The 1-dimensional discrete Voronoi game
Operations Research Letters
The discrete Voronoi game in R consists of two competing players P1 and P2 and a set of N users placed on a line-segment. The players alternately place one facility each on the line-segment for R-rounds, where the objective is to maximize their own total payoffs. We prove bounds on the worst-case (over the arrangement of the N users) payoffs of the two players, and discuss algorithms for finding the optimal strategies of the players in the 2-round game.
Banik, Aritra; Bhattacharya, Bhaswar B.; Das, Sandip; and Das, Sreeja, "The 1-dimensional discrete Voronoi game" (2019). Journal Articles. 929.