Bilateral MultiIssue Negotiation

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Bilateral Multi-Issue Negotiation

• Speaker Raymund J. Lin, D85725004

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Negotiation

• When people are trying to resolve conflicts
  between several parties, they negotiate.
• single-issue two-party problems
• multi-issue multi-party

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Bilateral Multi-Issue Negotiation

• Multi-issue, two party
• Multi-issue negotiations are considered
  integrative \citeraiffanegotiationart1982,
  where all parties may find mutually beneficial
  outcomes, i.e., win-win solutions. However, the
  complexity of a multi-issue negotiation increases
  rapidly as the number of issues increases, which
  means that people need more time and rationale in
  handling the negotiation problem.

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Negotiation Support Systems

• The development of Negotiation Support Systems
  (NSSs) and negotiating software agents (NSAs)
  have been proved to be able to reduce
  significantly the negotiation time and alleviate
  the negative effects of human cognitive biases
  and limitations \citelomuscionegotiationclassifi
  cation2001 \citesandholmnegotiationcomponent200
  0 \citemaesagent1999 \citeforoughinegotiatio
  nprocess1998.

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Negotiation Analysis

• decision analysis
• game theory
• Negotiation analysis \citesebeniusNA92 is used
  to generate prescriptive advice to the supported
  party given a descriptive assessment of the
  opposing parties. \citeKerstenmodeling2001

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Uncertainty

• Problems can arise if assessment of the opposing
  parties are not available or vague.
• For one-sided uncertainty, there is a protocol
  where the uninformed agent makes all the offers
  and the informed agent either accepts or rejects
  offers \citevincentbargaining1989.
• Alternatively the uninformed agent can try to
  model the opponent using a Bayesian network or an
  influence diagram \citevassilevabilateralnegotia
  tion2002.

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Types of Games

• Perfect
• Each information set is a singleton.
• Certain
• Nature does not move after any player moves.
• Symmetric
• No player has information different from other
  players when he moves, or at the end nodes.
• Complete
• Nature does not move first, or her initial move
  is observed by every player.

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A Game of Incomplete Information

• The use of the word uncertainty in this paper
  should not be confused with a game of
  uncertainty. We are handling an imperfect,
  asymmetric, incomplete but certain game, where
  there is a two-sided uncertainty about the
  preferences of the opponents who are bargaining.

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Two-sided Uncertainty

• The problem of two-sided uncertainty can be
  addressed using recursive modeling
  \citegmyrecursivemodel1995. Nevertheless, for
  complex multi-issue negotiations, it could be
  computationally intractable.

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Incomplete Information

• The solution to the bilateral negotiation problem
  of incomplete information is addressed in the
  literature by giving a continuous distribution or
  discrete probabilities over the other agent's
  \emphtype and using Bayesian rule to learn the
  type during the negotiation. The negotiation
  protocol used is sequential alternating protocol
  (SAP) \citerubinsteinperfectequilibrium1982.

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Sequential Equilibra

• For single issue negotiation that negotiates on
  price, the type of the other agent is represented
  by its reservation price. These distributions are
  common knowledge. As a result, there is no
  subgame-perfect equilibrium, which requires that
  the predicted solution to a game be a Nash
  equilibrium in every subgame. Rubinstein analyzed
  it using a stronger equilibrium concept of
  sequential equilibra \citerubinsteinperfectequil
  ibrium1982.

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Sequential Equilibra cont.

• It requires that each uncertain player's belief
  be specified given every possible history, and
  Bayes rules are used to make beliefs consistent.
  However, if the other agent's behavior deviates
  from the equilibrium path, an update problem may
  occur since non-equilibrium paths are assigned
  zero probability.
• This may result in incentives for agents to
  deviate from the equilibrium, so as to increase
  the number of possible outcomes
  \citefaratinautomatednegotiation2000.

