Stackelberg game formulation of prize competition design for seeking shortest path solutions

Prize competitions have been an open approach of soliciting expertise and creativity from the public to increase business success or solve problems. In spite of many successes, there are yet needs for an effective design methodology. To investigate methodology development, we consider a problem of shortest path solution seeking consisting of one path solution seeker (PSS) and multiple providers (PSPs). PSS has a coarse overall grasp of a transportation network and each PSP knows part of the network in detail and has a good path finding capacity. To find short path between two cities, the PSS divides the network into several sections and holds prize competitions in all sections to solicit shortest path solutions among specified pairs of cities. PSS further connects procured solutions into one desired shortest path. Moreover, to protect PSPs' intellectual rights, they first submit the distance of path only. Then the PSP with shortest path submission in each section turns over the route of path and is awarded the prize. In this paper, we formulate the optimal prize setting problem for PSS considering competitive submission strategies of PSPs. We model the hierarchical behaviors between PSS and PSPs as a Stackelberg game. Stackelberg equilibrium can be further investigated based on the model and serve the purpose of prize competition design for applications to collective innovation seeking.