Reverse Auctions & Voting Mechanisms. 2 Outline Definitions Auction Types Auction Mechanisms Mechanism Design Revenue Equivalence Mechanism Design (Again)

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Reverse Auctions & Voting Mechanisms Slide 2 2 Outline Definitions Auction Types Auction Mechanisms Mechanism Design Revenue Equivalence Mechanism Design (Again) Contract Net Coalition Formation Voting Slide 3 3 Auctions and Reverse Auctions An auction is: a mechanism for establishing a contract for the sale of goods/services by a single seller (possibly through an auctioneer) to one of a number of potential buyers. A reverse auction is: a mechanism for establishing a contract for the sale of goods/services by one of a number of potential sellers to a single buyer. Slide 4 4 Auction Types How do people value items offered for auction? In a private value auction the value of the item depends only on the agents individual preferences; e.g. the sale of bananas In a common value auction the value of the item depends entirely on how others value it; e.g. the sale of stocks and shares In a correlated value auction the value of the item depends both on the agents preferences and how others value it; e.g. the sale of art Slide 5 5 Auction Mechanisms (1) English: first-price, open-cry The dominant strategy in an English auction is for a participant to bid the current price plus some delta until the agent reaches its reservation price. First-price sealed-bid There is no dominant strategy for this type of auction. Dutch: descending price This is equivalent to the first-price sealed-bid auction. Vickrey: second-price sealed-bid If agents value items on the private value basis, then the dominant strategy is to bid their true valuation Slide 6 6 Auction Mechanisms (2) All auction mechanisms allocate item Pareto efficiently to the bidder who wants it the most if the item is valued solely on individual preference The Vickrey and English auctions do not encourage counter-speculation (both have a dominant strategy) Slide 7 7 Mechanism Design Suppose that you are setting up an Internet-based auction house. You want to advertise your service as using an auction mechanism that maximises the revenue raised for your clients. Which auction makes the seller the most money? Slide 8 8 If bidders have independent private valuations for the good in sale, all auction mechanisms lead To the same expected revenue to the auctioneer, and To the same expected profits of the bidders, which award object to bidder that submits highest bid regardless of the specific payment rule of the auction E.g., the equilibrium expected payments in first price sealed bid auction are the same as in the English auction. Revenue Equivalence Slide 9 9 Mechanism Design Again If, however, the bidders are risk-averse then Dutch auction and First-price auction give higher expected revenues. This is because a risk-averse agent can insure himself by bidding more than would be required to secure the item. Most auctions are not private value. In correlated value auctions the English auction with more than 3 bidders leads to higher revenue. This is because increasing price causes others to increase their valuation. Slide 10 10 The Contract Net (1) The Contract Net Protocol (CNet) is the most common one- shot reverse auction. The protocol is as follows: An agent recognises that it has a problem. It announces that it needs the problem solved. Agents may bid for the contract to solve the problem. The contract is awarded. The successful agent solves the problem. Slide 11 11 The CNet (2) Diagrammatically: I have a problem (a) Recognising the problem(b) Task announcement (c) Bidding(d) Awarding the contract Slide 12 12 The CNet (3) CNet Protocol: Standardised by FIPA One-to-many protocol AUML Slide 13 13 Recognising the Problem Agent recognises it has a problem it wants help with The agent has a goal to achieve, and either: Realises it cannot achieve the goal in isolation (it may not have the capability), or Realises it would prefer not to achieve the goal in isolation The quality of the solution that another agent can supply is higher, or a solution can be found more quickly through delegation Slide 14 14 Announcement Agent with problem to be solved (the manager) sends out an announcement of the problem The announcement must include: a description of the task, constraints (e.g. deadlines, quality constraints), and meta-task information (e.g. deadline for receipt of bids). The announcement is then broadcast to all bidders Slide 15 15 Bidding Agents that receive the announcement decide for themselves whether they wish to bid for the task The factors involved in this choice are: Agent must decide if it is capable of doing the task; and Agent must determine quality constraints & pricing info (if relevant). If they choose to bid, then they submit a tender Slide 16 16 Awarding and Expediting The manager agent upon receipt of bids Chooses a bid and awards the contract to someone Result is communicated to agents that submitted bids The successful contractor then does