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Analysis Difficulties

• Derivation from equilibrium behavior cannot be
  ruled out in games via SAP with two-sided
  uncertainty. The situation could be worse for
  multi-issue negotiation, since types of agents
  increase dramatically as the number of issues
  increases. Besides, in a multi-issue negotiation,
  it is not necessarily true that the agreement
  that is worst for one agent is best for another,
  or vise versa. This makes the analysis of the
  intentions of each offer proposed by the opponent
  significantly more difficult.

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Random Selection Process ?

• In the decision making behaviors of human, people
  rely on random selection processes, such as
  flipping a coin, to handle a decision that
  involves too much uncertainty and subsequently it
  becomes difficult for them to rationally judge a
  decision. However, considering the problem of
  computation complexity, the question resides in
  the possibility for agents participating in a
  multi-issue negotiation with two-sided
  uncertainty to simply flip a coin to decide on
  every issue.

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A Mediation Game

• As commented in \citeraiffanegotiationart1982,
  it is neither feasible nor logical to do so.
  Flipping a coin on every issue will not generate
  mutually beneficial outcomes. We propose a
  mediation protocol that is based the Single
  Negotiation Text (SNT) device suggested by Roger
  Fisher \citefishermediation1978. This protocol
  presents a deal construction game to both
  protagonists, where they actively participate in
  this construction process to find a mutually
  beneficial agreement.

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A Scenario

• let us say that there are two companies A and B,
  which have control over different resources, such
  that they do same jobs with different costs.
  There is a case that some customer would like to
  have his tasks being done with the price of m
  dollars. A and B discover that if one of them is
  going to do the tasks alone, the profit is almost
  zero (equal bargaining power). On the contrary,
  if they can negotiate a plan of task sharing, the
  profit can increase. However, how they can divide
  the set of tasks and the money at the same time
  fairly without disclosing too much confidential
  information, given that they may have to compete
  with each other in another case, becomes the main
  challenge.

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Assumptions

• Expected Utility Maximizer
• One-off Negotiation
• Asymmetric Abilities
• Inter-independent Issues
• Two-sided Uncertainty
• Inter-agent Comparison of Utility

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Single Negotiation Text

• A mediation device suggested by Roger Fisher
  \citefishermediation1978.
• During the negotiation, the mediator firstly
  devised and proposed a deal (SNT-1) for the
  consideration of the two protagonists.
• The mediator is not trying to push the first
  proposal, but that it is meant to serve as an
  initial, single negotiating text---a text to be
  criticized by both sides and then modified in an
  iterative manner. Modifications to the SNT-1 will
  be made by the mediator based on the criticisms
  of the two sides.

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Fairness

• The SNT technique is to be used as a means of
  focusing the attention of both sides on the same
  composite text. The important thing is that this
  process appear to be fair to both sides, not
  divisive.

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SNT-1

• SNT-1 can be generated by locating a converging
  point from a dance of packages (see
  Figure\reffigju) or a focal point (for
  example, the mid-value on each continuous
  factor). When trying to generate the SNT-1, both
  agents must know that they are not haggling about
  a final contract, but a starting point for the
  pursuit of joint gains.

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Iteration

• After the SNT-1 has been located, both
  protagonists then try to improve it
  simultaneously or by taking turns.
• The mediator will take both protagonists'
  criticisms or suggestions into consideration, and
  generate a new version of SNT for further
  revisions. This process continues until all the
  issues are settled.

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The Challenge

• The SNT technique had been applied by U.S. on the
  mediation of Egyptian-Israeli conflict in early
  1977, known as Camp David Negotiations. Part of
  the story can be found in \citeraiffanegotiation
  art1982.
• The challenge of SNT, as noted by Raffia, is How
  can we devise negotiating processes that will
  encourage more honest revelations and less
  strategic behavior?

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Def deal

• A deal D is represented by a binary string in A's
  view
• h b1,b2,,bni h c1,c2,,cp,r1,r2, ,rqi
• ci represents a bit that will result in negative
  utility (cost) for A when false (ci 0), while
  ri is a bit that will generate positive utility
  (revenue) for A when true (ci 1).

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Def deal cont.

