1. Networks in Economics and Finance Michele Tumminello DSEAS – University of Palermo 05/20/2014 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 International School on Network Science May 19-23, 2014

2. Outline „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Networks and allocation of resources: the concept of clearing prices. Networks to describe a simple market: the theory of competitive equilibrium Networks to describe preferential trading patterns at London Stock Exchange

3. Allocation of resources: learning outcomes „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 To understand the concept of perfect matching in bipartite networks To understand how the price of goods serves to decentralize the market To understand the concept of market-clearing prices

4. Bipartite Network „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Type 1 Type 2 There are two types of nodes and nodes of the same type are NOT connected in a bipartite network There are two types of nodes and nodes of the same type are NOT connected in a bipartite network Easley and Kleinberg, Networks Crowds and Markets (2010)

5. The problem of finding a perfect matching „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Type 1Type 2 Problem: Assigning each student a room that he/she would be happy to accept Allocation of resources Perfect Matching: It is an assignment of nodes on the left to nodes on the right, in such a way that (i)each node is connected by an edge to the node it is assigned to, (ii) no two nodes on the left are assigned to the same node on the right.

6. The problem of finding a perfect matching „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Type 1Type 2 Problem: Assigning each student a room that he/she would be happy to accept Allocation of resources Perfect Matching: It is an assignment of nodes on the left to nodes on the right, in such a way that (i)each node is connected by an edge to the node it is assigned to, (ii) no two nodes on the left are assigned to the same node on the right.

7. Do all bipartite networks have a perfect matching? „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 NO

8. Constricted Set (of nodes) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 S N(S) S is any set of nodes of a given type (students in this case) N(S) is the set of all the neighbors of nodes belonging to S (rooms in this case) We say that S is a constricted set if S contains (strictly) more nodes (3 in this case) than N(S) does (2 in this case) Easley and Kleinberg, NCM (2010)

9. Constricted Set and Perfect Matching „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 S N(S) If a bipartite network has a constricted set then it does NOT admit perfect matching Easley and Kleinberg, NCM (2010)

10. Matching theorem (König 1931) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 If a bipartite network (with equal numbers of nodes on the left and right) has no perfect matching, then it must contain a constricted set.

11. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Is the search of perfect matching an optimization process? What is the utility function?

12. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Suppose that agents not only give a preference, but also indicate a value for each preference, quantifying their degree of happiness. The result is a weighted bipartite network Type 1Type 2 Allocation of resources 7 4 5 8 6 8 9 7 15 5 What is the “optimal” way to allocate resources in this case? It is assumed that any missing link corresponds to a link with weight 0 Optimal Assignment: The matching that maximizes the sum of weights.

13. Prices and Market Clearing „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Is a central authority really necessary? NO

14. Prices and Market Clearing „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 a a b b c c x x y y z z Houses Sellers Buyers Valuations (v) a=12, b=4, c=2 a=8, b=7, c=6 a=7, b=5, c=2 Easley and Kleinberg, NCM (2010)

15. Prices and Market Clearing „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 a a b b c c x x y y z z Houses Sellers Buyers Valuations (v) a=12, b=4, c=2 a=8, b=7, c=6 a=7, b=5, c=2 Easley and Kleinberg, NCM (2010) papa pbpb pcpc Prices

16. Payoff „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 If a buyer buys a house at price p and her evaluation of the house was v then her payoff is Payoff = v - p What happens if p>v?

17. Prices and Market Clearing „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 a a b b c c x x y y z z Houses Sellers Buyers Valuations (v) a=12, b=4, c=2 a=8, b=7, c=6 a=7, b=5, c=2 Easley and Kleinberg, NCM (2010) p a =2 p b =1 p c =0 Prices Suppose that each buyer chooses the house(s) that maximizes her payoff v-p These prices don’t help to find perfect matching! Is house “a” too cheap?

