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- W3048344877 abstract "In this paper, we propose and study an optimization problem of the fashion game on graphs, which can be regarded as a graph extension of matching pennies. There are two kinds of players in a graph G: Conformists and Rebels. All players choose their actions from an identical set of the two symmetric actions, say {0,1}. An action profile π of G is a mapping from the vertex set of G to the action set {0,1}. A conformist (resp. rebel) likes people having the same (resp. different) action with her and dislikes people having the different (resp. same) action. The utility u(v,π) of a player v under the action profile π is the number of neighbors she likes minus the number of neighbors she dislikes. The utility u(G,π) of G under π is the minimum utility among all players. Let t be an integer. A graph G is said to be t-satisfiable if there is an action profile of G such that all players have utilities at least t. The utility of G, denoted by u(G), is the maximum t such that G is t-satisfiable. We provide simple characterizations to determine the utilities of paths, cycles, and complete graphs. We design a linear-time algorithm to determine the utility of a tree. We obtain lower bounds of utilities of graphs containing only rebels, t-degenerate graphs, and the kth power of paths, respectively. We also prove that for any fixed integer t≥−2, the problem of deciding if a graph containing both conformists and rebels is t-satisfiable is NP-complete, and for any fixed integer t≥1, the problem of deciding if a graph containing only rebels is t-satisfiable is also NP-complete. We finally propose some further research problems on this topic." @default.
- W3048344877 created "2020-08-13" @default.
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- W3048344877 date "2020-11-01" @default.
- W3048344877 modified "2023-09-23" @default.
- W3048344877 title "Fashion game on graphs" @default.
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- W3048344877 doi "https://doi.org/10.1016/j.disopt.2020.100606" @default.
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