• The money earned is mapped to the ri bits. Each
  ri represents a bag of money used for exchange.
  As suggested in citep. 216raiffanegotiationart
  1982, the issues to be negotiated should be in
  comparable magnitude of importance, so that
  protagonists might then agree to resolve each
  issue separately by the toss of a coin. Therefore
  we let the amount of a bag of money be

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Def profits

• The total cost (TC) and total revenue (TR) of a
  deal D is
• TCA(D)?1 j p CostA(cj) (1-cj).
• TRA(D)?1 j q RevenueA(rj) rj.
• TCB(D)?1 j p CostB(cj) (cj).
• TRB(D)?1 j q RevenueB(rj) (1-rj).
• The profit gained is
• Profiti(D) TRi(D) - TCi(D).
• For each agent, a rational deal D must satisfy
  Profit(D) gt 0.

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Def utility

• The utility of a deal D is
• Utilityi(D) Profiti(D) ?1 j p Costi(cj).
• The utility generated by a set of bits OCR,
  where C is a set of cost bits and R is a set of
  revenue bits, is

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Game

• Players two players in our scenario
• Actions
• Information
• Strategies
• Payoff
• Outcome
• Equilibrium

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Sequtial Match
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Fairness Constructiveness

• This mediation process can produce a fair and
  constructive outcome if both agents do choose
  their preferred bits sequentially.
• For a fair outcome, we mean that each agent will
  have a probability 0.5 of getting the utility
  from a bit if they are faced with a direct
  conflict. Otherwise, they can trade their less
  preferred bits for more preferred bits to get a
  constructive outcome, which means that both
  agents get higher final utility than flipping a
  coin on every bit.

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Strategic Move

• However, an agent can strategically choose a less
  preferred bit firstly to increase its final
  utility.

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The DOT Strategy

• We named it the Delay of Trades (DOT) strategy.
  (4-DOT, 3-DOT)

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3-DOT

• 4-DOT
• O2(Conflict ? Win) xg. O3(Conflict ? Lose)
• 3-DOT
• O2(Lose ? Conflict) xg. O3(Conflict ? Lose)

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Note

• In the DOT abstraction, when we say U(O1)
  U(O2), we mean that
• For Every bit bj 2 O1 and every bit bk 2 O2
• U(bj) U(bk)
• Also
• (O1) (O2)

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Utility Gain in the DOT Strategy

• 4-DOT
• From
• To
• Gain

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Utility Gain in the DOT Strategy

• 3-DOT
• From
• To
• Gain

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Success Condition of DOT

• For A to success
• A must know Bs utility function
• B must report his preference honestly
• (B does not know As utility function)

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The Mediation Protocol
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The Binary Match Game

• Since A and B may partially agree on the some of
  the issues, some part (bits) in SNT-2 will be
  fixed, which means that these bits can not be
  further modified in the next stage. A and B then
  concentrate on the resolution of the remaining
  issues until all issues are settled.

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Trades

• The bits bi and bj (iltgt j) is said to be traded
  if one of them is assigned a value 1 (in A's
  favor) and the other is assigned a value 0 (in
  B's favor).
• A good trade occurs when a less preferred bit is
  traded for a more preferred bit from both agents'
  view. On the contrary, a bad trade may occur when
  a more preferred bit is traded for a less
  preferred.
• If a trade is beneficial to only one of them, but
  indifferent to the other, we call it a
  single-interest trade.

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Negotiation Strategy

• A negotiation strategy is a function from the
  history of the negotiation to the current action
  (bits relocation) that is consistent with the
  mediation protocol.

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The BH Strategy

• Since the SNT-1 is randomly traded, it is fair
  but not constructive. A and B may have different
  ideas on how the 1-bits and 0-bits should be
  relocated.
• According to A's utility function, there exists a
  better half ?½?, such that (?)d(?)/2e and 8
  bi2?, 8 bj2bar?, UA(bi)gtUA(bj). If A generates
  SNT(A,t) by relocating 1-bits in SNT-t to the
  better half ?, we say that A is using the BH
  (better half) strategy.

