nwtrade09 - Networked Trade: Theory and Behavior Networked...

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Networked Trade: Theory and Behavior Networked Life CIS 112 Spring 2009 Prof. Michael Kearns
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s trate g ic   g a m e s Na s h  e q uilib rium ne two rke d  g am e s be ha vi o r trade   e c o no m ie s pric e   e q uilibrium ne two rke d  trade b e ha vi o r
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Trade Economies S uppo s e  the re  a re  a bunc h o f diffe re nt  goods  or commodities  wheat, milk, rice, paper, raccoon pelts, matches, grain alcohol,… commodity = no differences or distinctions within a good: rice is rice We may all have different initial amounts or  endowments I might have 10 sacks of rice and two raccoon pelts you might have 6 bushels of wheat, 2 boxes of matches etc. etc. etc. Of course, we may want to  trade  or  exchange  some of our goods I can’t eat 10 sacks of rice, and I need matches to light a fire it’s getting cold and you need raccoon mittens etc. etc. etc. How should we engage in trade? What should be the  rates  of trade? how many sacks of rice per box of matches? These are among the oldest questions in markets and economics Obviously can be specialized to “modern” markets (e.g. stocks)
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Cash and Prices S uppo s e  we  intro duc e  a n ab s tra c t re s o urc e  c alle d  cash no inherent value simply meant to facilitate trade; “encode” pairwise exchange rates And now suppose we introduce  prices  in cash (from where?) i.e. rates of exchange between each “real” good and cash e.g. a raccoon pelt is worth $5.25, a box of matches $1.10 Then if we all believed in cash  and  the prices… we might try to  sell  our initial endowments for cash then use the cash to  buy  exactly what we most want But will there really be: others who want to buy all of our endowments? (demand) others who will be selling what we want? (supply) how might we find them? A complex, distributed market coordination problem
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Mathematical Microeconomics Ha ve   k abstract goods  or  commodities  g1, g2, … , gk Have  n consumers  or “players” Each player has an  initial endowment  e = (e1,e2,…,ek) > 0 Each consumer has their own  utility function: assigns a subjective “valuation” or utility to any amounts of the k goods e.g. if k = 4, U(x1,x2,x3,x4) = 0.2*x1 + 0.7*x2 + 0.3*x3 + 0.5*x4 (* = multiplication) this is an example of a  linear  utility function lots of other possibilities; e.g. diminishing utility as amount becomes large here g2 is my “favorite” good --- but it might be expensive generally assume utility functions are  insatiable always some bundle of goods you’d prefer more
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nwtrade09 - Networked Trade: Theory and Behavior Networked...

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