Optimal two-stage elimination contests for crowdsourcing

As a new business model, crowdsourcing contest is a means of open innovation. To further improve the efficiency of crowdsourcing contests, two-stage elimination contests are often used as a selection mechanism by firms. This paper explores two forms of elimination mechanisms: sub-elimination and sequential-elimination. Using game theory and auction theory approaches, we model the game between a contest seeker and participants and derive the equilibrium results under these two forms, including the equilibrium decisions and corresponding expected payoff for the contest seeker and the effort strategy at each stage and total expected surplus for all participants. Our results show that: (i) Under both forms, it is optimal to have exactly two participants competing with each other in the final stage; (ii) In equilibrium in the sub-elimination contest, all participants exert more effort in each stage when the number of participants remaining is smaller. The equilibrium effort strategy of high-ability participants has the same trend in a sequential-elimination contest, but the low-ability participant's equilibrium effort level in the final contest is first decreasing and then increasing in the number of remaining participants; (iii) The optimal two-stage elimination form is sequential-elimination for the contest seeker when compared with no-elimination and sub-elimination because under sequential-elimination, all participants in the second stage will exert more effort, leading to higher-quality solutions. Additionally, we find that this form is also preferred by high-ability participants.