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Networks in Economics and Finance

International School on Network Science May 19-23, 2014. 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. Outline.

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Networks in Economics and Finance

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  1. International School on Network Science May 19-23, 2014 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

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

  3. Allocation of resources: learning outcomes • 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 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

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

  5. The problem of finding a perfect matching 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 • 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. Type 1 Type 2 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

  6. The problem of finding a perfect matching 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 • 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. Type 1 Type 2 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

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

  8. Constricted Set (of nodes) N(S) 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) „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

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

  10. Matching theorem (König 1931) 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. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

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

  12. 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 What is the “optimal” way to allocate resources in this case? Allocation of resources 7 5 8 4 Optimal Assignment: The matching that maximizes the sum of weights. 6 8 It is assumed that any missing link corresponds to a link with weight 0 9 7 15 5 Type 1 Type 2 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

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

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

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

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

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

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

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

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

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

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

  23. Constructing Market Clearing Prices • Set all the prices equal to 0 • Construct the preferred-seller graph and check whether there is a perfect matching • If there is a perfect matching then we are done • If not, find a constricted set of buyers, S, and their neighbors N(S) • 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 • Go to step 2 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

  24. Concepts to take home • 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 „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

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

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

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

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

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

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

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

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

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

  34. Trading Rules • 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. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

  35. Suggestions for traders • 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. „Infocommunication technologies and the society of future (FuturICT.hu)” TÁMOP-4.2.2.C-11/1/KONV-2012-0013

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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