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Artificial Payment Card Market: A Multi-Agent Approach Biliana Alexandrova-Kabadjova, CCFEA, EssexCCFEA Edward Tsang, CCFEA, EssexCCFEA Andreas Krause, Management School, Bath Slide 2 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Agent-based Payment Card Market ModelPayment Card Market Costumer Merchant Interactions at the Point Of Sale Payment Card provider Costumers fees and benefits Merchants fees and benefits Government: public interest drives regulations Connected (topology)topology Possible Objectives: Maximize profit Maximize market share Learning optimal strategies Consistent patterns observed with static agents Decisions, decisions Slide 3 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Payment Methods Set of payment methods Set of payment methods Cash is the benchmark payment method Cash is the benchmark payment method All other payment methods are called All other payment methods are called Card Payments For each Card Payment consumers and merchants face different benefits and costs For each Card Payment consumers and merchants face different benefits and costs Slide 4 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 The Merchants Set of merchants Set of merchants Each merchant offers the same good Each merchant offers the same good The price of the good is The price of the good is Fixed marginal cost Fixed marginal cost Each merchant has a fixed location Each merchant has a fixed location Slide 5 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 The Consumers Set of consumers Set of consumers Each consumer has a fixed income Each consumer has a fixed income The common utility is Consumer's preferences Each consumer has a fixed position Each consumer has a fixed position Slide 6 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Network structure Consumer-Merchant Merchant 2 Merchant Merchant 1... Consumer Each Consumer Each Consumer has access to where and could be Small World or local connections Slide 7 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Card Payments benefits and costs Benefits The consumer for each unit of good obtains a benefit of The merchant for each unit of good sold obtains a benefit Costs The issuer charges the consumer for each unit of good a common fee of and for every period a membership fee of The acquirer charges the merchant for each unit of good sold a common fee and for every period a membership fee of Slide 8 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Decisions Modelled Consumers Which merchant to chose? Which card to use? Which card to subscribe to? Merchants Which card to accept? Card Payment Provider Consumers benefits and costs Merchants benefits and cost Publicity cost Slide 9 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Consistent Observations: Static Agents Runs converged after 1,000 iterations Case 1: customers only record all cards accepted Only two cards survived, one dominating Case 2: customers take note of common cards with each merchant visited More cards survived Case 3: customers know cards accepted by merchants and merchants know cards owned by visiting customers All cards survived Indifferent whether cards have varying benefit Slide 10 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Customer Benefits Merchant Fixed Fee Customers decision to use the card Customers decision to hold a card Merchants decision to hold a card # of Merchants accepting the card Banks Profits Publicity Cost Customer Fixed Fee Merchant Benefits Banks Market Share # of Customers using the card # of Merchants using the card # of Customers having the card Decisions dependency (from the banks point of view) Slide 11 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Learning optimal strategies Each card makes the following decisions: Each card makes the following decisions Publicity cost, fixed/variable fees to consumers/merchants PBIL used to evolve strategies PBIL Converged after 3,000 runs; observations being analysed Card 1 decisions Card 2 decisions Card n decisions Probabilistic Model on the decisions Market simulation: Interaction between consumers and merchants Slide 12 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Population-based Incremental Learning (PBIL) Statistical approach Related to ant-colonies, GA Model M: x = v1 (0.5) x = v2 (0.5) y = v3 (0.5) y = v4 (0.5) Sample from M solution X, eg Evaluation X Modify the probabilities 0.6 0.4 0.6 0.4 Slide 13 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Conclusion, Credit Card Payment Analysis Market behavior is complex and hard to analyze APCM is useful for studying the card market It is a good model of consumers and merchants behavior Could be used to predict demands GPBIL could be used for searching strategies under certain requirements Observation: rich results e.g. Market info determines outcomes More information less dominance Slide 14 Why Agent Modelling? The accumulation of knowledge Slide 15 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Why Modelling? Scientific Approach Modelling allows scientific studies. Human expert opinions are valuable, But best supported by scientific evidences Multiple Expertise models can be built by multiple experts at the same time The resulting model will have the expertise that no single expertise can have. Models are investments Models will never leave the institute as experts do. Investments can be accumulated. Slide 16 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Why Agent Modelling Agent modelling