We consider settings in which voters vote in sequence, each voter knows the votes of the earlier voters and the preferences of the later voters, and voters are strategic. This can be modeled as an extensive-form game of perfect information, which we call a Stackelberg voting game. We first propose a dynamic-programming algorithm for finding the backward-induction outcome for any Stackelberg vot...

In this paper, we study the core stability of the dominating set game which has arisen from the cost allocation problem related to domination problem on graphs. Let G be a graph whose neighborhood matrix is balanced. Applying duality theory of linear programming and graph theory, we prove that the dominating set game corresponding to G has the stable core if and only if every vertex belongs to ...

In 1953 David Gale noticed that for every n-person game in extensive form with perfect information modeled by an arborescence (a rooted tree) some special Nash equilibrium in pure strategies can be found by an algorithm of successive elimination of leaves, which is now called the backward induction. (The result can be easily extended from the trees to the acyclic directed graphs.) He also notic...

Random minimaxing, introduced by Beal and Smith [3], is the process of using a random static evaluation function for scoring the leaf nodes of a full width game tree and then computing the best move using the standard minimax procedure. The experiments carried out by Beal and Smith, using random minimaxing in Chess, showed that the strength of play increases as the depth of the lookahead is inc...

Random minimaxing, introduced by Beal and Smith 1], is the process of using a random static evaluation function for scoring the leaf nodes of a full width game tree and then computing the best move using the standard minimax procedure. The experiments carried out by Beal and Smith, using random minimaxing in Chess, showed that the strength of play increases as the depth of the lookahead is incr...

Neutrosophic graph (NG) is a powerful tool in theory, which capable of modeling many real-life problems with uncertainty due to unclear, varying, and indeterminate information. Meanwhile, the fuzzy graphs (FGs) intuitionistic (IFGs) may not handle these as efficiently NGs. It difficult model imprecise information vagueness real-world scenarios. Many optimization are modeled solved using well-kn...