Silvia Rossi. Auctions. Lezione n. Corso di Laurea: Informatica. Insegnamento: Sistemi multi-agente. A.A.

Transcription

1 Silvia Rossi Auctions Lezione n. 16 Corso di Laurea: Informatica Insegnamento: Sistemi multi-agente A.A

2 Reaching Agreements - Auctions (W: 7.2, MAS: 11.1) 2

3 Any negotiation mechanism that is: Auctions as Structured Negotiations market-based (determines an exchange in terms of currency) mediated (auctioneer) well-specied (follows rules) Defined by three kinds of rules: rules for bidding rules for what information is revealed rules for clearing 3

4 Dened by three kinds of rules: rules for bidding who can bid, when what is the form of a bid Auctions as Structured Negotiations restrictions on offers, as a function of: bidder's own previous bid auction state (others' bids) eligibility (e.g., budget constraints) expiration, withdrawal, replacement rules for what information is revealed rules for clearing

5 Dened by three kinds of rules: Auctions as Structured Negotiations rules for bidding rules for what information is revealed when to reveal what information to whom rules for clearing

6 Dened by three kinds of rules: Auctions as Structured Negotiations rules for bidding rules for what information is revealed rules for clearing when to clear at intervals on each bid after a period of inactivity allocation (who gets what) payment (who pays what)

7 How should agents bid in these auctions? Intuitive comparison of 5 auctions English Dutch Japanese 1 st -Price 2 nd -Price Duration Info Revealed #bidders, increment 2 nd -highest val; bounds on others starting price, clock speed winner s bid #bidders, increment all val s but winner s fixed none fixed none Jump bids yes n/a no n/a n/a Price Discovery yes no yes no no Regret no yes no yes no

8 Second-Price Alice wants to get the best price she can for her house. There are two potential buyers, Horace and Maurice. If she knew the maximum each would be willing to pay, her problem would be easy. However, although she doesn't know their reservation prices, she is not entirely ignorant. It is common knowledge that each potential buyer has a reservation price of either three million or four million dollars, and that each value is equally likely. 8

9 Each bidder secretly seals his bid in an envelope. Second-price auction The envelopes are then publicly opened, and the house is sold to the highest bidder, but not at the price he bid. Instead it is sold to him at the highest price bid by a loser. The advantage of such an arrangement, the auctioneer explains, is that it induces rational people to bid their true reservation prices. 9

10 Example Horace, for example, would reason like this: Suppose that Maurice's bid is for less than my reservation price; Then I want to win the auction, and I can do so just by bidding my own reservation price truthfully. If Maurice bids more than my reservation price; Then I don t want to win and I can guarantee not doing so by bidding my own reservation price truthfully. 10

11 Vickrey Auctions The auction proceeds either by English (ascending auction) or by sealed-bid protocol The winner is the bidder with the highest bid The winner pays the amount which the second-highest bidder bid This protocol reduces the extent of the winner s curse The amount paid by the winner is equal to the price the winner would get if he/she sold it immediately in another auction

12 Vickrey Auctions Vickrey auctions susceptible to antisocial behavior Lying auctioneer

13 Second-Price proof Truth-telling is a dominant strategy in a secondprice auction. Assume that the other bidders bid in some arbitrary way. We must show that i's best response is always to bid truthfully. We'll break the proof into two cases: 1 Bidding honestly, i would win the auction 2 Bidding honestly, i would lose the auction 13

14 Bidding honestly, i is the winner If i bids higher, he will still win and still pay the same amount If i bids lower, he will either still win and still pay the same amount... or lose and get utility of zero. 14

15 Bidding honestly, i is not the winner If i bids lower, he will still lose and still pay nothing If i bids higher, he will either still lose and still pay nothing... or win and pay more than his valuation. 15

16 A much more complicated strategy space extensive form game English and Japanese auctions bidders are able to condition their bids on information revealed by others in the case of English auctions, the ability to place jump bids intuitively, though, the revealed information doesn't make any difference in the IPV setting. Theorem Under the independent private values model (IPV), it is a dominant strategy for bidders to bid up to (and not beyond) their valuations in both Japanese and English auctions. 16

