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- W654887908 abstract "We introduce a game which is played by two players on a connected graph G. The players I and II alternatively choose vertices of the graph until all vertices are taken. The set of vertices chosen by player I is denoted by ΠI, and by II is denoted by ΠII. Let d(x,π)=∑y∈πd(x,y) and let M(π)=min{d(x,π)∣x∈π} be the median value of a profile π⊆V(G). The objective of player I is to maximize M(πII)−M(πI) and the objective of player II is to minimize M(πII)−M(πI). The winner of the game is the player with the smaller median value of her profile. We give a necessary condition for a tree so that player I (who begins the game) has a winning strategy for the game. We prove also that for hypercubes and some other symmetric graphs the player II has a strategy to draw the game. Complete bipartite graphs are considered as well." @default.
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- W654887908 date "2015-08-01" @default.
- W654887908 modified "2023-09-30" @default.
- W654887908 title "The median game" @default.
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- W654887908 doi "https://doi.org/10.1016/j.disopt.2015.05.002" @default.
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