Electoral strategies in a dynamical democratic system. Geometric models

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

doi:10.1016/j.ejor.2005.05.019

Cited by 8 publications

(10 citation statements)

References 6 publications

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“…Their locations in the policy plañe are denoted by U,t 2 , determined by the policies they offer. All the political positions appearing in the voter population are represented by a finite set of types H = {p-l ,... ,p"} c R 2 (Roemer, 2001;Abellanas et al, 2006).…”

Section: The Modelmentioning

confidence: 99%

“…A simpler versión of the model has already been dealt with in previous work (Abellanas et al, 2006), but has now been adapted to reflect better the reality of many countries. Both competing parties that constitute the major parties of a country are allowed to alter their political positions on two Ítems especially relevant for the citizens to obtain more followers.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, the Nash equilibrium study is proposed in a variation of the political competition game with neighborhood restrictions, as proposed by the authors in Abellanas et al (2006). The variation proposed in this work is focused on the consideration of neighborhoods for both parties who try to win the máximum number of voters.…”

Section: Introductionmentioning

confidence: 99%

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

Abellanas

López

Hitos

2010

European Journal of Operational Research

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This paper considers a problem of political economy in which a Nash equilibrium study is performed in a proposed game with restrictions where the two major parties in a country vary their position within a politically flexible framework to increase their number of voters. The model as presented fits the reality of many countries. Moreover, it avoids the uniqueness of equilibrium positions. The problem is stated and solved from a geometric point of view.

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Abellanas

López

Hitos

2010

European Journal of Operational Research

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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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“…The perpendicular bisector of the players' locations partitions the plane into two regions. Each player is considered to capture those points which lie closer to their own position than to that of the other player [3][4][5][6][7][8]. The pay-off of each player is then the total weight of the captured points.…”

Section: Introductionmentioning

confidence: 99%

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

Dolores¹,

Hitos²,

Manuel³

2013

AJOR

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International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

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Electoral strategies in a dynamical democratic system. Geometric models

Cited by 8 publications

References 6 publications

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

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

Weak equilibrium in a spatial model

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

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