مدل‌سازی ساختار ائتلاف بهینه با استفاده از مفهوم پاسخ هسته

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استاد، دانشگاه تهران.

2 دانشجوی دکتری، دانشگاه تهران.

چکیده

تشکیل ائتلاف گامی مهم در جهت توسعه رفاه جمعی به­واسطه بهبود عملکرد است. این مهم در دو رویکرد پژوهشی عمده پیگیری می­شود: توسعه رویکردهای الگوریتمیک برای دستیابی به ساختار ائتلاف بهینه با هدف حداکثر‌کردن رفاه جمعی؛ رویکرد نظریه بازی‌های همکارانه جهت توزیع عادلانه و پایدار عایدی ائتلاف. هدف پژوهش حاضر ادغام نقاط قوت دو رویکرد بالا به‌منظور دستیابی به ساختار ائتلافی بهینه و پایدار است. نوآوری پژوهش، مدل‌سازی ریاضی برای گنجاندن شرط پایداری در قالب مفهوم پاسخ هسته در مسئله افراز بهینه و غلبه بر رویه‌های غیرمتمرکز تشکیل ائتلاف و توزیع عایدی است؛ سپس عملکرد مدل ایجاد ساختار ائتلاف‌های بهینه هم‌پوشان و غیر‌هم‌پوشان توسط مثالی عددی بررسی می‌­شود. نتایج نشان می‌دهد که تشکیل ائتلاف به بهبود رفاه جمعی منجر می‌شود. این بهبود با افزایش حد بالای تعداد افراد مجاز برای حضور در ائتلاف به میزانی معین، روندی صعودی با شیب کاهنده دارد و پس از آن تغییر نمی‌کند. این امر ناشی از دلایل متعددی است که مانع ایجاد ائتلاف عظیم میان بازیکنان می‌­‌‌شود و حاکی از آن است که هنگام تشکیل ائتلاف‌های بزرگ باید منافع حاصل با پیچیدگی‌های مدیریتی و هزینه‌های هماهنگی و ارتباطات میان افراد مقایسه شود.

کلیدواژه‌ها

عنوان مقاله [English]

Modeling the Optimal Coalition Structure Using the Core Solution Concept

نویسندگان [English]

  • Mohammadreza Mehregan 1
  • Ghahreman Abdoli 1
  • Elham Razghandi 2
1 Professor, University of Tehran .
2 Ph.D Student, University of Tehran.
چکیده [English]

Coalition formation is an important step towards developing the social welfare by improving the performance. This is pursued in two main research streams: (i) algorithmic approaches to achieve the optimal coalition structure and (ii) cooperative game theory to distribute the coalition payoff based on fairness and stability criteria. The aim of this paper is to integrate the strengths of the two approaches in order to achieve an optimal and stable coalition structure. The main innovation of the paper is using mathematical modeling to incorporates stability condition in a set partitioning problem through core solution concept to overcome decentralized procedures of coalition formation and payoff distribution. A numerical example is used to investigate the performance of overlapping and non-overlapping optimal coalition structure models. The results show that cooperation leads to improve social welfare. This improvement has an ascending trend with a decreasing slope and does not change after increasing the upper limit of players allowed to join the coalition to the certain extent. This is due to several reasons which prevent players to form grand coalition and suggests that, to form large coalitions, one should compare achieved gains with the managerial complexities and the increased costs of coordination and communication between players.

کلیدواژه‌ها [English]

  • Coalition
  • Optimal Coalition Structure
  • Stability
  • Core
  • Cooperative Game Theory
  • Overlapping Coalition Structure
  • Mathematical Modeling

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