Academic journal article Economic Inquiry

Endogenous Timing in Contests with Delegation

Academic journal article Economic Inquiry

Endogenous Timing in Contests with Delegation

Article excerpt

I. INTRODUCTION

Contests with delegation, where each player hires a delegate to expend effort or resources on the player's behalf to win a prize, are common. (1)

An example is litigation between a plaintiff and a defendant in which each litigant hires an attorney who expends his effort to win the lawsuit on behalf of his client. Another example is a rent-seeking contest in which each firm hires a lobbyist who expends his effort to acquire a monopoly or a procurement contract from the government on behalf of his client. Yet another example is a patent contest in which each firm hires a group of independent researchers or university professors who conduct research to obtain a patent on behalf of their employer. Delegation is attractive to players because they each can use superior ability by hiring a delegate with more ability than herself, and achieve strategic commitments through delegation.

In such contests with delegation, we believe, delegates decide endogenously when to expend their effort after signing delegation contracts. Indeed, pursuing their self-interest, the delegates may well endogenize the order of their moves, and communicate it with each other before they expend their effort. We believe also that players take it into account, when designing their contracts for the delegates, that the delegates will endogenize the order of their moves. It is these ideas that motivate this paper.

Accordingly, the purpose of this paper is to systematically study contests with delegation in which delegates decide endogenously when to expend their effort after signing delegation contracts and before they expend their effort. We study two-player contests with delegation, focusing on not only the equilibrium delegation contracts between players and their delegates but also the equilibrium orders of the delegates' moves. Specifically, we set up and analyze the following three-stage game. In the first stage, two players each hire a delegate, and they simultaneously announce their contracts written with their delegates. Each player's contract specifies how much her delegate will be paid if he wins the contest and how much if he loses it. In the second stage, each delegate decides when to expend his effort, and the delegates announce their decisions simultaneously. In the third stage, the delegates expend their effort according to their decisions in the second stage to win the prize on behalf of their employers.

We show that, in equilibrium, the delegate hired by the higher-valuation player chooses his effort level after observing his counterpart' s, and his expected payoff is greater than that of his counterpart. This advantage of the delegate of the higher-valuation player can be explained by the fact that his employer, the higher-valuation player, offers better contingent compensation (as it will be defined in Section II) to him than the lower-valuation player does to her delegate.

We compare the outcomes of the endogenous-timing framework--the three-stage game presented above--with those of the simultaneous-move framework, the game which is the same as the three-stage game with the exception that the delegates choose their effort levels simultaneously and this order of their moves is given exogenously. An interesting result is that each player offers her delegate a better contract in the endogenous-timing framework than in the simultaneous-move framework. Another interesting result is that, unless the valuation for the prize of the higher-valuation player is significantly greater than that of the lower-valuation player, then each delegate's expected payoff is greater in the endogenous-timing framework than in the simultaneous-move framework, whereas each player's expected payoff is less in the endogenous-timing framework than in the simultaneous-move framework.

In summary, pursuing their self-interest, the delegates decide endogenously when to expend their effort given contracts between the players and the delegates. …

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