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      Agent Technology for e-Commerce

            Chapter 9: Negotiation II

                          Maria Fasli
Agent Technology for e-Commerce

      A coalition is a set of agents that agree to cooperate in order to
       achieve a common objective
      The incentives for creating/joining a coalition can be:
         Monetary: reduction of cost or increased profit

         Risk reduction (or allowing someone else to assume risk)

         Increase in market size or share

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                             Coalition formation
   Coalition formation can be studied in the context of characteristic
     function games (CFG):
    A set N of agents in which each subset is called a coalition

    The value of a coalition S is given by a characteristic function vS

    CS: the coalition structure is the set of all coalitions such that
     every agent belongs to one
    The solution of a game with side payments is a coalition
     configuration which consists of a partition S of N, the coalition
     structure CS, and an n-dimensional payoff vector

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   Coalition formation in CFG games involves two activities:
    Coalition structure generation

    Division of the value of the generated coalition structure among
     all agents

   The two activities are intertwined

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                    Coalition structure generation
   The formation of an optimal, maximum welfare coalition structure is
     trivial when the coalition values are:
    Super-additive: there is at least one optimal coalition structure,
     the grand coalition
    Sub-additive: the optimal coalition structure is the one in which
     every agent acts on their own

   When games are neither sub-additive or super-additive some
    coalitions are best off merging whereas others are not

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      The objective is to maximize the social welfare of the agents by
      finding an optimal coalition structure CS*:

      where V(CS) is the value of a coalition structure:

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      The number of coalition structures CS is exponential in the
       number of coalitions S, the agent must search among O(nn)
       coalition structures to find the optimal one
      The number of coalitions is

      Not all coalition structures can be enumerated unless n is small
      Can the agents approximate the optimal coalition structure?
      Can they search through a subset LM such that:

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   Coalition structures for four agents

  • The lowest two levels of the ordering (j=1 and j=2) the agents have
  seen all the possible coalition structures
  • The agents must at least inspect 2n-1 different coalition structures
  in order to determine a worse-case bound
  • If more time for computation is available more coalition structures
  can be inspected
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                              Division of payoffs
   Payoff division is important as it affects the stability of the coalition
   Many coalition formation algorithms rely on game theory concepts

   The Core

           The strongest solution concept; it may be empty
           Agents may switch indefinitely between coalitions
           The Core may contain multiple solutions – the agents need to
            agree on one: the nucleolus
           Calculating the Core is an NP-hard problem

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   The Shapley value:
    Agent i is a dummy if vSi-vS=vi for every coalition S that does
     not include i
    Agents i and j are interchangeable if for all S with either i or j, vS
     remains the same if i is replaced by j

   We require a set of payoffs that satisfy:
    Symmetry: if i and j are interchangeable then pi=pj

    Dummies: if i is a dummy, then pi=v{i}

    Additivity: for two games v and w, pi in v+w is equal to pi in v
     plus pi in w

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   The Shapley value satisfies these conditions and sets the payoffs to

      It always exists and is unique
      Pareto efficient
      It guarantees that individual agents and the grand coalition have
       an incentive to stay with the coalition structure
      No guarantee that all subgroups of agents are better off in the
       coalition structure than by splitting out into a coalition of their

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                             Customer coalitions
      Suppose you want to buy a PC, you can do so at retail price
      If nine of your friends are interested in the same type of PC, you
       can join forces and ask retailers to make you a better offer as this
       is a bulk purchase
      What the discount is depends on the number of PCs
      The vendor has an incentive to lower the price, as otherwise the
       sale will be lost

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   Supplier incentive to sell wholesale
   Utility to sell wholesale:

   The utility of selling n items retail:

   The utility of selling n items wholesale:

   Up to some number nretail, the supplier does not have an incentive to
     sell wholesale as marketing costs are identical

