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- W10366041 abstract "Consider a two players all pay contest with success functions of the ratio type and with countable and arbitrarily fine effort space. This work shows that when the costs or valuations are symmetric the contest is always iteratively dominance solvable. If the contest is asymmetric this is not necessarily the case, since a simple condition on the best reply functions must be fulfilled. As an example we show that the Tullock contest fulfills such condition, and hence it is always dominance solvable. Since a dominated strategy is never played with positive probability in a mixed strategy equilibrium this work rules out the existence of mixed strategy equilibria in a certain class of contests. Contests have often been studied for their analytic tractability compared to auctions: they would usually present a pure strategy equilibrium instead of mixed strategy one (see Konrad (2009) for a review of the literature). Although the existence of such pure strategy equilibrium has been shown before (see Perez-Castrillo and Verdier (1992), Okuguchi and Szidarovszky (1997) and Nti (1999)), previous studies did not rule out the existence of multiple equilibria in the mixed strategy extension of the game. This work deals with this question, showing that if the effort space is countable and sufficiently fine under certain conditions the pure strategy equilibrium is the unique one in the mixed strategy extension of the game. More precisely we will show that if the costs or valuations are symmetric then the contest is always iteratively dominance solvable. If the contest is asymmetric then this is not necessarily the case. In this work we identify a simple condition on the best reply functions such that if it is fulfilled the contest is iteratively dominance solvable. Moreover we show that the classical Tullock contest fulfills such condition and hence is always iteratively dominance solvable. Since dominated strategies are never played with positive probability in a mixed strategy equilibrium, we can conclude that when the contest is it∗Department of Economics, Stockholm School of Economics. Alberto.Vesperoni@hhs.se" @default.
- W10366041 created "2016-06-24" @default.
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- W10366041 date "2013-01-01" @default.
- W10366041 modified "2023-09-24" @default.
- W10366041 title "Dominance solvable contests" @default.
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