Skip to main content
Log in

A Game-theoretic approach to analyze interacting actors in GRL goal models

  • Original Article
  • Published:
Requirements Engineering Aims and scope Submit manuscript

Abstract

Goal-oriented requirements engineering aims to capture desired goals and strategies of relevant stakeholders during early requirements engineering stages, using goal models. Goal-oriented modeling techniques support the analysis of system requirements (especially non-functional ones) from an operationalization perspective, through the evaluation of alternative design options. However, conflicts and undesirable interactions between requirements produced from goals are inevitable, especially as stakeholders often aim for different objectives. In this paper, we propose an approach based on game theory and the Goal-oriented Requirement Language (GRL) to reconcile interacting stakeholders (captured as GRL actors), leading to reasonable trade-offs. This approach consists in building a payoff bimatrix that considers all actor’s valid GRL strategies, and computing its Nash equilibrium. Furthermore, we use two optimization techniques to reduce the size of the payoff bimatrix, hence reducing the computational cost of the Nash equilibrium. The approach goes beyond existing work by supporting nonzero-sum games, multiple alternatives, and inter-actor dependencies. We demonstrate the applicability of our game-theoretic modeling and analysis approach using a running example and two GRL models from the literature, with positive results on feasibility and applicability, including performance results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. See https://en.wikipedia.org/wiki/List_of_games_in_game_theory for a list of games and their characteristics.

  2. Scripts and generated data are attached to the revision and will be available online upon acceptance.

References

  1. Affleck A, Krishna A (2012) Supporting quantitative reasoning of non-functional requirements: A process-oriented approach. In: Proceedings of the International Conference on Software and System Process, ICSSP ’12, pp. 88–92. IEEE Press, Piscataway, NJ, USA https://doi.org/10.5555/2664360.2664375

  2. Akhigbe O, Alhaj M, Amyot D, Badreddin O, Braun E, Cartwright N, Richards G, Mussbacher G (2014) Creating quantitative goal models: Governmental experience. In: E. Yu, G. Dobbie, M. Jarke, S. Purao (eds.) Conceptual Modeling, Lecture Notes in Computer Science, pp. 466–473. Springer. https://doi.org/10.1007/978-3-319-12206-9

  3. Amyot D, Ghanavati S, Horkoff J, Mussbacher G, Peyton L, Yu E (2010) Evaluating goal models within the goal-oriented requirement language. Int J Intell Syst 25:841–877. https://doi.org/10.1002/int.v25:8

    Article  Google Scholar 

  4. Amyot D, Shamsaei A, Kealey J, Tremblay E, Miga A, Mussbacher G, Alhaj M, Tawhid R, Braun E, Cartwright N (2012) Towards advanced goal model analysis with jUCMNav. In: Advances in Conceptual Modeling, pp. 201–210. Springer. https://doi.org/10.1007/978-3-642-33999-8

  5. Anda AA, Amyot D (2019) Arithmetic semantics of feature and goal models for adaptive cyber-physical systems. In: 2019 IEEE 27th International Requirements Engineering Conference (RE), pp. 245–256. IEEE CS https://doi.org/10.1109/RE.2019.00034

  6. Boehm B, Bose P, Horowitz E, Lee MJ (1995) Software requirements negotiation and renegotiation aids. In: Proceedings of the 17th international conference on Software engineering, ICSE ’95, pp. 243–253. ACM, New York, NY, USA https://doi.org/10.1145/225014.225037

  7. Bryl V, Giorgini P, Mylopoulos J (2006) Designing cooperative IS: exploring and evaluating alternatives. On the Move to Meaningful Internet Syst 2006:533–550. https://doi.org/10.1007/11914853_32

    Article  Google Scholar 

  8. Bryl V, Giorgini P, Mylopoulos J (2006) Requirements analysis for socio-technical systems: Exploring and evaluating alternatives. Tech. rep., DIT-06-006, University of Trento, Italy http://eprints.biblio.unitn.it/965/1/006.pdf

