Computing equilibria for constraint-based negotiation games with interdependent issues

Negotiation with interdependent issues and nonlinear, non-monotonic utility functions is difficult because it is hard to efficiently explore the contract space. This paper presents a new result in automated negotiations with interdependent issues, complete information and time constraints. We consider that agents express their preferences using constraints defined as one interval per issue and that we represent their constraint sets as intersection graphs. We model negotiations as a bargaining game and we show that the equilibrium solution is one of the maximal cliques of the constraint graph. Consequently, we find that the problem of computing the equilibrium solution has polynomial-time complexity when the number of issues is fixed.

[1]  R. Möhring.  Algorithmic graph theory and perfect graphs , 1986 .

[2]  A. Rubinstein.  Perfect Equilibrium in a Bargaining Model , 1982 .

[3]  Issues , 2004 .

[4]  Frances M. T. Brazier,et al.  Expressing Intervals in Automated Service Negotiation , 2010 .

[5]  Ahmad Kardan,et al.  A Multi-issue Negotiation Mechanism with Interdependent Negotiation Issues , 2008, Second International Conference on the Digital Society.

[6]  Jacques Wainer,et al.  Scheduling meetings through multi-agent negotiations , 2007, Decis. Support Syst..

[7]  B. Peyton,et al.  An Introduction to Chordal Graphs and Clique Trees , 1993 .

[8]  N. R. Jennings,et al.  Multi-Issue Negotiation with Deadlines , 2006, J. Artif. Intell. Res..

[9]  Hiromitsu Hattori,et al.  Multi-issue Negotiation Protocol for Agents: Exploring Nonlinear Utility Spaces , 2007, IJCAI.

[10]  Robert E. Tarjan,et al.  Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[11]  Valentin Robu,et al.  Modeling complex multi-issue negotiations using utility graphs , 2005, AAMAS '05.

[12]  Mark Klein,et al.  Negotiating Complex Contracts , 2003, AAMAS '02.

[13]  Nicholas R. Jennings,et al.  An analysis of feasible solutions for multi-issue negotiation involving nonlinear utility functions , 2009, AAMAS.

[14]  M. Klein,et al.  A Multi-Phase Protocol for Negotiation with Interdependent Issues , 2007, 2007 IEEE/WIC/ACM International Conference on Intelligent Agent Technology (IAT'07).

[15]  M. Golumbic.  Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57) , 2004 .

[16]  Yan Jin,et al.  Roles of Negotiation Protocol and Strategy in Collaborative Design , 2008 .

[17]  Elhadi M. Shakshuki,et al.  Negotiation Strategies for Agent-based Meeting Scheduling System , 2007, Fourth International Conference on Information Technology (ITNG'07).

[18]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[19]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[20]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..

[21]  Nicholas R. Jennings,et al.  Approximate and online multi-issue negotiation , 2007, AAMAS '07.

[22]  Takayuki Ito,et al.  A Preliminary Analysis of Computational Complexity of the Threshold Adjusting Mechanism in Multi-issue Negotiations , 2007, 2007 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology - Workshops.

[23]  D. R. Fulkerson,et al.  Incidence matrices and interval graphs , 1965 .