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Algorithmic and Economic Aspects of Networks Nicole Immorlica

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Networked Markets Garmets Market Marseille Fish Market Labor Markets

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Why Network Trust, predicability, referrals, incomplete contracts, friction, moral hazard/adverse selection price, reputation

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Labor Markets “You hear about jobs through your friends.” – Granovetter better

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Boorman’s Model Network of strong and weak ties Preferential flow of information about job opennings through network

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Strong and Weak Ties Weak + λ∙Strong = Time

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Information Flow 1)People need jobs with prob. μ. 2)People hear about jobs with prob. δ. 3)People tell (stronger) friends about jobs.

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Boorman’s Results Study trees, fix degree of strong/weak ties, consider equilibria via simulation 1)As cost of strong ties, # strong ties. 2)As unemployment prob., # strong ties.

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What’s Missing? network architecture, e.g., weak ties more likely to be bridges correlation in employment state over time and network structure

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Carvo-Armengol & Jackson Drop strong/weak distinction, but incorporate time.

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Information Flow 1)People need jobs with prob. μ. 2)People hear about jobs with prob. δ. 3)People tell friends about jobs.

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Tarred with the Same Brush Time causes correlation in employment: you are more likely to find a job if more of your friends have jobs

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Persistance of (Lack of) Luck The longer you are unemployed, the less likely you will find a job tomorrow: because you are more likely to have more unemployed neighbors

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Education Agents can pay cost c i to be educated. educated – apply previous model uneducated – payoff zero

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Poverty Traps Payoff: 0.5 – c i Payoff: 0.6 – c i Payoff: 0.69 – c i Payoff: 0.65 – c i

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Networked Exchange Theory Network represents potential trades what prices result?

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Nash Bargaining How to split a dollar? Matt ($0.50)Mykell ($0.50) If negotiations fail, you get nothing.

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Nash Bargaining How to split a dollar? Trevor ($0.70)William ($0.30) If negotiations fail, Trevor gets $0.60, William gets $0.20.

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Nash Bargaining Any division in which each agent gets at least the outside option is an equilibrium. Yet …. agents usually agree to split the surplus.

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Nash Bargaining If when negotiation fails, - A gets $a - B gets $b Then when succeed, - A gets $(a + s/2) - B gets $(b + s/2) s = (1 – a – b) is the surplus

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Nash Bargaining Nash: “Agents will agree to split the surplus.” Motivated by axiomatic approach, optimization approach, and outcome of particular game- theoretic formulations.

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Bargaining in Networks Value of outside option arises as result of network structure.

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Bargaining in Networks William ($0.50) Arun ($0.50) Bach ($0) Matt ($0) Mykell ($0) Transactions worth $1. Only one transaction per person!

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Bargaining in Networks Almost all the money.

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Bargaining in Networks v v gets between 7/12 and 2/3 in negotiation to left.

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Bargaining in Networks v v gets between 1/2 and 1 in negotiation to left.

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Cook and Yamagishi A solution for a network G is a matching M and a set of values ν u for each node u s.t., - For (u,v) in M, ν u + ν v = 1 - For unmatched nodes u, ν u = 0

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Stable Outcomes Node u could negotiate with unmatched neighbor v and get (1 - ν v ). Outside option of u is α u = maximum over unmatched neighbors v of (1 - ν v ).

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Stable Outcomes Defn. An outcome is stable if for all u, ν u ≥ α u. Notice there are many stable outcomes, so which one should we expect to find?

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Balanced Outcomes Each individual bargaining outcome should agree with the Nash bargaining solution. s uv = 1 - α u - α v ν u = α u + s/2 And similarly for ν v.

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Computing Balanced Outcomes A balanced outcome exists if and only if a stable outcome exists. Balanced outcomes can be computed and characterized using Edmonds-Galai decompositions. [Kleinberg-Tardos STOC’08]

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Assignment: Readings: – Social and Economic Networks, Chapter 10 – The two Kearns papers or a paper on labor markets of your choosing (see refs in book) Reaction to paper Presentation volunteers?

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