Searching for equilibrium positions in a game of political competition with restrictions

Abellanas, Manuel; López, Ma Dolores; Hitos, Javier Rodrigo

doi:10.1016/j.ejor.2009.04.002

Cited by 6 publications

(5 citation statements)

References 26 publications

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“…The objective considered by the authors was to obtain the optimum situations for the party in this environment, that is, the positions such that the region of corresponding Voronoi diagram contains the greatest number of voters. This model was later extended to encompass more practical situations in a follow-up paper by the Abellanas et al [1]. These problems have roots in the maximum coverage problems discussed in this paper, and are generally solved by computational geometric techniques.…”

Section: Potential Applicationsmentioning

confidence: 99%

New variations of the maximum coverage facility location problem

Bhattacharya

Nandy

2013

European Journal of Operational Research

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Consider a competitive facility location scenario where, given a set U of n users and a set F of m facilities in the plane, the objective is to place a new facility in an appropriate place such that the number of users served by the new facility is maximized. Here users and facilities are considered as points in the plane, and each user takes service from its nearest facility, where the distance between a pair of points is measured in either L 1 or L 2 or L ∞ metric. This problem is also known as the maximum coverage (MaxCov) problem. In this paper, we will consider the k-MaxCov problem, where the objective is to place k (⩾1) new facilities such that the total number of users served by these k new facilities is maximized. We begin by proposing an O(nlogn) time algorithm for the k-MaxCov problem, when the existing facilities are all located on a single straight line and the new facilities are also restricted to lie on the same line. We then study the 2-MaxCov problem in the plane, and propose an O(n 2) time and space algorithm in the L 1 and L ∞ metrics. In the L 2 metric, we solve the 2-MaxCov problem in the plane in O(n 3 logn) time and O(n 2 logn) space. Finally, we consider the 2-Farthest-MaxCov problem, where a user is served by its farthest facility, and propose an algorithm that runs in O(nlogn) time, in all the three metrics.

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Section: Potential Applicationsmentioning

confidence: 99%

New variations of the maximum coverage facility location problem

Bhattacharya

Nandy

2013

European Journal of Operational Research

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“…An important contribution of this model is that some of the determined positions of equilibrium do not fulfil the requirement that the two parties must choose the same strategy. This is a problem that usually arises in competition models between two players and for which different solutions have typically been found: restricting the positions of the players, studying mixed-strategy Nash equilibrium, weakening the definition of equilibrium, studying uncovered sets or considering valence issues, among others (see, for example, Abellanas et al, 2006Abellanas et al, , 2010Abellanas et al, , 2011Roemer, 2001;McKelvey, 1976;Stokes, 1963;Díaz-Báñez et al, 2011). The use of arcs of tolerance is a new solution to this problem, that has plausible interpretations in various areas aside from political competition.…”

Section: Discussionmentioning

confidence: 99%

“…Political competition models developed in the plane in which equilibrium positions are sought (Nash, 1951) establish that in situations of economic and social stability, such balance, if fact existing, is unique and in a central position with respect to voters' preferences (see Plott, 1967;Kramer, 1973;McKelvey, 1976). Thus political parties must present similar moderate stances in order to achieve the greatest number of voters (Abellanas et al, 2010(Abellanas et al, , 2011Roemer, 2001;López and Rodrigo, 2009).…”

Section: Introductionmentioning

confidence: 99%

Searching for optimal positions through directional data in a political competition model

López

Rodrigo

Lantarón

2018

IJOR

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This paper considers an application of directional data to political science. A model is presented in which the political preferences of the type of voters of a population are represented as points of the circumference unit with the political parties searching for optimal positions on this in order to gain the most support of that finite set of voter types. Strategies have been developed to search for optimal positions in the case of one party and Nash equilibrium positions are found in the game with two parties. The results reveal how the different parties redirect their stances to adapt to changing situations generated by economic or social circumstances affecting citizen preferences.

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“…Various approaches have been presented in the literature in an attempt to resolve this situation: restricting the positions of the players, studying mixed-strategy Nash equilibria, or studying uncovered sets, among others (see, for example, Abellanas et al 2006Abellanas et al , 2010Roemer 2001;McKelvey 1986).…”

Section: Introductionmentioning

confidence: 99%

Weak equilibrium in a spatial model

et al. 2010

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Spatial models of two-player competition in spaces with more than one dimensión almost never have pure-strategy Nash equilibria, and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to avoid the uniqueness of the equilibrium position. As a result, a "región of equilibrium" appears, which can be located by geometric methods. In this área, the players can move around in an "almost-equilibrium" situation and do not necessarily have to adopt the same position.

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Searching for equilibrium positions in a game of political competition with restrictions

Cited by 6 publications

References 26 publications

New variations of the maximum coverage facility location problem

New variations of the maximum coverage facility location problem

Searching for optimal positions through directional data in a political competition model

Weak equilibrium in a spatial model

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