Optimal Allocation Of Prizes Research Articles

Allocation of Prizes in Contests with Participation Constraints

We study all-pay contests with an exogenous minimal effort constraint where a player can participate in a contest only if his effort (output) is equal to or higher than the minimal effort constraint. Contestants are privately informed about a parameter (ability) that affects their cost of effort. The designer decides about the size and number of prizes. We analyze the optimal prize allocation for the contest designer who wishes to maximize either the total effort or the highest effort. It is shown that if the minimal effort constraint is relatively high, the winner-take-all contest in which the contestant with the highest effort wins the entire prize sum does not maximize the expected total effort or the expected highest effort. Rather, a random contest in which the entire prize sum is equally allocated to all the participants yields a higher expected total effort as well as a higher expected highest effort.

ON THE WINNER-TAKE-ALL PRINCIPLE IN INNOVATION RACES

What is the optimal allocation of prizes in an innovation race? Should the winner take all or is it preferable that first inventors share the market with late independent duplicators? This paper re-examines the issue taking into account that the incentives to innovate depend not only on industry profits but also on the division of profits between early and late inventors. In our baseline model two firms race for an innovation in continuous time. In the winner-take-all system as soon as one firm innovates the other stops investing in RD in the alternative more permissive system the laggard continues to invest to duplicate the innovation and when it also succeeds the market becomes a duopoly. We compare the two regimes on welfare grounds finding that the winner-take-all system can be socially optimal in a broad set of circumstances much broader than envisioned by the recent literature. We discuss why we arrive at di§erent results than the early literature and the policy implications of our analysis.

Attracting the Best and the Brightest: Asymptotics and Optimal Prize Structure of All-Pay Contests with Heterogeneous Participants

Tournaments are frequently adopted to procure goods and services for which spot markets do not exist, contracts are incomplete and outcomes cannot be verified in a court. Examples of such procurement contests include R&D tournaments held by the government agencies and large corporations. It is widely acknowledged that open participation is undesirable in such contests and tools such as entry fees and contestant selection auctions are suggested to restrict participation. With rapid evolution of the Internet and the Web, a new generation of procurement tournaments has emerged. The Web now allows almost any firm or individual to organize its own minor tournament, sometimes with just a few mouse clicks. A number of companies use this opportunity to run contests in which contestants develop and submit ideas or products, and prizes are awarded to one or more winners chosen by the company conducting the contest. All of these tournaments are characterized by the absence of entry fees, open participation, sunk efforts and a significant number of contestants. This paper presents an economic model of an all-pay contest with heterogeneous contestants. There is a contest sponsor that values K contest submissions. The contest offers L prizes and there are N risk-averse, wealth-constrained contestants who differ in their skills (their ability to produce quality solutions), and who turn in their submissions simultaneously. Our first result shows that every such game of incomplete information satisfying the Single Crossing Condition has a unique symmetric Bayes-Nash equilibrium in pure strategies, and that equilibrium effort levels are monotonic in ability. Thus, the equilibrium of the contest is efficiently ranking in that it ranks the winners in the decreasing order of their abilities. Next, we derive the asymptotic behavior of the bid function and the submission qualities. We show that, asymptotically, only the support of the type distribution and the cost function at the support determine the contest outcome, therefore, in the limit, the game has a particularly simple structure. Next, we show how that the speed of convergence to the asymptotics is of order 1/N and the asymptotic outcome can be used to construct an upper bound on the outcome in any finite sample game. Finally, we show how our result can be applied to derive the asymptotically optimal allocation of prizes for the profit-maximizing tournament sponsor and show that the optimal solution of the finite-sample allocation problem converges to the asymptotic one as the number of participants grows. In particular, it is shown that when the contestants are risk-neutral, the sponsor's optimal contest design places most of the budget on the top prize and sets the remaining prizes at their lowest possible levels (the minimum necessary to facilitate the transfer of the intellectual property). When the contestants are sufficiently risk-averse, the firm may optimally offer more prizes than there are the desired submissions, thus awarding prizes even to submissions it does not eventually want. As the aggregate surplus of contestants converges to zero when the number of participants grows, the profit maximizing prize structure is asymptotically socially optimal.

On the Winner-Take-All Principle in Innovation Races

What is the optimal allocation of prizes in an innovation race? Should the winner take all, or is it preferable that the original inventor shares the market with subsequent independent duplicators? Some recent papers in law and economics have argued that the latter, more permissive solution is socially preferable under mild conditions. We re-examine that issue, arguing that a permissive regime may turn the innovation race into a waiting game, reducing the power of incentives, and may invite socially wasteful duplicative R&D expenditures. In a model that accounts for these effects, the winner-take-all system turns out to be preferable in a broad set of circumstances, especially in highly innovative industries.

The Optimal Allocation of Prizes in Contests

We study a contest with multiple, nonidentical prizes. Participants are privately informed about a parameter (ability) affecting their costs of effort. The contestant with the highest effort wins the first prize, the contestant with the second-highest effort wins the second prize, and so on until all the prizes are allocated. The contest's designer maximizes expected effort. When cost functions are linear or concave in effort, it is optimal to allocate the entire prize sum to a single “first” prize. When cost functions are convex, several positive prizes may be optimal. (JEL D44, J31, D72, D82)