©2003, zoran despotovic, epfl-i&c, laboratoire de systèmes d'informations répartis...

©2003, Zoran Despotovic, EPFL-I&C, Laboratoire de systèmes d'informations répartis

Double Auctioning in a P2P environment(an attempt)

Zoran DespotovicEPFL-I&C-IIF

Distributed Information Systems Laboratory{zoran.despotovic}@epfl.ch


Overview

1. A Bit of Microeconomics2. Single-sided Auctions3. Double-sided Auctions4. Double Auctioning in P2P?


1. Microeconomics

• Microeconomics: a set of theories with the aim to help us gain an understanding of the process by which scarce resources are allocated among alternative users, and of the role of prices and markets in this process

• Scarce resource: the demand at a zero price exceeds the available supply


The Market Equilibrium

• The demand and supply curves• The competitive equilibrium price

• The main problem: how to determine the CE price when no one knows the curves

Quantity

Price

Q0

P0

Supply

Demand


A more realistic example

2 4 6 8 10Quantity

2

4

6

8

10

Price


2. Single-sided auctions

• One seller and many buyers (or vice versa)

• What mechanism should the seller choose to get at least the equilibrium price no matter how the buyers behave?

2 4 6 8 10Quantity

2

4

6

8

10

Price


Single-sided Auctions - Four Main Types

• English auction (open cry ascending bid)– Increase the price until only one buyer remains; this

buyer pays the price of his last bid

• Dutch (descending offer)– Start with a high price and decrease it until a buyer

accepts it;

• Sealed-bid first price– All buyers submit sealed bids; the buyer with the highest

bid wins the item and pays the price of his bid

• Sealed-bid second price (Vickrey – Nobel Prize)– All buyers submit sealed bids; the buyer with the highest

bid wins the item and pays the price of the second highest bid


The Four Auction Types – Buyers‘ View

• English Auction: bid until your reservation price is reached• Vickrey Auction: bid your reservation price!

– Incentive compatible

• Sealed-bid first price: bid slightly below your reservation price

• Dutch Auction: same as the sealed-bid first price auction

• The sellers‘ gain? The same expected value with all four types – the second highest valuation! (Revenue equivalence theorem)


3. Double Auctions

• Sealed-bid Double Auction (Call Market):– The bidders (both buyers and sellers) submit sealed bids

and offers– The auctioneer constructs the D-S curves, determines

the price and clears the market

• Truthful bidding is not an equlibrium but all equilibria are within O(1/M) of the truthful bidding and the expected inefficiency of any equilibrium is O(1/M2)


The Continuous Double Auction

• The rules:– A number of traders entitled to buy or sell one or more

units of a given commodity– All the traders are allowed to make verbal „shouts“

(quotes) of a price: „I am selling at $10“, „I am buying at $6“

– At any time, any buyer (seller) is free to accept a seller‘s (buyer‘s) offer (bid). When this happens the buyer and the seller are assumed to enter into a binding contract

• Nice. But, why another Nobel prize (V. Smith)?


Convergence towards the CE price


4. Double Auctioning in P2P?

• Call Markets– Where to keep the bids and how to make them sealed

(auctioneer)

• The CDA:– Binding contracts for bid or sell accepts– Everything is publicly observable– No deviations from the rules are possible– The mechanism is not self-enforceable


The CDA in P2P?

• Peers may be tempted to reply to offers and bids not by taking (or leaving) the observed prices but by offering new, better ones. This cannot be observed!

1 2

3

t=0; sell offer

t=10ms; receive

offer; send accept

t=12ms; receive

offer; send accept

t=20ms; receive accept

t=24ms; receive accept


Our Idea

• Introduce the possibility for the peers to reply with new offers explicitly into the mechanism

• Set the price at the middle point between two offers

• Trading prices? Do they converge towards the CE price?– Good news:

• good convergence in the fully periodic case• The market can be cleared easily


Simulations

• Choose some reasonable bidding strategies and observe how the system behaves when these strategies are used by the bidders– When to submit a bid and what price to bid– For how long to collect the answers– To which bids to answers and with what price– How to evolve eventual answers with time

• Starting point: Zero Intelligence Plus (ZIP) traders


Mathematica – a piece of advice

• Don‘t write a Mathematica simulation quickly! Time needed for debugging it is inversely proportional to the time you spend to write it! Especially if you are used to Java or C++.

©2003, zoran despotovic, epfl-i&c, laboratoire de systèmes d'informations répartis...

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