Sequential contests with synergy and budget constraints

Sequential Contests with Synergy and Budget Constraints We study a sequential Tullock contest with two stages and two identical prizes. The players compete for one prize in each stage and each player may win either one or two prizes. The players have either decreasing or increasing marginal values for the prizes, which are commonly known, and there is a constraint on the total effort that each player can exert in both stages. We analyze the players' allocations of efforts along both stages when the budget constraints (effort constraints) are either restrictive, nonrestrictive or partially restrictive. We show that when the players are either symmetric or asymmetric and the budget constraints are restrictive, independent of the players' values for the prizes, each player allocates his effort equally along both stages of the contest. JEL Classification: D44, O31 and O32 Keywords: budget constraints, sequential contests and Tullock contests Reut Megidish Department of Economics Ben-Gurion University of the Negev Beer--Sheva 84105 ISRAEL Email: [email protected] For further Discussion Papers by this author see: www.cepr.org/pubs/new-dps/dplist.asp?authorid=171199 Aner Sela Department of Economics Ben-Gurion University of the Negev Beer--Sheva 84105 ISRAEL Email: [email protected] For further Discussion Papers by this author see: www.cepr.org/pubs/new-dps/dplist.asp?authorid=156699 Submitted 01 May 2011 Sequential Contests with Synergy and Budget Constraints Reut Megidish and Aner Sela May 1, 2011 Abstract We study a sequential Tullock contest with two stages and two identical prizes. The players compete for one prize in each stage and each player may win either one or two prizes. The players have either decreasing or increasing marginal values for the prizes, which are commonly known, and there is a constraint on the total e¤ort that each player can exert in both stages. We analyze the players’allocations of e¤orts along both stages when the budget constraints (e¤ort constraints) are either restrictive, nonrestrictive or partially restrictive. We show that when the players are either symmetric or asymmetric and the budget constraints are restrictive, independent of the players’values for the prizes, each player allocates his e¤ort equally along both stages of the contest. Keywords: Sequential contests, Tullock contests, budget constrains. JEL classi…cation: D44, O31, O32We study a sequential Tullock contest with two stages and two identical prizes. The players compete for one prize in each stage and each player may win either one or two prizes. The players have either decreasing or increasing marginal values for the prizes, which are commonly known, and there is a constraint on the total e¤ort that each player can exert in both stages. We analyze the players’allocations of e¤orts along both stages when the budget constraints (e¤ort constraints) are either restrictive, nonrestrictive or partially restrictive. We show that when the players are either symmetric or asymmetric and the budget constraints are restrictive, independent of the players’values for the prizes, each player allocates his e¤ort equally along both stages of the contest. Keywords: Sequential contests, Tullock contests, budget constrains. JEL classi…cation: D44, O31, O32