- Voronoi
Submitted manuscript, 259 KB, PDF document

**Voronoi game on disjoint open curves.** / Dziubinski, Marcin Konrad.

Research output: Working paper

Dziubinski, MK 2008 'Voronoi game on disjoint open curves' Economics Working Paper Series, The Department of Economics, Lancaster University.

Dziubinski, M. K. (2008). *Voronoi game on disjoint open curves*. (Economics Working Paper Series). The Department of Economics.

Dziubinski MK. Voronoi game on disjoint open curves. Lancaster University: The Department of Economics. 2008. (Economics Working Paper Series).

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title = "Voronoi game on disjoint open curves",

abstract = "Two players are endowed with resources for setting up N locations on K open curves of identical lengths, with N > K greater than or equal to 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that, if an analogical game is played on disjoint closed curves, the second mover advantage is in place only if K = 1, while for K > 1 both players have a tying strategy. It was also shown that this results hold for open curves of identical lengths when rules of the game additionally require players to take exactly one location in the rst round. In this paper we show that the second mover advantage is still in place for K greater than or equal to 1 and 2K -1 less than or equal to N, even if the additional restriction is dropped, while K is less than or euqal to N <2K -1 results in the first mover advantage. We also study a natural variant of the game, where the resource mobility constraint is more stringent so that in each round each player chooses a single location and we show that the second mover advantage re-appears for K is less than or equal to N <2K -1 if K is an even number.",

keywords = "Competitive locations, Disjoint spaces, Winning/Tying strategies, Equilibrium con gurations.",

author = "Dziubinski, {Marcin Konrad}",

year = "2008",

language = "English",

series = "Economics Working Paper Series",

publisher = "The Department of Economics",

type = "WorkingPaper",

institution = "The Department of Economics",

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TY - UNPB

T1 - Voronoi game on disjoint open curves

AU - Dziubinski, Marcin Konrad

PY - 2008

Y1 - 2008

N2 - Two players are endowed with resources for setting up N locations on K open curves of identical lengths, with N > K greater than or equal to 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that, if an analogical game is played on disjoint closed curves, the second mover advantage is in place only if K = 1, while for K > 1 both players have a tying strategy. It was also shown that this results hold for open curves of identical lengths when rules of the game additionally require players to take exactly one location in the rst round. In this paper we show that the second mover advantage is still in place for K greater than or equal to 1 and 2K -1 less than or equal to N, even if the additional restriction is dropped, while K is less than or euqal to N <2K -1 results in the first mover advantage. We also study a natural variant of the game, where the resource mobility constraint is more stringent so that in each round each player chooses a single location and we show that the second mover advantage re-appears for K is less than or equal to N <2K -1 if K is an even number.

AB - Two players are endowed with resources for setting up N locations on K open curves of identical lengths, with N > K greater than or equal to 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that, if an analogical game is played on disjoint closed curves, the second mover advantage is in place only if K = 1, while for K > 1 both players have a tying strategy. It was also shown that this results hold for open curves of identical lengths when rules of the game additionally require players to take exactly one location in the rst round. In this paper we show that the second mover advantage is still in place for K greater than or equal to 1 and 2K -1 less than or equal to N, even if the additional restriction is dropped, while K is less than or euqal to N <2K -1 results in the first mover advantage. We also study a natural variant of the game, where the resource mobility constraint is more stringent so that in each round each player chooses a single location and we show that the second mover advantage re-appears for K is less than or equal to N <2K -1 if K is an even number.

KW - Competitive locations

KW - Disjoint spaces

KW - Winning/Tying strategies

KW - Equilibrium congurations.

M3 - Working paper

T3 - Economics Working Paper Series

BT - Voronoi game on disjoint open curves

PB - The Department of Economics

CY - Lancaster University

ER -