  9. Chung L, Nixon BA, Yu E, Mylopoulos J (1999) Non-functional requirements in software engineering. Kluwer Academic Publishers Group, Dordrecht, Netherlands

    MATH  Google Scholar 

  10. Deb N, Chaki N, Ghose AK (2016) i*tonusmv: A prototype for enabling model checking of i* models. In: 24th IEEE International Requirements Engineering Conference, RE 2016, Beijing, China, September 12-16, 2016, pp. 397–398 https://doi.org/10.1109/RE.2016.62

  11. Dufwenberg M, Stegeman M (2002) Existence and uniqueness of maximal reductions under iterated strict dominance. Econometrica 70(5):2007–2023. https://doi.org/10.1111/1468-0262.00360

    Article  MathSciNet  MATH  Google Scholar 

  12. Easterbrook S (1991) Handling conflict between domain descriptions with computer-supported negotiation. Knowl Acquisition 3(3):255–289. https://doi.org/10.1016/1042-8143(91)90007-A

    Article  Google Scholar 

  13. Franch X (2006) On the quantitative analysis of agent-oriented models. In: Dubois E, Pohl K (eds) Advanced information systems engineering. Springer, Berlin Heidelberg, pp 495–509. https://doi.org/10.1007/11767138

    Google Scholar 

  14. Fudenberg D, Tirole J (1991) Game theory (3. pr.). MIT Press

  15. Fuxman A, Mylopoulos J, Pistore M, Traverso P (2001) Model checking early requirements specifications in tropos. In: 5th IEEE International Symposium on Requirements Engineering (RE 2001), 27-31 August 2001, Toronto, Canada, pp. 174–181 https://doi.org/10.1109/ISRE.2001.948557

  16. Giorgini P, Mylopoulos J, Sebastiani R (2005) Goal-oriented requirements analysis and reasoning in the tropos methodology. Eng Appl Artif Intell 18:159–171. https://doi.org/10.1016/j.engappai.2004.11.017

    Article  Google Scholar 

  17. Hassine J, Alshayeb M (2014) Measurement of actor external dependencies in GRL models. In: Proceedings of the Seventh International i* Workshop co-located with the 26th International Conference on Advanced Information Systems Engineering (CAiSE 2014), Thessaloniki, Greece, June 16-17, 2014. http://ceur-ws.org/Vol-1157/paper22.pdf

  18. Hassine J, Amyot D (2016) A questionnaire-based survey methodology for systematically validating goal-oriented models. Requir Eng 21(2):285–308. https://doi.org/10.1007/s00766-015-0221-7

    Article  Google Scholar 

  19. Hassine J, Amyot D (2017) An empirical approach toward the resolution of conflicts in goal-oriented models. Soft Syst Model 16(1):279–306. https://doi.org/10.1007/s10270-015-0460-6

    Article  Google Scholar 

  20. Horkoff J, Yu ESK (2009) Evaluating goal achievement in enterprise modeling - an interactive procedure and experiences. In: The Practice of Enterprise Modeling, Second IFIP WG 8.1 Working Conference, PoEM 2009, Stockholm, Sweden, November 18-19, 2009. Proceedings, pp. 145–160 https://doi.org/10.1007/978-3-642-05352-8_12

  21. Horkoff J, Yu ESK (2009) A qualitative, interactive evaluation procedure for goal- and agent-oriented models. In: E.S.K. Yu, J. Eder, C. Rolland (eds.) Proceedings of the Forum at the CAiSE 2009 Conference, Amsterdam, The Netherlands, 8-12 June 2009, CEUR Workshop Proceedings, vol. 453. CEUR-WS.org http://ceur-ws.org/Vol-453/paper04.pdf

  22. IBM: Ibm cplex optimizer. https://www.ibm.com/analytics/cplex-optimizer. Last Accessed May 2020

  23. ITU-T: Recommendation Z.151 (10/18), User Requirements Notation (URN) language definition, Geneva, Switzerland (2018). http://www.itu.int/rec/T-REC-Z.151/en

