Two-Party Political Competition: A Geometric Study of the Nash Equilibrium in a Weighted Case
نویسنده
چکیده
This paper investigates an abstract game of political competition between two parties. All political positions are represented by points in a plane, and the parties choose positions that are as close as possible to the greatest number of voters, that are divided into a finite number of types. To adapt the problem to various political landscapes (different countries, for example), one simply assumes that the distribution of voters is not uniform. This complexity can be represented by simply assigning an appropriate weight to each position in the policy plane. The existence of Nash equilibria in the game is studied by a geometric argument. This approach, in addition to representing the voting population as a finite distribution of weights, represents the innovation of the present work. An algorithm has been developed in order to search for the equilibrium position of a given population. Mathematics Subject Classification: 91B02, 91B012, 91B50, 90, 52 2716 M. D. López, J. Rodrigo and I. Lillo
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