# Multi-player Multi-issue Negotiation with Mediator using CP-nets

### Thiri Haymar Kyaw, Sujata Ghosh, Rineke Verbrugge

#### Abstract

This paper presents a simple interactive negotiation approach for conflicts in everyday life with incomplete information. We focus on mediation to obtain an agreement while going through alternating offers over a finite time bargaining game. The mediator searches and proposes a jointly optimal negotiation text for all players participating in the negotiation process based on their conditional preference networks (CP-nets). The players make a decision whether to accept or reject by examining their utility CP-nets. We develop two algorithms for the mediator and the players. If the first negotiation text cannot be accepted by all players, the mediator offers the next negotiation texts by searching for jointly optimal solutions. This negotiation process continues until an agreement is achieved or a deadline is reached. This proposed approach can support multi-issue, multi-party negotiation to achieve an agreement during a finite number of rounds with near optimal outcomes.

#### References

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- Algorithm 2: Negotiation by Mediator.
- 1: Input:
- 2: Player N: N = (1; 2; : : : ; n)
- 3: CPN1;CPN2; : : : ;CPNn //Players' CP-nets
- 4: S1; S2; :::; Sn //Players' proposals
- 5: maxP 0:9; avgP 0:5 //maximum and average acceptable probability
- 6: Agreement 0; JointOptimal 0/; t 0
- 7: threshold 0:3
- 8: while Agreement 6= 1 and t 6 f inalRound do
- 9: for i = 1 to n do
- 10: for j = 1 to n do
- 11: Search acceptableProbability (Si; S j : i 6= j)
- 12: end for
- 13: end for
- 14: Mark all Si; S j: acceptableProbability < threshold;
- 15: while maxP > avgP do
- 16: for i = 1 to n do
- 17: for j = 1 to n do
- 18: if 9Si : (acceptableProbability(Si; S j) = maxP ; i 6= j) then
- 19: JointOptimal Si
- 20: else
- 21: Search alternativeOptimal(Si) //Other proposals with same maxP
- 22: if 9Sl : (acceptableProbability(Sl ; S j) = maxP; l 6= j) then
- 23: JointOptimal Sl
- 24: else
- 25: maxP maxP 0:1
- 26: end if
- 27: end if
- 28: end for
- 29: end for
- 30: end while
- 31: Propose JointOptimal
- 32: if 8 Player k 2 N accept Proposal then
- 33: Agreement 1
- 34: else if Player k (k 2 N) rejects Si then
- 35: Ask new proposal to Player k
- 36: Update Si (i = k)
- 37: maxP 0:9
- 38: end if
- 39: end while
- 40: if Agreement = 0 and t = finalRound then
- 41: Announce finalRound and Ask for evaluating all proposals to Players
- 42: end if

#### Paper Citation

#### in Harvard Style

Kyaw T., Ghosh S. and Verbrugge R. (2013). **Multi-player Multi-issue Negotiation with Mediator using CP-nets** . In *Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-8565-38-9, pages 99-108. DOI: 10.5220/0004256900990108

#### in Bibtex Style

@conference{icaart13,

author={Thiri Haymar Kyaw and Sujata Ghosh and Rineke Verbrugge},

title={Multi-player Multi-issue Negotiation with Mediator using CP-nets},

booktitle={Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2013},

pages={99-108},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004256900990108},

isbn={978-989-8565-38-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - Multi-player Multi-issue Negotiation with Mediator using CP-nets

SN - 978-989-8565-38-9

AU - Kyaw T.

AU - Ghosh S.

AU - Verbrugge R.

PY - 2013

SP - 99

EP - 108

DO - 10.5220/0004256900990108