ; 0 : 430 ; 0 : 000 ; 0 : 000). Nonlinea r sea rch costs can yield m o re com plex, even chaotic, m ixtures of strategies. 13

Fixed + Adaptive Buy ers Supp ose sm all fraction of buy ers �xate on sea rch-1, rega rdless of what strategy is optim al, while other buy ers adapt. 4% Fixed Sea rch-1 Buy ers 1.0 4 0.8 5 0.6 w i 0.4 c i = 0.05 + 0.02 (i – 1) 0.2 min = 0.04 w 1 2 1 0.0 0 1 2 3 4 5 6 × 10 3 Time Initial state: = (0 : 040 ; 0 : 200 ; 0 : 000 ; 0 : 000 ; 0 : 760). Final state: = (0 : 040 ; 0 : 000 ; 0 : 000 ; 0 : 960 ; 0 : 000). Mixture of �xed and adaptive buy er b ehavio r can lead to strategies other than just sea rch-2 co-existing with sea rch-1. 14

F uture W o rk Study dynam ics of adaptive buy ers and sellers � Investigate strategic interpla y of shopb ot p ricing � Dynam ic p ricing of p rice and p ro duct info rm ation in full- � �edged economy of soft w a re agents, consisting of buy ers, sellers, and econom ically m otivated shopb ots Shopb ot Econom ics fo rm s pa rt of the Info rm ation Econom ies p roject at IBM Resea rch Institute fo r Advanced Com m erce. The p roject goal is to: accurately describ e and p redict collective interactions of billions of economically m otivated soft w a re agents, and use insights so gained to design agent strategies, p roto cols, and infrastructures. Project description and resea rch pap ers available at: www.research .ib m.c om/i nfo eco n 15