<Para ID="Par1">In this paper we suggest a new class of search games, namely, screening and hiding versus search games. This new class of search games is motivated by the book Search and Screening by Koopman who is the founder of the modern search theory. In our game a hider is not just trying to find the best...</para>

A search game on a finite and complete graph is studied between a (immobile) hider and a seeker. A strategy for the hider is to choose a node where he hides, except for a specified node. A strategy for the seeker is an ordering of nodes in which the seeker starts at the specified node, examines...

We define a duality of solutions in coalitional games that we call a twisted duality. This twisted duality extends the rule of self-duality in bankruptcy problems. After showing that the prekernel and prenucleolus exhibit twisted duality, we define a twisted reduced game property and...

It is shown that the prekernel and the pre-nucleolus of a cooperative game coincide with the kernel and the nucleolus for the reasonable set of the game respectively.