Dynamic Service Pricing for Brokers in a Multi-Agent Economy Prithviraj Dasgupta Dept. of Electrical and Computer Engineering University of California Santa Barbara, CA 93106
[email protected]
Abstract We study the price dynamics in a multi-agent economy consisting of buyers and competing sellers, where each seller has limited information about its competitors’ prices. In this economy, buyers use shopbots while the sellers employ automated pricing agents or pricebots. Derivative fol¨ strategy for lowing (DF) provides a simple, albeit naive, dynamic pricing in such a scenario. In this work, we refine the DF algorithm and introduce a model optimizer (MO) algorithm that re-estimates the price-profit relationship for a seller at every interval more efficiently. Simulations using the MO pricebots indicate that it outperforms DF even though it has no additional information about the market.
1. Introduction Shopbots, or comparison shopping agents that reduce the search costs for buyers are becoming a reckoning force in e-commerce [1]. Competition created by increasingly pervasive and powerful shopbots are inducing sellers to be extremely responsive in their pricing strategies. To keep up with the constant demands for adjustments of prices, sellers will be forced to employ pricebots, or autonomous software agents that set prices on their behalf. Before employing bots in the real world, we believe that there is the need to understand and anticipate the collective behavior of such economically motivated software agents. This work focuses on a simple model of an information economy involving groups of pricebots employing dynamic posted pricing. Our particular emphasis is on the price dynamics engendered by small groups of myopic and selfish software agents that try to maximize their payoff from the market. Recent work on automated dynamic pricing assumes that a seller has complete information about the market, such as the distribution of buyer preferences or its competitors’ prices [2]. In contrast, we investigate price-setting algo-
Rajarshi Das Institute for Advanced Commerce IBM T. J. Watson Research Center Yorktown Heights, NY 10598
[email protected]
rithms that enable sellers to improve their profit without explicit knowledge of their competitors’ pricing decisions.
2. Model We study the price dynamics in a simple model of the shopbot economy proposed by Greenwald and Kephart [2]. In this model, the market consists of S sellers who compete to provide B buyers (B S ) with a single indivisible commodity, such as a specific book. Each buyer has a valuation pcap corresponding to the maximum price it is willing to pay for the item. Buyers are of two types depending on their search strategy for a seller: (i) a bargain hunting buyer employs a shopbot to select the seller that offers the lowest price and purchases the good if the price offered by the seller is below pcap , and (ii) random selecting buyer selects a seller at random and purchases the good if the price offered by the seller is below pcap . A seller’s goal in this model is to maximize its immediate profit by setting a price pt for a single unit of the good which has a production cost of pco . In this economy, the sellers have incentive to lower their price as the lowest price seller obtains the maximum market share. If a seller is not offering the lowest price, then its best strategy is to offer the highest price the market will bear. [2] views the price setting problem as a one-shot game and shows that pricebots using a myoptimal or a no-regret pricing strategies give rise to cyclical price-wars. These strategies, which are informationally intensive and require the details of the buyer demand function, competitors prices and payoffs, can outperform and take advantage of informationally limited strategies such as a DF. Here, we introduce a model optimizer algorithm that uses the same amount of information as a DF, but exhibits superior performance.
3. Dynamic Pricing Algorithms Derivative Follower (DF) simply experiments with fixed-size incremental increases (decreases) in price, and as
1.8
1.2
1.6
1 1.4
DF
1.2
0.8
Price
ADF
Price
ADF
0.6
FP
1 0.8 0.6
0.4
FP
0.4
MOE
0.2 0.2
0 0
0
0.5
1
1.5
2
2.5
3
0
0.5
1
1.5
2
2.5
4
3
Number of quotes requests x 10
4
Number of quotes requests x 10
Figure 2. Price dynamics with competing FP, ADF, and MOE pricebots.
Figure 1. Competing FP, DF, and ADF pricebots.
1.2
long as the observed level of profitability increases it continues to move its price in the same direction. If the profit level decreases, it changes the direction of the price movement. Adaptive Step-size Derivative Follower (ADF) dynamically reduces or expands the step-size of price increments. This modification allows the prices to settle down to their asymptotic values or to quickly explore new price ranges. Model Optimizer (MO) looks for a relationship between price and profit in each time step, and builds an internal model by nonlinear regression of historical data with time-discounted weighting. In the subsequent time step, the pricebot sets a price which maximizes profit in its internal model. We also introduce a related strategy MOE, a model optimizer with exploration, which attempts to achieve a balance between exploration and exploitation by making occasional random jumps in its price settings. For comparison purposes we also employ a fixed price seller FP, charging a price $0:5, in our simulations.
MOE 1
MOE 2
1
MOE 3 Price
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
Numer of quote requests x 10
4
2.5
3
Figure 3. Price wars among MOE pricebots.
landscape and obtain higher profits by setting lower prices. Figure 3 shows the price-dynamics of a group of competing MOE pricebots. These informationally-limited pricebots exhibit cyclical price-wars similar to those observed among pricebots in [2] which were endowed with detailed information about the current market conditions. Our results underscore the role machine learning and optimization can play in designing economically motivated software agents in information-limited environments.
4. Results In our simulations, each buyer has pcap = $1:0, each seller has pco = $0:1, and 75% of the buyers are bargainhunting buyers while the rest are random-selecting buyers. Results from simulation show that while ADF can outperform DF and undercut FP only to the extent necessary to maximize its profit, it can occasionally overshoot and lose track of the FP seller (Figure 1). In Figure 2, we show that a MOE does not suffer from this problem, while it can still find the price to just undercut the lowest price seller. Even though MOE enters the market with a price higher than the prices set by FP or ADF, it is able to explore the price-profit
References [1] D. Clark. Shopbots become agents for business change. IEEE Computer, 33(2), 2000. [2] A. Greenwald and J. Kephart. Shopbots amd pricebots. In Proceedings of IJCAI, Stockholm, 1999.
2
