A Logical Multidemand Bargaining Model with Integrity Constraints
Xiaoxin Jing
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275 People's Republic of China
Department of Philosophy, College of Political Science and Law, Capital Normal University, Beijing, 100048 People's Republic of China
e-mail: [email protected]
Search for more papers by this authorDongmo Zhang
Intelligent System Lab, School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, NSW 2751 Australia
e-mail: [email protected]
Search for more papers by this authorCorresponding Author
Xudong Luo
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275 People's Republic of China
Author to whom all correspondence should be addressed; e-mail: [email protected]Search for more papers by this authorJieyu Zhan
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275 People's Republic of China
e-mail: [email protected]
Search for more papers by this authorXiaoxin Jing
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275 People's Republic of China
Department of Philosophy, College of Political Science and Law, Capital Normal University, Beijing, 100048 People's Republic of China
e-mail: [email protected]
Search for more papers by this authorDongmo Zhang
Intelligent System Lab, School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, NSW 2751 Australia
e-mail: [email protected]
Search for more papers by this authorCorresponding Author
Xudong Luo
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275 People's Republic of China
Author to whom all correspondence should be addressed; e-mail: [email protected]Search for more papers by this authorJieyu Zhan
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275 People's Republic of China
e-mail: [email protected]
Search for more papers by this authorAbstract
This paper proposes a logical model of multi-demand bargaining with integrity constraints. We also construct a simultaneous concession solution to bargaining games of this kind and show that the solution is uniquely characterized by a set of logical properties. Moreover, we prove that the solution also satisfies the most fundamental game theoretic properties such as symmetry and Pareto optimality. In addition, by lots of simulation experiments we study how the number of conflicting demands, bargainers' risk attitude, and bargainer number influence the bargaining success rate and efficiency as well as the agreement quality.
References
- 1Xiong N, Christensen H, Svensson P. Agent negotiation of target distribution enhancing system survivability. Int J Intell Syst 2007; 22(12): 1251–1269.
- 2Huang Z, Huang Q. To reach consensus using uninorm aggregation operator: A gossip-based protocol. Int J Intell Syst 2012; 27(4): 375–395.
- 3Nash JF, Jr. The bargaining problem. Econometrica 1950; 18(2): 155–162.
- 4Binmore K, Rubinstein A, Wolinsky A. The Nash bargaining solution in economic modelling. RAND J Econ 1986; 17(2): 176–188.
- 5Shubik M. Game theory in the social sciences: Concepts and solutions. Cambridge, MA: MIT Press; 2006.
- 6Raiffa H. The art and science of negotiation. Cambridge, MA: Harvard University Press; 1982.
- 7Jennings NR, Faratin P, Lomuscio AR, Parsons S, Wooldridge MJ, Sierra C. Automated negotiation: Prospects, methods and challenges. Group Decis Negot 2001; 10(2): 199–215.
- 8Fatima SS, Wooldridge M, Jennings NR. An agenda-based framework for multi-issue negotiation. Artif Intell 2004; 152(1): 1–45.
- 9Zhang D. A logic-based axiomatic model of bargaining. Artif Intell 2010; 174(16–17): 1307–1322.
- 10Kraus S, Sycara K, Evenchik A. Reaching agreements through argumentation: A logical model and implementation. Artif Intell 1998; 104: 1–69.
- 11Parsons S, Sierra C, Jennings NR. Agents that reason and negotiate by arguing. J Logic Comput 1998; 8(3): 261–292.
- 12Luo X, Jennings NR, Shadbolt N, Leung H-f, Lee JH-m. A fuzzy constraint based model for bilateral, multi-issue negotiations in semi-competitive environments. Artif Intell 2003; 148(1): 53–102.
- 13Zhang D, Zhang Y. An ordinal bargaining solution with fixed-point property. J Artif Intell Res 2008; 33(1): 433–464.
- 14Zhan J, Luo X, Sim KM, Feng C, Zhang Y. A fuzzy logic based model of a bargaining game. In: Knowledge science, engineering and management, Lecture Notes in Artificial Intelligence, Vol 8041. Berlin: Springer; 2013. pp 387–403.
- 15Konieczny S, Ramón P-P. Merging information under constraints: A logical framework. J Logic Comput 2002; 12(5): 773–808.
- 16Zhang D, Foo N. Infinitary belief revision. J Philos Logic 2001; 30(6): 525–570.
- 17Gärdenfors P, Makinson D. Revisions of knowledge systems using epistemic entrenchment. In: Proc 2nd Conf on Theoretical Aspects of Reasoning about Knowledge; 7–9 March 1988. California, USA. pp 83–95.
- 18Roth AE. Axiomatic models of bargaining. Technical report, David K. Levine; 1979.
- 19Ghosh A, Kale S, Lang K, Moseley B. Bargaining for revenue shares on tree trading networks. arXiv preprint arXiv:1304.5822; 2013.
- 20Booth R. Social contraction and belief negotiation. In: Proc 8th Int Conf on Principles and Knowledge Representation and Reasoning; 22–25 April 2002. Toulouse, France. Vol 2, pp 375–384.
- 21Zhang D, Foo N, Meyer T, Kwok R. Negotiation as mutual belief revision. In: Proc 19th National Conf on Artificial Intelligence; 25–29 July 2004. California, USA. pp 317–322.
