ions for Model-Checking Game-theoretic Properties in Combinatorial Auctions E.M. Tadjouddine F. Guerin W. Vasconcelos Univ. of Aberdeen, Dept. of Computing Science, Aberdeen AB24 3UE, UK [email protected], [email protected], [email protected]

An invariant subtraction game is a 2-player impartial game defined by a set of invariant moves (k-tuples of non-negative integers) M. Given a position (another k-tuple) x = (x1, . . . , xk), each option is of the form (x1 − m1, . . . , xk − mk), where m = (m1, . . . ,mk) ∈ M (and where xi − mi ≥ 0, for all i). Two players alternate in moving and the player who moves last wins. The set of non-ze...

In this paper we study a single player game consisting of n black checkers and m white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general n and m is nm+n+m. We have also presented an optimal algorithm to generate an optimal move sequence of the game consisting of n black checkers and m white checkers, and finally, we prese...

We introduce two new iteration games: the game G, which is a strengthening of the weak iteration game, and the game G, which is somewhat stronger than G but weaker than the full iteration game of length ω1. For a countable M elementarily embeddable in some Vη, we can show that II wins G(M,ω1) and that I does not win the G (M).

In the article m dimensional lexicographic noncooperative games   ) ,..., ( 1 m   are defined for the players’ } ,..., 2 , 1 { n N  for which there exists a characteristic function T m v v v v ) ,..., , ( 2 1  . Some main features are proved of v function in a lexicographic case. A lexicographic cooperative game is called a couple   v N , , where v is a real vectorfunction on N subsets ...

The m-business landscape never stops to change and the impacts on the mobile market are constant as players reposition themselves on the market according to the new opportunities and threats brought by rapid technological developments. This paper provides a conceptual tool to better understand this player arena and its objective is threefold. The first one is to analyse the role of the key acto...

The main content of the note is a proof of the conjecture of Hamidoune-Las Vergnas on the directed switching game in the case of Lawrence oriented matroids. C.E. Shannon has introduced the switching game for graphs circa 1960. It has been generalized and solved for matroids by A. Lehman [4]. A switching game on graphs and oriented matroids was introduced by Y. O. Hamidoune and M. Las Vergnas [3...