IJE TRANSACTIONS A: Basics Vol. 31, No. 7 (July 2018) 1445-1453    Article in Press

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R. Tavakkoli-Moghaddam, M. Fadaei, A. Taleizadeh and D. Mohammaditabar
( Received: November 15, 2017 – Accepted: February 08, 2018 )

Abstract    Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regarded as a fairness criterion in cooperative games when deciding on choosing the solution concepts in coordination contracts, it is crucially important for players to check if the solution concepts available in contract menu possesses this property. To this end, we show that some solution concepts such as the Shapley value, and the -value have invariance property with respect to benefit/cost allocation but some others such as Equal Profit Method (EPM) and Master Problem variant I ( ), have not. Furthermore, a measure for fairness with respect to equitable payoffs and disutility is defined and related to invariance property. To validate the proposed approach, two numerical examples extracted from the existing literature for different problems in benefit/cost cooperative games are solved and analyzed. The results of this research can be generalized for all solution concepts in cooperative games and is applicable for n-person games.


Keywords    Game theory; Cooperative games; Coordination contract; Solution concepts; Shapley value; Fairness.


چکیده    راهکارهای تخصیص در بازیهای همکارانه، مبتنی بر بازی های منفعت یا بازی های هزینه است.اگرچه بازیهای هزینه و بازی های منفعت از نظر استراتژیک معادل یکدیگر هستند ولی این موضوع در مورد راهکارهای تخصیص صدق نمی کند. بهمین دلیل یک ویژگی جدید تحت عنوان ویژگی بی تفاوتی نسبت به تخصیص هزینه/منفعت در این مقاله تعریف گردیده است. با توجه به اینکه چنین ویژگی را میتوان بعنوان معیار منصفانه بودن تخصیص در بازیهای همکارانه هنگام تصمیم گیری در مورد انتخاب راهکارهای تخصیص قلمداد کرد، برای بازیکنان کنترل اینکه آیا راهکار تخصیص موردنظر دارای این ویژگی باشد از اهمیت خاصی برخوردار است. بدین منظور، ما نشان می دهیم که برخی راهکارهای تخصیص منجمله عدد شاپلی، و عدد تاو دارای ویژگی بی تفاوتی نسبت به تخصیص هزینه/منفعت هستند اما برخی دیگر منجمله روش سود یکسان و روش مسئله اصلی نوع 1 دارای این ویژگی نیستند. علاوه بر این، معیاری برای اندازه گیری منصفانه بودن با توجه به سود تخصیص یافته و عدم مطلوبیت، تعریف شده و رابطه آن با ویژگی بی تفاوتی بررسی شده است. برای اعتبارسنجی رویکرد پیشنهادی، دو مثال عددی که داده های آن از ادبیات تحقیق زنجیره تامین مربوط به بازی های هزینه منفعت برداشته شده است، حل و مورد تجزیه و تحلیل قرار گرفته است. نتایج این تحقیق را میتوان برای سایر راهکارهای تخصیص بازیهای همکارانه نیز تعمیم داد و حتی در بازی های n نفره بکار بست.

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