17 First-Price and Dutch In both first-price and Dutch, a bidder must decide on the amount he's willing to pay, conditional on having placed the highest bid. despite the fact that Dutch auctions are extensive-form games, the only thing a winning bidder knows about the others is that all of them have decided on lower bids e.g., he does not know what these bids are this is exactly the thing that a bidder in a first-price auction assumes when placing his bid anyway. Note that this is a stronger result than the connection between second-price and English. 17

18 So, why are both auction types held in practice? Discussion First-price auctions can be held asynchronously Dutch auctions are fast, and require minimal communication: only one bit needs to be transmitted from the bidders to the auctioneer. How should bidders bid in these auctions? 18

19 So, why are both auction types held in practice? Discussion First-price auctions can be held asynchronously Dutch auctions are fast, and require minimal communication: only one bit needs to be transmitted from the bidders to the auctioneer. How should bidders bid in these auctions? They should clearly bid less than their valuations. There's a tradeo between: probability of winning amount paid upon winning Bidders don't have a dominant strategy any more. 19

20 Risk 20

21 Let s i denote the bid of player i, and v i denote his true valuation. Utility If player i wins, his payoff is u i = v i s i ; If he loses, it is u i = 0. 21

22 Analysis 22

23 Analysis 23

24 Analysis 24

25 More tha two bidders Still, first-price auctions are not incentive compatible hence, unsurprisingly, not equivalent to second-price auctions proven using a similar argument, but more involved calculus a broader problem: that proof only showed how to verify an equilibrium strategy. How do we identify one in the first place? 25

26 Revenue Equivalence Which auction should an auctioneer choose? To some extent, it doesn't matter... 26

27 Revenue Equivalence Thus, when bidders are risk neutral and have independent private valuations, all the auctions we have spoken about so far English, Japanese, Dutch, and all sealedbid auction protocols are revenue equivalent. 27

28 Risk Attitudes What kind of auction would the auctioneer prefer? Buyer is not risk neutral: no change under various risk attitudes for second price in first-price, increasing bid amount increases probability of winning, decreases profit. This is good for risk-averse bidder, bad for risk-seeking bidder. Risk averse, IPV: First > [Japanese = English = Second] Risk seeking, IPV: Second > First 28

29 Risk Attitudes What kind of auction would the auctioneer prefer? Buyer is not risk neutral: no change under various risk attitudes for second price in first-price, increasing bid amount increases probability of winning, decreases profit. This is good for risk-averse bidder, bad for risk-seeking bidder. Risk averse, IPV: First > [Japanese = English = Second] Risk seeking, IPV: Second > First Auctioneer is not risk neutral: revenue is fixed in first-price auction (the expected amount of the second-highest bid) revenue varies in second-price auction, with the same expected value thus, a risk-averse seller prefers first-price to second-price. 29

30 For risk-averse bidders (i.e. bidders that would prefer to get the good even if they paid slightly more for it than their private valuation), Dutch and first-price sealed-bid protocols lead to higher expected revenue for the auctioneer. This is because in these protocols, a risk-averse agent can 'insure himself by bidding slightly more for the good than would be offered by a risk-neutral bidder. Risk-averse auctioneers, however, do better with Vickrey or English auctions. 30

31 Revenue Equivalence and Non-Equivalence All of the four auction protocols produce the same expected revenue to the auctioneer in private value auctions where the values are independently distributed, and bidders axe riskneutral. 31

32 Lies and Collusion The various auction protocols are susceptible to lying on the part of the auctioneer, and collusion among bidders, to varying degrees All four auctions (English, Dutch, First-Price Sealed Bid, Vickrey) can be manipulated by bidder collusion A dishonest auctioneer can exploit the Vickrey auction by lying about the 2 nd -highest bid Shills can be introduced to inflate bidding prices in English auctions

33 Design choices for market mechanisms Number and frequency of rounds Who can participate? Rules for participant collaboration and proxies Rules for utterances Can participant leave before the end? Rules for termination How winner is selected? What price does the winner pay? What price do the others pay? What can happen subsequently?

