How multiple crowdsourcers compete for smartphone contributions?

Mobile crowdsourcing provides us various exciting and profitable applications. All the mobile crowdsourcing systems purchase sensing services from a population of smartphone users. The issue of competition arises. However, few studies address this issue, which significantly affects the functionality of crowdsourcing systems. In this paper, we study the problem of price competition among multiple crowdsourcers in a free market, where smartphone users are able to withdraw from the current crowdsourcer if they can gain more utility from other crowdsourcers. We formulate the price competition as a dynamic non-cooperative game, where each crowdsourcer independently decides its own price aiming at highest profit and all smartphone users join the crowdsourcers at their satisfaction. In practice, a crowdsourcer may not know strategies of others which are unrevealed information. We propose a distributed learning algorithm that every crowdsourcer learns from its historic information to achieve the Nash equilibrium in the market. We studied and identified the suitable learning speed to make the price adaption converge to the Nash equilibrium. All the results are supported by both theoretical analysis and simulations.