  24. Jiang X, Pauly A (2014) Efficient decomposition of bimatrix games (extended abstract). Elect Proc Theoret Comput Sci 146:75–81. https://doi.org/10.4204/eptcs.146.10

    Article  MathSciNet  MATH  Google Scholar 

  25. jUCMNav: v7.0.0. http://softwareengineering.ca/jucmnav, University of Ottawa, Canada. Last Accessed May 2020

  26. Jureta I, Faulkner S, Schobbens PY (2008) Clear justification of modeling decisions for goal-oriented requirements engineering. Requir Eng 13(2):87–115. https://doi.org/10.1007/s00766-007-0056-y

    Article  Google Scholar 

  27. Knuth DE, Papadimitriou CH, Tsitsiklis JN (1988) A note on strategy elimination in bimatrix games. Operats Res Lett 7(3):103–107. https://doi.org/10.1016/0167-6377(88)90075-2

    Article  MathSciNet  MATH  Google Scholar 

  28. van Lamsweerde A (2008) Requirements engineering: from craft to discipline. In: Proceedings of the 16th ACM SIGSOFT International Symposium on Foundations of Software Engineering (FSE 2008), pp. 238–249. ACM https://doi.org/10.1145/1453101.1453133

  29. van Lamsweerde A (2009) Reasoning about alternative requirements options. In: Conceptual Modeling: Foundations and Applications - Essays in Honor of John Mylopoulos, pp. 380–397 https://doi.org/10.1007/978-3-642-02463-4_20

  30. Lee K, Lee S (2015) Applying game theoretic approach to goal-driven requirements trade-off analysis for self-adaptation. In: 39th Annual Computer Software and Applications Conference, COMPSAC Workshops 2015, Taichung, Taiwan, July 1-5, 2015, pp. 330–335 https://doi.org/10.1109/COMPSAC.2015.158

  31. Liaskos S, McIlraith SA, Sohrabi S, Mylopoulos J (2011) Representing and reasoning about preferences in requirements engineering. Requir Eng 16(3):227. https://doi.org/10.1007/s00766-011-0129-9

    Article  Google Scholar 

  32. Mirbel I, Villata S (2012) Enhancing goal-based requirements consistency: An argumentation-based approach. In: M. Fisher, L. van der Torre, M. Dastani, G. Governatori (eds.) Computational Logic in Multi-Agent Systems, Lecture Notes in Computer Science, vol. 7486, pp. 110–127. Springer Berlin Heidelberg https://doi.org/10.1007/978-3-642-32897-8_9

  33. Murukannaiah PK, Kalia AK, Telang PR, Singh MP (2015) Resolving goal conflicts via argumentation-based analysis of competing hypotheses. In: D. Zowghi, V. Gervasi, D. Amyot (eds.) 23rd IEEE International Requirements Engineering Conference, RE 2015, Ottawa, ON, Canada, August 24-28, 2015, pp. 156–165. IEEE Computer Society https://doi.org/10.1109/RE.2015.7320418

  34. Nash J (1951) Non-cooperative games. Ann Math 54(2):286–295. https://doi.org/10.2307/1969529

    Article  MathSciNet  MATH  Google Scholar 

  35. Nuseibeh B, Easterbrook S (2000) Requirements engineering: a roadmap. In: Proceedings of the Conference on The Future of Software Engineering, ICSE’00, pp. 35–46. ACM, New York, NY, USA https://doi.org/10.1145/336512.336523

  36. Osborne M (2004) An introduction to game theory. Oxford Univ. Press, New York, USA

    Google Scholar 

  37. Osborne MJ, Rubinstein A (1994) A course in game theory. MIT press

  38. Pauly A (2010) How incomputable is finding Nash equilibria? J Univ Comput Sci 16(18):2686–2710. https://doi.org/10.3217/jucs-016-18-2686

