We focus on the problem of finding (the size of) a minimal winning coalition in a multi-player game. We prove that deciding whether there is a winning coalition of size at most k is NP-complete, while deciding whether k is the optimal size is DP-complete. We also study different variants of our original problem: the function problem, where the aim is to effectively compute the coalition; more s...

A vector equilibrium problem is generally defined by a bifunction which takes values in a partially ordered vector space. In particular, when this space is endowed with a componentwise ordering, the vector equilibrium problem can be decomposed into a family of equilibrium subproblems, each of them being governed by a bifunction obtained from the initial one by selecting some of its scalar compo...

3 Methodology review 6 3.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.1 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2.1 Comparison of algorithms . . . . . . . . . . ....

1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 2 Department of Mathematical Sciences, Florida Institute of Techynology, Melbourne 32901, USA 3 Department of Mathematics, Aligarh Muslim University, Aligarh-202 002, India 4 Department of Mathematics, Faculty of Applied Sciences, Integral University, Lucknow 226026, India 5 D...