18. Prices and Market Clearing „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 a a b b c c x x y y z z Houses Sellers Buyers Valuations (v) a=12, b=4, c=2 a=8, b=7, c=6 a=7, b=5, c=2 Easley and Kleinberg, NCM (2010) p a =5 p b =2 p c =0 Prices Suppose that each buyer chooses the house(s) that maximizes her payoff v-p The prices {5,2,0} are Market-Clearing Prices

19. Is the set of market-clearing prices unique? „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 NO

20. Prices and Market Clearing „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 a a b b c c x x y y z z Houses Sellers Buyers Valuations (v) a=12, b=4, c=2 a=8, b=7, c=6 a=7, b=5, c=2 Easley and Kleinberg, NCM (2010) p a =3 p b =1 p c =0 Prices Suppose that each buyer chooses the houses that maximize her payoff v-p The prices {3,1,0} are Market-Clearing Prices… Sellers can choose the buyer

21. Prices and Market Clearing „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 a a b b c c x x y y z z Houses Sellers Buyers Valuations (v) a=12, b=4, c=2 a=8, b=7, c=6 a=7, b=5, c=2 Easley and Kleinberg, NCM (2010) p a =3 p b =1 p c =0 Prices Suppose that each buyer chooses the houses that maximize her payoff v-p The prices {3,1,0} are Market-Clearing Prices… Sellers can choose the buyer

22. Theorem: Existence of Market-Clearing Prices „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 For any set of buyer valuations, there exists a set of market-clearing prices.

23. Constructing Market Clearing Prices „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 1.Set all the prices equal to 0 2.Construct the preferred-seller graph and check whether there is a perfect matching 3.If there is a perfect matching then we are done 4.If not, find a constricted set of buyers, S, and their neighbors N(S) 5.Each seller in N(S) synchronously raises her price by 1 unit. If necessary we reduce the prices of all the houses of the same amount so that the smallest price is 0 6.Go to step 2

24. Concepts to take home „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Nodes of bipartite networks are of two types, and each edge connects a node of one type to a node of the other type Perfect matching in a bipartite network is used to allocate resources Prices can replace the “central authority” in the process of finding the optimal allocation of resources (market- clearing prices) Single-item auction can be seen as a particular case of matching market

25. Is there something important that we are missing? „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 What is the “cost” of sellers?

26. The Apple Market „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 “Experiments with Economics Principles” T. Bergstrom and J.H. Miller McGraw-Hill Companies, Inc. (1996)

27. The Apple Market „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Crowd

28. The Apple Market „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Crowd of buyers and sellers

29. Terminology „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Transaction: it is a deal between a buyer and a seller, consummated in the form of a filled-in sales contract which is delivered to the market manager. Round: a round of trading begins when the market manager declares trades to be open and ends when transactions cease.

30. Information Sheets for Participants „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Each participant receives an information sheet

31. Example of information sheet (seller) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 7

32. Example of information sheet (buyer) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 8

33. Sales Contract „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Each transaction between a buyer and a seller must be recorded on a sales contract

34. Trading Rules „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 A participant cannot buy or sell more than 1 bushel of apples in a round. A participant does not have to make a trade. It is better to make no trade than to trade at a loss. Each pair of traders should turn in only one sales contract for their transaction. A participant should return to her seat after she has traded and turned in a sales contract.

35. Suggestions for traders „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 You don’t have to deal with the first person you encounter. Different people have different Buyer’s Value and Seller’s cost. So, be ready to shop around! You want “Buy low” and “Sell high”, in order to make greater profits.

36. Class experiment: settings „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Session 1. 15 participants: S L = 4 low-cost suppliers (SC=10$), S H = 2 high-cost suppliers (SC=30$), B L = 6 low-value demanders (BV=20$), B H = 3 high-value demanders (BV=40$). value=20 value=40 cost=10 cost=30 B L =6 B H =3 S L =4 S H =2 The weight of links, that is the number of trades between two groups of participants, depends on the outcome of the experiment. The weight of links, that is the number of trades between two groups of participants, depends on the outcome of the experiment.