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   Customer incentive to buy wholesale
   A customer’s utility:
   ucustomer = vitem – pitem – cstorage
    Maximum utility range: MUR(nmin,nmax) – utility is high while
      the management or storage costs remain low
    If nwholesaleMUR then the customer can purchase the items at
      wholesale price
    But the customer needs to be given incentives to buy larger
      quantities, i.e, the supplier needs to lower the price

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      In practice, individual consumers very rarely require large
       enough quantities so that they can purchase at wholesale prices
      But by forming coalitions, consumers can increase the quantity
       purchased so as to be charged wholesale prices
      The utility of the coalition is now MURcoalition = MURi
      If nwholesaleMURcoalition then the coalition can make a wholesale

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                              Coalition protocols
   The general stages involved in a coalition protocol are:
    Negotiation: The coalition leader/representative negotiates with
    Coalition formation: The initiator/leader invites potential
     members to join the coalition; possible admission constraints
    Leader election/voting: The members may elect a leader. Not all
     protocols have this stage
    Payment collection: The coalition leader/representative collects
     payments and pays supplier.
    Execution/distribution: The transaction is executed; the goods
     arrive and they are distributed to the members of the coalition

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                      Issues in coalition protocols
      Coalition stability
      Distribution of utility and costs
      Trust
         Negotiation stage

         Payment collection stage

         Distribution stage

      Distribution of risk
         Risk of transaction failure

         Risk of coalition failure

         Price uncertainty

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                              Coalition protocols
      Assume a coalition leader (L), a set of suppliers S={s1,s2,…,sk}
       and a set of potential coalition members M={m1,m2,…,mn}
      Based on the order in which the negotiation and coalition
       formation stages take place there are two types:
         Post-Negotiation

         Pre-Negotiation

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                        Post-negotiation protocol
   1.   LCS: L advertises the creation of a coalition with certain
        parameters (deadline, maximum number etc.)
   2.   Each miM considers whether to join the coalition and sends
        necessary message mi  L: “Join the Coalition”
   3.   At the expiration of the coalition deadline/size limit, the leader
        enters the negotiation with the suppliers si  S using its private
        protocol/strategy and decides on a deal
   4.   L collects money from group members, and arranges for the
        shipping and distribution of goods

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    Trust in the coalition leader is required

    Shills can start coalitions

   Trust can be established in a number of ways
    Leaders can be elected

    A trusted third party can be appointed to conduct the negotiations

    The coalition leader could be compelled to open every step of the
     negotiation to the scrutiny of group members
    Members can vote on the suppliers’ bids – but time-consuming

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                         Pre-negotiation protocol
   1.   L conducts negotiations with the suppliers S, using its private
   2.   L opens the coalition to potential coalition members, disclosing
        the details of the deal agreed
   3.   Each miM considers whether to join the coalition and sends
        necessary message mi  L: “Join the Coalition”
   4.   After a certain period of time elapses, or the coalition gains
        some minimum number of members, L closes the coalition to
        new members and executes the transaction

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    An insufficient number of members join the coalition

    The deal must be re-negotiated, resulting in a higher price and,
      possibly, more members leaving the coalition

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    L presents not an estimated group size, but a range of sizes.

    The supplier bids with a step function P = Fbid(quantity)

    The risk in the transaction is shifted onto the coalition members
     due to the price uncertainty
    A buyer’s decision on whether to join depends on its estimate of
     the probability that the final price will be lower than its preservation:
      pmax-coalition >= preservation >= pmin-coalition
    A dominant strategy for a buyer would be to wait until the
     coalition is almost closed for new members

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                   Distribution of costs and utility
   The coalition leader can operate on:
    Non-Profit: ccoalition is distributed either equally among all
     participants or on the sub-lot size basis. Can form on a per need
     basis or be stable ‘buyer's clubs’ that exist over time
    For-Profit:

       Consolidator: Pre-negotiates a deal with the supplier given an

        estimated group size, and then re-sells the items individually,
        keeping enough of the savings to cover ccoalition and profit
       Rebater: Sells the items at retail price minus a small rebate,

        and keeps the rest of the savings

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