CSCI 2350: Social & Economic Networks Price setting in Matching - - PDF document

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CSCI 2350: Social & Economic Networks

Price setting in Matching Markets

Reading: Ch 11.1 of EK

Bargaining & Power in Networks

Reading: Ch. 12 of EK

Mohammad T . Irfan

Tradesparq

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Reminder: Market clearing price (MCP)

u MCP: prices for which there exists a perfect

matching in the preferred seller graph

u Algorithm

1.

Initialize prices to 0

2.

Buyers react by choosing their preferred seller(s)

3.

If resulting graph has a perfect matching then done! Otherwise, the neighbors of a constricted set increases price by 1 unit; (Normalize the prices—by decreasing all prices by the same amount so that at least one price is 0); Go to step 2 u MCP maximizes the social welfare

Price-setting in real world

Stock market

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Stock markets

u Stock exchanges – determine ~MCP

u NYSE: algorithm + designated market maker (DMM) u NASDAQ: algorithm only

u Trading systems – match buyers & sellers

u Direct Edge, Goldman Sachs,

Investment Technologies Group (ITG)

Order book

u 1. Limit order (big traders)

u A: sell 100 shares at >= $5/share u B: sell 100 shares at >= $5.5/share u C: buy 100 shares at <= $4/share u D: buy 100 shares at <= $3.5/share

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Oder book

u 2. Market order (small traders)

u Buy 150 shares at market price => 100 shares at

$5/share and 50 shares at $5.5/share Before After

Trading large volumes of shares

u Hedge funds, insurance companies, mutual funds

(Fidelity, Vanguard), banks, etc. trade in large volumes

u 1. Split the volume into small fragments– why? u 2. Dark pool

u Examples: Goldman Sach’s Sigma-X, ITG u Trade large volumes at market price without

revealing identity

u Accounts for 15% of US volume (2014) u Pros: Reduced impact on market, lower transaction

cost

u Cons: Lack of transparency, exchange prices may not

reflect the real market, predatory trading by hedge funds

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Bargaining & Power in Economic Networks

Chapter 12

Power

u Is it an individual property? u Or a result of social relations?

u Richard Emerson (1962) u Social relation between two people produces

“values” for them

u Imbalance of values è power u Division of values: Network exchange theory

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Who is most powerful?

u B u Why?

u Dependence: A and C completely depend on B u Exclusion: B can exclude A or C from being his

“best friend”

u Satiation: B will maintain relationship only if he

gets a better share

u Betweenness: B has the highest betweenness

centrality measure u Which one is in effect?

Experimental setup

u A small network u Each individual is a node of the graph u Each edge contains a fixed amount of $

u Endpoints negotiate how to split that amount of $

u One-exchange rule: Each node can do

transaction with at most one neighbor

u Results in a matching, which may not be a perfect

matching u This experiment is run for multiple rounds

$1 $1 $1 $1

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Experimental results and analysis Mathematical framework

Stable outcomes

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Stable outcomes in network exchange

u Outcome = (matching, values) u Opportunity + Incentive à unstable

Stable outcomes

u Limitations of stable outcomes

u Extreme values

u Explanation – ultimatum game

u Ambiguity

u Solution – Nash bargaining

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Ultimatum game

u Difference between real-world experimental

• utcomes and stable outcomes

u Stable outcomes sometimes go to the extreme

u Explanation

u People play a different game than the one on

paper!

u A little dramatic here!

u https://www.youtube.com/watch?v=BfE4ZL08twA

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Nash bargaining solution

Resolves ambiguity in stable

• utcomes