34 Evaluation of auction mechanisms Traditional economic-theoretic criteria Maximization of revenue to single seller Efficiency of resource allocation Other economic criteria Social welfare Allocation efficiency (eg, Pareto-optimal outcomes) Individual rationality Stability against manipulation Low transaction costs Rule transparency Buyer vs. seller market power

35 Luca, come regalo di Natale, riceve un ipod da 5Gb. Tale oggetto ha valore nullo per Luca in quanto già possiede in ipod da 40Gb e decide così di metterlo all asta. Supponendo che solo 3 persone siano interessate a partecipare all asta e che la loro valutazione dell oggetto sia 25, 37 e 40. Quale sarebbe il profitto di Luca se l asta fosse una second-price sealed-bid o una first price? 35

36 Why and how do agents work together? Important to make a distinction between: benevolent agents self-interested agents Working Together

37 Benevolent Agents If we own the whole system, we can design agents to help each other whenever asked In this case, we can assume agents are benevolent: our best interest is their best interest Problem-solving in benevolent systems is cooperative distributed problem solving (CDPS) Benevolence simplifies the system design task enormously!

38 Self-Interested Agents If agents represent individuals or organizations, (the more general case), then we cannot make the benevolence assumption Agents will be assumed to act to further their own interests, possibly at expense of others Potential for conflict May complicate the design task enormously

39 Task Sharing and Result Sharing Two main modes of cooperative problem solving: task sharing: components of a task are distributed to component agents result sharing: information (partial results, etc.) is distributed

40 The Contract Net A well known task-sharing protocol for task allocation is the contract net: 1. Recognition 2. Announcement 3. Bidding 4. Awarding 5. Expediting

41 In this stage, an agent recognizes it has a problem it wants help with. Agent has a goal, and either Recognition realizes it cannot achieve the goal in isolation does not have capability realizes it would prefer not to achieve the goal in isolation (typically because of solution quality, deadline, etc.)

42 Announcement In this stage, the agent with the task sends out an announcement of the task which includes a specification of the task to be achieved Specification must encode: description of task itself (maybe executable) any constraints (e.g., deadlines, quality constraints) meta-task information (e.g., bids must be submitted by ) The announcement is then broadcast

43 Bidding Agents that receive the announcement decide for themselves whether they wish to bid for the task Factors: agent must decide whether it is capable of expediting task agent must determine quality constraints & price information (if relevant) If they do choose to bid, then they submit a tender

44 Awarding & Expediting Agent that sent task announcement must choose between bids & decide who to award the contract to The result of this process is communicated to agents that submitted a bid The successful contractor then expedites the task May involve generating further managercontractor relationships: sub-contracting

45 How to specify tasks? specify quality of service? Issues for Implementing Contract Net select between competing offers? differentiate between offers based on multiple criteria?

46 The Contract Net An approach to distributed problem solving, focusing on task distribution Task distribution viewed as a kind of contract negotiation Protocol specifies content of communication, not just form Two-way transfer of information is natural extension of transfer of control mechanisms

47 Four Phases to Solution, as Seen in Contract Net 1. Problem Decomposition 2. Sub-problem distribution 3. Sub-problem solution 4. Answer synthesis The contract net protocol deals with phase 2.

48 The collection of nodes is the contract net Contract Net Each node on the network can, at different times or for different tasks, be a manager or a contractor When a node gets a composite task (or for any reason can t solve its present task), it breaks it into subtasks (if possible) and announces them (acting as a manager), receives bids from potential contractors, then awards the job (example domain: network resource management, printers, )

49 Node Issues Task Announcement Task Announcement Manager

50 Idle Node Listening to Task Announcements Manager Potential Contractor Manager Manager

51 Node Submitting a Bid Bid Manager Potential Contractor

52 Manager listening to bids Bids Manager Potential Contractor Potential Contractor

53 Manager Making an Award Award Manager Contractor

54 Contract Established Contract Manager Contractor

55 Domain-Specific Evaluation Task announcement message prompts potential contractors to use domain specific task evaluation procedures; there is deliberation going on, not just selection perhaps no tasks are suitable at present Manager considers submitted bids using domain specific bid evaluation procedure

56 Contract-net

57 Iterated Contract-net