Dynamic Analysis of an Electoral Campaign
I analyse two differential games describing electoral campaigns where two candidates invest so as to increase the number of their respective voters. In both cases, parties overinvest and the number of voters is larger than in the social optimum. I extended both models to n candidates, so as to derive the socially optimal number of candidates. This yields non-univocal results, in that the number of candidates maximizing social welfare when a benevolent planner controls their efforts may be higher or lower than the optimal number of candidates given the non-cooperative investment behavior of parties, according to the shape of cost functions and he dynamic behavior of consensus associated with investment.
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