37. Round 1 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 value=20 value=40 cost=10 cost=30 B L =6 B H =3 S L =4 S H =2 1 2 2 Total number of trades = (sum of the weights of links) = 5

38. Total payoff „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 The total payoff is the sum of the individual payoffs of buyers and sellers: The total payoff is the sum of the value of all buyers minus the cost of all the sellers that have traded in the round. The total payoff does NOT depend on the transaction prices

39. Round 1 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 value=20 value=40 cost=10 cost=30 B L =6 B H =3 S L =4 S H =2 1 2 2 Total payoff= (20-10) + (20-10) + (40-10) + (40-10) + (40-30) = 90 Average price = (20 + 15 + 20 + 20 + 31)/5 = 21.2

40. Summary of results „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Round 1: Trades = 5 Total payoff = 90 Average price = 21.2 Round 2: Trades = 5 Total payoff = 90 Average price = 25.0 Round 3: Trades = 6 Total payoff = 80 Average price = 23.5

41. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Competitive Equilibrium

42. Supply and demand curves Price smaller than 10 $ 4 low-cost suppliers (SC=10$) 2 high-cost suppliers (SC=30$) 6 low-value demanders (BV=20$) 3 high-value demanders (BV=40$) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

43. Supply and demand curves Price = 10 $ 4 low-cost suppliers (SC=10$) 2 high-cost suppliers (SC=30$) 6 low-value demanders (BV=20$) 3 high-value demanders (BV=40$) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

44. Supply and demand curves 10 $ < Price < 20 $ 4 low-cost suppliers (SC=10$) 2 high-cost suppliers (SC=30$) 6 low-value demanders (BV=20$) 3 high-value demanders (BV=40$) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

45. Supply and demand curves Price = 20 $ 4 low-cost suppliers (SC=10$) 2 high-cost suppliers (SC=30$) 6 low-value demanders (BV=20$) 3 high-value demanders (BV=40$) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

46. Supply and demand curves 20 $ < Price < 30 $ 4 low-cost suppliers (SC=10$) 2 high-cost suppliers (SC=30$) 6 low-value demanders (BV=20$) 3 high-value demanders (BV=40$) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

47. Supply and demand curves Price = 30 $ 4 low-cost suppliers (SC=10$) 2 high-cost suppliers (SC=30$) 6 low-value demanders (BV=20$) 3 high-value demanders (BV=40$) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

48. Supply and demand curves 30 $ < Price < 40 $ 4 low-cost suppliers (SC=10$) 2 high-cost suppliers (SC=30$) 6 low-value demanders (BV=20$) 3 high-value demanders (BV=40$) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

49. Competitive equilibrium „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Trades = 4 Total payoff = 100 Price = 20 value=20 value=40 cost=10 cost=30 B L =6 B H =3 S L =4 S H =2 0 1 3 Competitive Equilibrium maximizes the total payoff and minimizes the number of trades

50. Competitive Equilibrium VS Experiments „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Trades = 4 Total payoff = 100 Price = 20 CE: Round 1: Trades = 5 Total payoff = 90 Average price = 21.2 Round 2: Trades = 5 Total payoff = 90 Average price = 25.0 Trades = 6 Total payoff = 80 Average price = 23.5

51. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Deviations from competitive equilibrium are likely to occur in the experiments, in terms of both trading configurations and transaction prices Bergstrom and Kwok, J. Econ. Educ. (2005);

52. Synchronous Bazaar (SB) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Traders randomly meet (SYNCHRONOUSLY) and a transaction occurs when mutual gains are possible. JH Miller and MT, submitted (2013)

53. Synchronous Bazaar (SB) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 vLvL vHvH cLcL cHcH BLBL BHBH SLSL SHSH n LH n HH n LL

54. Aynchronous Bazaar (AB) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Traders randomly meet (ASYNCHRONOUSLY) and a transaction may occur when mutual gains are possible. JH Miller and MT, submitted (2013)

