With the increasingly wide use of sensor-embedded smartphones, we envision that there will be many crowdsourcers to acquire sensing data from a large population of smartphone contributors. They form a bilateral competition market, where crowdsourcers compete for the limited sensing service and smartphone contributors compete for the limited budget from crowdsourcers. Each crowdsourcer has to select an “optimal” budget that can attract enough smartphone contributions. Each smartphone contributor has to decide the crowdsourcers to join, while a congested crowdsourcer may result in a low reward. To achieve the respective goals of crowdsourcers and smartphone contributors, the underlying rational and characteristics in this bilateral competition market needs to be better understood. In this paper, we present a game theoretic study of such a bilateral competition market. To be more practical, we consider the bounded rationality of smartphone contributors. We formulate the dynamic behavior of smartphone contributors as an evolutionary game and present an algorithm for the implementation of evolution process. To model the competition among crowdsourcers, we use a non-cooperative game. We prove the existence of Nash equilibrium and propose an iterative algorithm to achieve the Nash equilibrium.