No Cover Image

Working paper 1 view

OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH

Yohan Pelosse Orcid Logo

Swansea University Author: Yohan Pelosse Orcid Logo

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...

Full description

Published:
URI: https://cronfa.swan.ac.uk/Record/cronfa71996
first_indexed 2026-05-31T09:16:14Z
last_indexed 2026-05-31T09:16:14Z
id cronfa71996
recordtype SURis
fullrecord <?xml version="1.0" encoding="utf-8"?><rfc1807 xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><bib-version>v2</bib-version><id>71996</id><entry>2026-05-31</entry><title>OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH</title><swanseaauthors><author><sid>455a04210e95a07e6fbea54f2cc4d6be</sid><ORCID>0000-0001-8546-918X</ORCID><firstname>Yohan</firstname><surname>Pelosse</surname><name>Yohan Pelosse</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2026-05-31</date><deptcode>SOSS</deptcode><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.</abstract><type>Working paper</type><journal/><volume/><journalNumber/><paginationStart/><paginationEnd/><publisher/><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic/><keywords/><publishedDay>0</publishedDay><publishedMonth>0</publishedMonth><publishedYear>0</publishedYear><publishedDate>0001-01-01</publishedDate><doi/><url/><notes/><college>COLLEGE NANME</college><department>Social Sciences School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SOSS</DepartmentCode><institution>Swansea University</institution><apcterm>Not Required</apcterm><funders/><projectreference/><lastEdited>2026-05-31T10:16:11.7709964</lastEdited><Created>2026-05-31T10:12:19.5842546</Created><path><level id="1">Faculty of Humanities and Social Sciences</level><level id="2">School of Social Sciences - Economics</level></path><authors><author><firstname>Yohan</firstname><surname>Pelosse</surname><orcid>0000-0001-8546-918X</orcid><order>1</order></author></authors><documents/><OutputDurs/></rfc1807>
spelling v2 71996 2026-05-31 OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH 455a04210e95a07e6fbea54f2cc4d6be 0000-0001-8546-918X Yohan Pelosse Yohan Pelosse true false 2026-05-31 SOSS 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. Working paper 0 0 0 0001-01-01 COLLEGE NANME Social Sciences School COLLEGE CODE SOSS Swansea University Not Required 2026-05-31T10:16:11.7709964 2026-05-31T10:12:19.5842546 Faculty of Humanities and Social Sciences School of Social Sciences - Economics Yohan Pelosse 0000-0001-8546-918X 1
title OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
spellingShingle OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
Yohan Pelosse
title_short OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
title_full OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
title_fullStr OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
title_full_unstemmed OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
title_sort OPTIMAL DYNAMIC DIFFERENCE-FORM CONTESTS: THE PROBABILISTIC DIRICHLET APPROACH
author_id_str_mv 455a04210e95a07e6fbea54f2cc4d6be
author_id_fullname_str_mv 455a04210e95a07e6fbea54f2cc4d6be_***_Yohan Pelosse
author Yohan Pelosse
author2 Yohan Pelosse
format Working paper
institution Swansea University
college_str Faculty of Humanities and Social Sciences
hierarchytype
hierarchy_top_id facultyofhumanitiesandsocialsciences
hierarchy_top_title Faculty of Humanities and Social Sciences
hierarchy_parent_id facultyofhumanitiesandsocialsciences
hierarchy_parent_title Faculty of Humanities and Social Sciences
department_str School of Social Sciences - Economics{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}School of Social Sciences - Economics
document_store_str 0
active_str 0
description 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.
published_date 0001-01-01T10:16:14Z
_version_ 1866694891220762624
score 11.106693

Similar Items