We construct a model in which all rational rent-seekers may be willing to accept a negative payoff in a Tullock contest in which the rent-seekers are driven by reciprocity motives. We show that in the reciprocal Tullock contest, a unique reciprocity equilibrium exists if the reciprocal concerns of rent-seekers are sufficiently small relative to their material concerns, and that otherwise, there are two reciprocity equilibria: a destructive equilibrium and a constructive equilibrium. The individual rent-seeking expenditure in the former equilibrium is more than that in the Nash equilibrium in the original Tullock contest; moreover, over-dissipation can occur in a destructive equilibrium even in the case of constant returns to expenditure. These results derived from our reciprocal contest model are consistent with observations in most existing experimental studies on the Tullock contest.
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I wish to thank Atsushi Kajii, Takashi Sekiguchi, and participants at the Summer Workshop on Economic Theory (SWET) 2010. My special thanks are due to the associate editor and two anonymous referees of this journal for helpful suggestions and comments. I am also grateful to Jun-ichi Itaya, Hideki Konishi, and Yoichi Hizen. However, all errors remain my own responsibility.
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