the task This may involve generating further manager-contractor relationships (i.e., sub-contracting) Slide 17 17 Implementation Issues Various issues must be addressed when implementing the CNet: How to specify tasks? How to specify the quality of service? How to select between competing offers? How to differentiate between offers based in multiple criteria? Slide 18 18 Limitations of the CNet The contract net protocol is one-shot What if the manager cannot (or doesnt wish to) distinguish between offers and wishes to go to another round? There is a single contract considered What if it is essential to consider more than one contract at a time? What if no single agent can fulfill the contract, but more than one agent in combination can deliver? Slide 19 19 The Iterated Contract Net CNet extended to multiple rounds Rather than simply accepting a single initial bid Manager may select a subset of the agents and request further bids. Eventually the manager will make the choice of a single contractor. Standardised FIPA protocol Slide 20 20 Coalition Formation (1) Suppose contract for the delivery of q units of item b What if no single agent can fulfill this contract? Modify the CNet protocol so that The manager can select a subset of agents Each agent may supply a part of the contract Furthermore, if the manager splits the supply, it may be able to get a better price for the whole contract Slide 21 21 Coalition Formation (2) Suppose manager requires q units of item b It receives bids from all agents, each bid of the form a i,q i,c i that is, agent a i offers q i units of b each at cost c i Manager stores bids in set Bids. While q > 0 and Bids {} do: Select bid a i,q i,c i Bids, with lowest cost per unit If q q i then accept quantity q from a i and reject all other bids from all other agents in Bids. If q q i then accept quantity q i from a i Update q q q i and Bids Bids { a i,q i,c i } Slide 22 22 Coalition Formation (3) What if more than one item is required? The algorithm must then be modified to select the subset of the bidding agents so that the required quantity of each item is obtained. What if the items are not independent? E.g. bidder may specify that if item 1 is accepted then item 2 must also be accepted. What if offers are all or nothing? As assumptions are relaxed, the problem becomes harder. Slide 23 23 Making group decisions Social choice theory (or voting theory) Voting protocols are strategic Agents have preferences over possible outcomes Agents take into account their own preferences as well as the other agents when deciding on how to vote Agents want to bring about their most preferred outcome (or to avoid the least wanted outcome) Voting protocols have intriguing properties! Slide 24 24 Social Welfare Functions We have a set of agents Ag = {1,..., n} Referred to as voters Participants of the group decision-making process Number of agents is finite We assume n is an odd number (to avoid ties) Voters make group decisions with respect to a set of possible outcomes or candidates = { 1, 2,...} For instance, could be the politicians of an election If = { 1, 2 } (two elements) then we have a pairwise election If more than 2 then we have a general voting scenario Voters aim at ranking or ordering candidates Sometimes just picking the top-ranked candidate Slide 25 Each voter has preferences over Preferences defined as an ordering over For example, an agents preference is ( 2, 3, 1 ), that is, the agent prefers 2 over 3, and prefers 3 over 1 Preference orders of agents 1,..., n is 1,..., n > i represents that outcome is ranked above outcome in agents i preference order i ( ) is the set of all preference orderings over 25 Social Welfare Functions (Contd) Slide 26 n times The fundamental problem of social choice theory is A social welfare function takes voters preferences and produces a social preference order: f : ( )... ( ) ( ) A simpler problem is to obtain just one of the possible candidates this is a social choice function: f : ( )... ( ) 26 Social Welfare Functions (Contd) Agents might naturally have different preference orders. So, given a collection of preference orders, one for each agent, how do we combine these to derive a group decision? Slide 27 We use > * to refer to the outcome of a social welfare function, that is, > * means that is ranked above in the social outcome We shall look next at voting procedures These are mechanisms for agents to use They did not happen by accident they were designed They have guarantees and properties; these are required otherwise agents would not use them A bad example: I own the ball, so I choose who to play... 27 Social Welfare Functions (Contd) Slide 28 Simplest and best-known voting procedure Commonly used to select a single candidate That is, it is a social choice function Can be generalised for a social welfare function How it works 1.Each voter submits their preference order 2.Mechanism counts how many times each outcome is ranked first in a preference order 3.Winner is outcome that appears

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