    Article  MathSciNet  MATH  Google Scholar 

  39. Robinson WN (1990) Negotiation behavior during requirements specification. In: Proceedings of the 12th international conference on software engineering, ICSE ’90, pp. 268–276. IEEE Computer Society Press, Los Alamitos, CA, USA https://doi.org/10.1109/ICSE.1990.63633

  40. Sadiq M, Jain SK (2014) Applying fuzzy preference relation for requirements prioritization in goal oriented requirements elicitation process. Int J Syst Assuran Eng Manag 5(4):711–723. https://doi.org/10.1007/s13198-014-0236-3

    Article  Google Scholar 

  41. Subramanian CM, Krishna A, Kaur A (2018) Game theory-based requirements analysis in the i* framework. Comput J 61(3):427–446. https://doi.org/10.1093/comjnl/bxx110

    Article  MathSciNet  Google Scholar 

  42. Sumesh S, Krishna A (2019) Mixed-strategic reasoning of the i * goal model completed research paper. In: Proceedings of the Twenty-Third Pacific Asia Conference on Information Systems http://www.pacis2019.org/wd/Submissions/PACIS2019_paper_447.pdf

  43. Sumesh S, Krishna A, Subramanian CM (2018) Optimal reasoning of opposing non-functional requirements based on game theory. In: B. Andersson, B. Johansson, S. Carlsson, C. Barry, M. Lang, H. Linger, & C. Schneider (Eds.), Designing Digitalization (ISD2018 Proceedings), Lund, Sweden http://aisel.aisnet.org/isd2014/proceedings2018/General/8

  44. Sumesh S, Krishna A, Subramanian CM (2019) Game theory-based reasoning of opposing non-functional requirements using inter-actor dependencies. Comput J 62(11):1557–1583. https://doi.org/10.1093/comjnl/bxy143

    Article  Google Scholar 

  45. Vinay S, Aithal S, Sudhakara G (2012) A quantitative approach using goal-oriented requirements engineering methodology and analytic hierarchy process in selecting the best alternative. In: A. Kumar M., S. R., T.V.S. Kumar (eds.) Proceedings of International Conference on Advances in Computing, Advances in Intelligent Systems and Computing, vol. 174, pp. 441–454. Springer India https://doi.org/10.1007/978-81-322-0740-5_54

  46. Von Neumann J, Morgenstern O (1944) Theory of Games Econom Behav. Princeton University Press, USA

    Google Scholar 

  47. Wohlin C, Runeson P, Höst M, Ohlsson MC, Regnell B, Wesslén A (2000) Experimentation in software engineering: an introduction. Kluwer Academic Publishers, Norwell, MA, USA

    Book  Google Scholar 

  48. Wright HK, Kim M, Perry DE (2010) Validity concerns in software engineering research. In: Proceedings of the FSE/SDP workshop on Future of software engineering research, pp. 411–414. ACM https://doi.org/10.1145/1882362.1882446

  49. Yu ESK (1997) Towards modelling and reasoning support for early-phase requirements engineering. In: Proceedings of the 3rd IEEE International Symposium on Requirements Engineering, RE’97, pp. 226–235. IEEE Computer Society https://doi.org/10.1109/ISRE.1997.566873

  50. Yu ESK (2001) Agent-oriented modelling: Software versus the world. In: M.J. Wooldridge, G. Weiß, P. Ciancarini (eds.) Agent-Oriented Software Engineering II, Second International Workshop, AOSE 2001, Montreal, Canada, May 29, 2001, Revised Papers and Invited Contributions, Lecture Notes in Computer Science, vol. 2222, pp. 206–225. Springer https://doi.org/10.1007/3-540-70657-7_14

Download references

Acknowledgements

The authors would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum & Minerals for funding this work through project No. IN171027.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jameleddine Hassine.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hassine, J., Kroumi, D. & Amyot, D. A Game-theoretic approach to analyze interacting actors in GRL goal models. Requirements Eng 26, 399–422 (2021). https://doi.org/10.1007/s00766-021-00349-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00766-021-00349-1

Keywords

Navigation