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Further Trades

• If both agents use the BH strategy to relocate
  the 1-bits and 0-bits in SNT-t, some good trades
  may be found.
• To encourage further trades, the conflicting bits
  (those not yet grayed) are separated into two
  divisions ? (better half) and ? (lesser half),
  marked as B and L in Figure.
• Now both ? and ? are treated as sets of
  conflicting bits to be resolved separately
  (enforcing trades within each division).

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Final Match

• When there are two bits left in SNT-t, both
  agents must submit their preferences over the
  combinations of h 1,0i and h 0,1i. If they agree
  on the same combination, the mediation is done.
  Otherwise, the mediator must flip a coin to
  decide that which combination is selected. We
  named this mediation protocol the Match-Game
  Mediation (MGM) Protocol.

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Pareto Optimal

• We say that a deal D dominates D0, and write DÂ
  D0, if and only if (UtilityA(D),
  UtilityB(D))À(UtilityA(D0), UtilityB(D0)) (it is
  better for at least one agent and not worse for
  the other).
• A deal D is called pareto optimal if there does
  not exist another deal D0 such that D0Â D.

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Preference Indifference

• If both agents use the BH strategy, and the
  information of preference indifference is
  disclosed, then both good trades and
  single-interested trades can be discovered by the
  proposed mediation protocol, since the MGM
  protocol exhaustively searches all possible
  trades utilizing the concept of divide and
  conquer. Therefore, the mediation result is
  pareto optimal.

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The DOT strategy in MGM
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Strategic Behavior in MGM

• The DOT strategy will generate higher utility if
  O1 can be successfully traded for O2 and O3 can
  be successfully traded for O4 at the same time.
  In case 1, if B wants to use the DOT strategy, it
  must strategically cause a conflict in the first
  match by reporting that O4 is not in his better
  half.

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Causing a Conflict

• There are two ways of causing a conflict
• Causing a full conflict B reports that its
  better half and A's are the same. B can
  strategically do so to delay the trades of bits
  till the second round.
• Causing a partial conflict In case 1, B can
  report that its better half does not include O4
  (but include O2), then O1 is traded for O2.

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Beneficial Strategic Behaviors

• In case 1, if B strategically cause a full
  conflict, O1 will be in the ? division of the
  next SNT, while O2 is in the ? division. We know
  that trades are only allowed within each
  division, but not across divisions. This
  strategic behavior does not benefit B. The same
  rationale forbids the strategic bahvior of
  causing a full conflict in case 3. But B can
  benefit from causing a full conflict in case 2.
• B can benefit from causing a partial conflict in
  case 1 and case 3.

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Nash Equilibrium

• A negotiation strategy s will be in equilibrium
  if the following condition holds under the
  assumption that A uses s, B prefer s to any other
  strategy.

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Case 1

• We assume K(E) µ E µ P(E)
• KA(UA), KB(UB), KA(KB(UA)) and KB(KA(UB)) is
  common knowledge.
• Then BH strategy is in equilibrium.

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Case 1 Proof

• Assume that A uses the BH strategy. If B also
  uses the BH strategy, the utility gained is the
  sum of the utility gained from good trades. Let
  Og denotes the bits that are traded, and Oc
  denotes the bits that cause conflicts. The deal
  is DOg Oc. Let BH(Og) denotes the bits in Og
  that are also in the better half, and LH(Og)
  denotes the bits in Og that are also in the
  lesser half.
• If a trade occurs, the 0-bit is in BH(Og) and the
  1-bit is in LH(Og), since B has relocated all the
  0-bits to the better half. Therefore, that trade
  is a good trade.
• The utility gained in this stage is
  U(BF(Og))-(U(Og)/2).

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Case 1 Proof

• Let ? denotes the average utility if both agents
  flip a coin to decide on every issue.
• The expected utility in the end of the mediation
  if equal to or greater than
• ? U(BF(Og))-(U(Og)/2), denoted as ?z.

