en Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original <span style="font-size:11pt"><span style="line-height:normal"><span style="text-autospace:none"><span new="" roman="" style="font-family:" times=""><i><span style="font-size:10.0pt"><span style="letter-spacing:-.25pt">Cooperative game theory is an important tool for analyzing cooperation and benefit allocation among coalition members, but classical models usually do not consider the existence of a minimum capacity required for cooperation to be activated. In this study, &ldquo;threshold coalition games&rdquo; are introduced, in which the formation of an effective coalition requires crossing a certain threshold of collective capacity. Also, a coalition activation index and a new rule called &ldquo;threshold allocation value&rdquo; are presented to determine the players&rsquo; shares, and their properties, including efficiency, symmetry, and uniqueness, are proven. Finally, a numerical example shows that the proposed model can model threshold-based cooperation structures coherently and provides a suitable framework for future research in cooperative game theory.</span></span></i></span></span></span></span><br> &nbsp; cooperative game theory, threshold coalition games, characteristic function, benefit allocation, coalition stability, mathematical modeling 56 81 http://iors.ir/journal/browse.php?a_code=A-10-6111-1&slc_lang=en&sid=1 Forouzesh Ghambari forouzesh.ghambari@gmail.com 00031947532846003206 00031947532846003206 Yes Payame Noor University of Markazi Mahdi Ahangari 00031947532846003207 00031947532846003207 No Urmia University of Technology