Blockchain has been an emerging technology, which comprises lots of fields such as distributed systems and Internet of Things (IoT). As is well known, blockchain is the underlying technology of bitcoin, whose initial motivation is derived from economic incentives. Therefore, lots of components of blockchain (e.g., consensus mechanism) can be constructed toward the view of game theory. In this paper, we highlight the combination of game theory and blockchain, including rational smart contracts, game theoretic attacks, and rational mining strategies. When put differently, the rational parties, who manage to maximize their utilities, involved in blockchain chose their strategies according to the economic incentives. Consequently, we focus on the influence of rational parties with respect to building blocks. More specifically, we investigate the research progress from the aspects of smart contract, rational attacks, and consensus mechanism, respectively. Finally, we present some future directions based on the brief survey with respect to game theory and blockchain.