- 22Meyer TA, Foo NY, Kwok R, Zhang D. Logical foundations of negotiation: Strategies and preferences. In: Proc 9th Int Conf on the Principles of Knowledge Representation and Reasoning; 2–5 June 2004. British Colombia, Canada. pp 311–318.
- 23Alchourrón CE, Grdenfors P, Makinson D. On the logic of theory change: Partial meet contraction and revision functions. J Symbolic Logic 2013; 50: 510–530.
- 24Chen W, Zhang D, Wu M. A sequential model for reasoning about bargaining in logic programs. In: Logic programming and nonmonotonic reasoning. Berlin: Springer; 2013. pp 239–244.
10.1007/978-3-642-40564-8_24 Google Scholar
- 25Vo QB, Li M. From axiomatic to strategic models of bargaining with logical beliefs and goals. In: Proc 11th Int Conf on Autonomous Agents and Multiagent Systems; 4–8 June 2012. Valencia, Spain. Vol 1, pp 525–532.
- 26Zhan J, Luo X, Ma W, Zhang Y. A multi-demand adaptive bargaining based on fuzzy logic. In: Proc 6th Int Conf on Agents and Artificial Intelligence. 6–8 March 2014, Loire Valley, France. pp 577–585.
- 27Zhan J, Luo X, Feng C, Ma W. A fuzzy logic based bargaining model in discrete domains: Axiom, elicitation and property. In: Proc 2014 IEEE Int Conf on Fuzzy Systems; 6–11 July 2014. Beijing, China. pp 424–431.
- 28Luo X, Miao C, Jennings NR, He M, Shen Z, Zhang M. KEMNAD: A knowledge engineering methodology for negotiating agent development. Comput Intell 2012; 28(1): 51–105.
- 29Luo X, Jennings NR., Shadbolt N. Acquiring user tradeoff strategies and preferences for negotiating agents: A default-then-adjust method. Int J Human Comput Stud 2006; 64(4): 304–321.
- 30Lin J, Mendelzon AO. Merging databases under constraints. Int J Coop Inform Syst 1998; 7(01): 55–76.
- 31Konieczny S, Ramón P-P. On the logic of merging. In: Proc 6th Int Conf on Principles of Knowledge Representation and Reasoning. Trento, Italy; 2–5 June 1998. pp 488–498.
- 32Zhang Y, Luo X, Leung H-f. Fuzzily constrained games. In: Proc 2013 IEEE/WIC/ACM Int Conf on Web Intelligence and Intelligent Agent Technology; 17–20 November 2013, Atlanta, GA, USA. pp 361–368.
- 33Dunne PE, van der Hoek W, Kraus S, Wooldridge M. Cooperative Boolean games. In: Proc 7th Int Joint Conf on Autonomous Agents and Multiagent Systems; 12–16 May 2008. Estoril Portugal. Vol 2, pp 1015–1022.
- 34Harrenstein P, van der Hoek W, Meyer J-J, Witteveen C. Boolean games. In: Proc 8th Conf on Theoretical Aspects of Rationality and Knowledge; 8–10 July 2001. Certosa di Pontignana, Italy. pp 287–298.
- 35Ågotnes T, Harrenstein P, van der Hoek W, Wooldridge M. Verifiable equilibria in Boolean games. In: Proc 23rd Int Joint Conf on Artificial Intelligence; 3–9 August 2013. Beijing, China. pp 689–695.
- 36Pan L, Luo X, Meng M, Miao C, He M, Guo X. A two-stage win-win multiattribute negotiation model: Optimazationa and then concession. Comput Intell 2013; 29(3): 577–626.
- 37Cao M, Luo X, Luo XR, Dai X. Automated negotiation for e-commerce decision making: A goal deliberated agent architecture for multi-strategy selection. Decis Support Syst 2015; 73: 1–14.
- 38Luo X, Zhang C, Jennings NR. A hybrid model for sharing information between fuzzy, uncertain and default reasoning models in multi-agent systems. Int J Uncertain Fuzziness Knowl-Based Syst 2002; 10(4): 401–450.
- 39Schwartz DG. Qualified syllogisms with fuzzy predicates. Int J Intell Syst 2014; 29(10): 926–945.
- 40Jing X, Luo X, Zhang Y. A fuzzy dynamic belief logic system. Int J Intell Syst 2014; 29(7): 687–711.
- 41Luo X, Lee JH-M, Leung H-f, Jennings NR. Prioritised fuzzy constraint satisfaction problems: Axioms, instantiation and validation. Fuzzy Sets Syst 2003; 136(2): 151–188.
- 42Ramk J. Incomplete fuzzy preference matrix and its application to ranking of alternatives. Int J Intell Syst 2014; 29(8): 787–806.
- 43Atiq ur Rehman E, Kerre E, Ashraf S. Group decision making by using incomplete fuzzy preference relations based on t-consistency and the order consistency. Int J Intell Syst 2015; 30(2): 120–143.
- 44Jing X, Zhang D, Luo X. A logic framework of bargaining with integrity constraints. In AI 2013: Advances in artificial intelligence. Lecture Notes in Computer Science, Vol 8272. Berlin: Springer; 2013. pp 1–13.
10.1007/978-3-319-03680-9_1 Google Scholar