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Case 1 Proof

• If B does not use the BH strategy, there is a
  0-bit at the position bj that is not relocated to
  the position bi in the better half. It makes
• a good trade becomes a conflict or
• creates a smaller good trade
• A good trade becomes a conflict when some lesser
  bit can be traded for the bi but now a conflict
  occurs at the bi. A smaller good trade is
  resulted from the successfully trading of some
  lesser bit for bj. But since U(bi) gt U(bj), a
  better trade is missed. In Theorem thmHMGM, it
  is proved that a delay of good trade is not
  possible, so that the benefits of trading some
  lesser bit for bi is lost forever. Note that
  there will not be a bad trade since A uses the BH
  strategy.

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Case 2

• KA(UA), KB(UB), KB(UA) and KA(UB) is common
  knowledge.
• Nash solution D arg max UA(D)XUB(D)

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Case 3

• KA(UA) and KB(UB) are common knowledge.
• For A (BHDOT)
• KA(UB) and KA(KB(UA)) ? DOT
• KA(UB) and KA(KB(UA)) ? DOT (Signaling)
• KA(UB) and PA(KB(UA)) ? DOT
• KA(UB) ? BH

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Proof

• No matter what As or Bs private knowledge is,
  As best strategy is
• BHDOT.
• BHDOT is dominant strategy eq.

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Information Disclosed

• Minimun preference information.
• For A,
• Knowledge of KA(UB) is not disclosed.

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Bargaining Power

• The design objective of the proposed mediation
  protocol is to provide a fair and constructive
  conflict-resolution mechanism between two agents
  assuming that they have same bargaining power.
  This assumption seems to limit the applications
  of our mediation mechanism at first, but we find
  that actually most negotiation cases occur when
  both negotiating players are having same
  bargaining power. This is because that if one of
  the players has greater bargaining power, he can
  force the other player to concede in the
  negotiation.

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Bargaining Power (cont.)

• citerubinsteinperfectequilibrium1982,fatimatime
  constraints2002 showed that the stronger player
  will claim all the pie while the weaker player
  gets almost nothing.
• In our scenario, both agents are competing the
  same case from the same customer. Therefore, they
  should have a same deadline. However, if one of
  them has lower costs of performing all the tasks
  in the case, it is considered stronger than the
  one with higher costs. The stronger agent does
  not need to negotiate with the weaker agent since
  there is no doubt that it will win the case.

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Forming Coalitions

• There has been a significant amount of work in
  game theory and multi-agent systems field in the
  area of coalition formation. However, as
  commented by Banerje \citebanerjepartners2002,
  almost all of them ignores the issues of how the
  coalitions generate their revenues or the nature
  of the problem solving adopted by individual
  agents after they form a coalition. This paper,
  on the other hand, addresses the problem of how
  the tasks and the money can be redistributed
  fairly and constructively when (or after) forming
  a coalition.

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Related Work

• Although various approaches \citezhenglearning19
  97,carmellearningmodels1996,gmyrecursivemodel199
  5 of modeling the opponent in the negotiation
  have been proposed in game theory and distributed
  artificial intelligence (DAI), they cannot
  produce a mutually beneficial negotiation outcome
  in a one-off multi-issue negotiation.

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Related Work (cont.)

• Some research therefore gives up the idea of
  modeling the opponent, but try to make an offer
  similar to the opponent's directly
  \citefaratinsimilarity2002,linfixedpie2002,
  so as to approximate the opponent's preference
  structure and generate a mutually beneficial
  outcome. However, these mechanisms cannot satisfy
  the requirement of game theoretic rationality,
  since there are no rational strategies in making
  concessions in a negotiation with two-sided
  uncertainty.

70
Conclusion

• We believe that the idea of creating a fair and
  constructive mediation game to resolve the
  conflicts in a multi-issue negotiation may point
  out another possible research direction.
• The mediator in this game does not necessarily
  exist, because the mediation process is fair and
  can be verified by both agents. Nevertheless,
  some fair random selection service is required to
  simulate a fair coin.

71
Future Work

• Multi-lateral Multi-Issue Negotiation