55. Asynchronous Bazaar (AB) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 vLvL vHvH cLcL cHcH BLBL BHBH SLSL SHSH n LH n HH n LL Normalization Trading probability

56. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 This model is obtained in the case of very limited patience. Then the trading probability is This model is obtained in the case of infinite patience, that is where s(x) is the step function

57. The effect of Asynchronicity „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Decreasing payoff/efficiency 40 low-cost suppliers (SC=10$) 20 high-cost suppliers (SC=30$) 40 low-value demanders (BV=20$) 20 high-value demanders (BV=40$) CE

58. The effect of Patience „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Decreasing payoff/efficiency 40 low-cost suppliers (SC=10$) 20 high-cost suppliers (SC=30$) 40 low-value demanders (BV=20$) 20 high-value demanders (BV=40$) CE

59. Concepts to take home „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Patience of agents (AB infinity ) tends to reduce the efficiency of the market, because it favors extramarginal traders. Impatience of agents (AB 1 ) introduces a selection mechanism that favors trading between agents with higher difference between the buyer value and seller cost, and, therefore, increases the probability that CE is attained. Synchronous pairing (SB) disfavors extramarginal traders, and, therefore, increases the probability that CE is attained.

60. A real system: The network of market members at London Stock Exchange (LSE) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

61. The network of market members at LSE „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 We have access to a version of the Rebuild Order Book of the London Stock Exchange with a codified identity of Market Members for the years 2004-2006. The data includes electronic transactions and off-book transactions (dealers’ market). Here we will focus on a highly liquid stock: BP.

62. The role of Market Members at LSE „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Market members (MMs) are not single investors. A MM may act on behalf of many different investors. A MM may act as an intermediary and/or can do client trading and/or proprietary trading.

63. Market venues at LSE „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Market members (MMs) can execute their trades by submitting their orders in the electronic book in an anonymous form or can execute a transaction in the dealers' off-book venue by directly interacting with other (known) MMs. Recorded transactions are anonymous in both cases. Electronic book Off-book venue MM

64. Scientific question „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Is the number of transactions occurred between two market members (MMs) consistent with a null hypothesis of random matching of MMs?

65. We consider the number of transactions between two market members in a given market venue, in a given time window „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Market member i acted as a buyer in Nib transactions Market member j acted as a seller in Njs transactions During the selected time period and in the considered venue the two market members did Nijbs transactions between them and all market members did Nt transactions

66. A statistical validation of the number of transaction between two market members „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 What is the probability that the Nijbs buy-sell transactions occurred by chance? Nt Suppose there are Nt transaction records in the investigated timewindow. Suppose we are interested to compare the occurrence of two given states B and S of two market members MM i and MM j. Market member MM i is buying Nib times whereas market member MM j is selling Njs times. Let us call Nijbs the buy-sell transactions between them. Nt Total # of transactionsNjs Nib Nijbs # of buying transactions of MM i # of selling transactions of MM j # of B-S transactions between the two MMs

67. Hypergeometric distribution „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Hypergeometric distribution: Expected number of co-occurrences (transactions): p-value associated with a detection of co-occurrences ≥ X: NibNjsNijbsNt In the present application to MMs we set N A =Nib, N B =Njs, X=Nijbs, and N=Nt

68. Corrections for multiple hypotheses testing and network construction „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 We set a directed link between two market members if the associated p-value is below a given statistical threshold.

69. BP (2005): weekly scale Electronic book OriginalBonferroni Off-book seller buyer „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

70. BP (2005): Number of links at weekly scale „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 A. Carollo, F. Lillo, R.N. Mantegna, MT, G. Vaglica, manuscript in preparation

71. Persistence of links: Lagged Mutual Information between Bonferroni networks „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

72. Concepts to take home „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 The off-book market at LSE shows a networked structure of preferential trading patterns. Such a structure is rather persistent. The electronic market does not show any structure of preferential trading patterns.

73. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013 Thank you for your attention!