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OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
Yohan Pelosse 
Swansea University Author:
Yohan Pelosse
Abstract
This paper characterizes the optimisation problem involved in the optimalallocation of an indivisible prize in two-players discrete time contests with exogenousstochastic deadline. The organizer can choose any lottery to allocate the prize to onecontestant. Its objective is to maximize its expected...
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa71996 |
| Abstract: |
This paper characterizes the optimisation problem involved in the optimalallocation of an indivisible prize in two-players discrete time contests with exogenousstochastic deadline. The organizer can choose any lottery to allocate the prize to onecontestant. Its objective is to maximize its expected revenue by implementing theprofile of strategies where both players exert their maximal effort levels, at theminimum prize. In our main result we show that the optimal prize is obtained when theplayers’ ’intertemporal incentive’ functions are the solution of an induced Dirichletproblem on a discrete Markov chain. This solution represents the expected realisationof the Markovian process describing the players’ relative progress hitting a ’benchmarkoutperformance’ (boundary). The Dirichlet solution is attained when the optimalallocation of the prize coincides with the piecewise linear difference-form contestsuccess function of Che and Gale (1998). This result notably permits to connect theoptimality of difference-form CSFs to the family of contests with a Markovian stochasticprocess. |
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| College: |
Faculty of Humanities and Social Sciences |