In the Maker-Breaker domination game played on a graph $G$, Dominator's goal is to select dominating set and Staller's claim closed neighborhood of some vertex. We study cases when Staller can win game. If Dominator (resp., Staller) starts game, then $\gamma_{\rm SMB}(G)$ SMB}'(G)$) denotes minimum number moves needs win. For every positive integer $k$, trees $T$ with SMB}'(T)=k$ are characteri...

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...

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...