allows Heterogeneity Geographical distribution Micro-behaviour to be modelled Representative models dont allow these Micro-behaviour makes the market Slide 17 Artificial Payment Card Market: A Multi-Agent Approach Technical Details Slide 18 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Motivation Growing importance of the payment cards in the context of modern economies Public interest in the pricing and rules governing this market The use of Multi-agent based system as a tool for analysis of economic problems The characteristics of the payment cards market, that allows us to model it as Multi-agent system Slide 19 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Payment Card Market Characteristics of the Payment Cards Electronic Payment Method Network Product in a two-sided market Participants Merchant Offers good Uses payment methods in order to accept cards Costumer Demands good Uses electronic cards Jointly produced service Card Issuer Merchant's Acquirer Slide 20 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Interactions at the POS Merchants Merchants Set of merchants M with |M|= N M Set of merchants M with |M|= N M Each merchant m M Each merchant m M offers a homogenous good at common price offers a homogenous good at common price faces marginal cost lower then the price faces marginal cost lower then the price Consumers Consumers Set of consumers C with | C |= Set of consumers C with | C |= N C Each consumer c C in one period Each consumer c C in one period visits one merchant, visits one merchant, buys a single unit of the good buys a single unit of the good gains utilities bigger then the price gains utilities bigger then the price Slide 21 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Consumers and Merchants Spatial Distribution Consumers and merchants have a fixed location on N x N lattice, where N C N M and N 2 = N M + N C Let M c is the set of merchants the consumers consider to go to The distance between c C and m M imposes a travel cost on the consumer it is denoted d c,m it is measure in Manhattan distance It is normalized to unity Network Connections Local connections - M c represents c nearest merchants Small world - Given the probability w =0.01, replace m M c with m M Random connections - Given the probability w =0.80, replace m M c with m M We assume that c faces the same cost d c,m to visit the new m Slide 22 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Payment Card Providers Set of payment networks P Set of payment networks P The benchmark payment method is the cash The benchmark payment method is the cash All other payment methods are called Card Payments All other payment methods are called Card Payments For each Card Payment consumers and merchants face different benefits and fees For each Card Payment consumers and merchants face different benefits and fees Benefits The consumer for each unit of good obtains benefit b p D b p The merchant for each unit of good sold obtains benefit p D p Fees Issuer charges consumer for every period a fixed fee F p D F p Acquirer charges merchant for each period a fixed fee of p D p In order to attract more consumers and merchants, expense in publicity In order to attract more consumers and merchants, expense in publicity It is denoted l p and it has a direct impact over the consumer and merchant decision to hold a card, l p D l p Slide 23 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Consumers Decisions: Which merchant and card to use? Which merchant to choose? Where P c,m is the common card the merchant and consumer have Which card to use? The card p P c,m with the highest b p Slide 24 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Consumers Decisions: Which card to hold? Which card to hold? Which card to subscribe to? Which card to drop? Here Slide 25 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Merchants Decisions Which card to hold? Which card to subscribe to? Which card to drop? Here Slide 26 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Payment Card Providers Decisions Solution space Solution space S = D b p x D p x D F p x D p x D l p S = D b p x D p x D F p x D p x D l p Rewritten as S = D 1 x D 2 x... x D 5 S = D 1 x D 2 x... x D 5 Joint probability distribution function Joint probability distribution function F S = F 1 x F 2 x... x F 5 F S = F 1 x F 2 x... x F 5 Objective Function Objective Function Maximum profit Maximum profit Above average market share Above average market share Slide 27 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Artificial Payment Card Market Costumer Merchant Interactions at the Point Of Sale Payment Card provider s S Profit and Market Share Slide 28 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Results 9 Cards Average Profit in the first 100 runs Average Profit in the last 100 runs Local Network4.092.329,505.179.486,23 Small World Network4.110.964,275.088.416,74 Random Network4.084.039,595.271.941,41 Slide 29 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Slide 30 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Slide 31 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Slide 32 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Local Transactions Number of interactions (set to 2,000 to 3,000) Slide 33 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Small World Transactions Number of interactions (set to 2,000 to 3,000) Slide 34 All rights reserved, Biliana Alexandrova, Edward Tsang & Andreas Krause 02 June 2014 Random Transactions Number of interactions (set to 2,000 to 3,000)