Over the past decade, blockchain technology has attracted tremendous attention from both academia and industry. The popularity of blockchains was originated from the concept of crypto-currencies to serve as a decentralized and tamper-proof transaction data ledger. Nowadays, blockchains as the key framework in the decentralized public data-ledger have been applied to a wide range of scenarios far beyond crypto-currencies, such as the Internet of Things, healthcare, and insurance. This survey aims to fill the gap between a large number of studies on blockchain networks, where game theory emerges as an analytical tool, and the lack of a comprehensive survey on the game theoretical approaches applied in blockchain-related issues. In this survey, we review the game models proposed to address common issues in the blockchain network. The focus is placed on security issues, e.g., selfish mining, majority attack and denial of service attack, issues regarding mining management, e.g., computational power allocation, reward allocation, and pool selection, as well as issues regarding blockchain economic and energy trading. Additionally, we discuss the advantages and disadvantages of these selected game theoretical models and solutions. Finally, we highlight important challenges and future research directions of applying game theoretical approaches to incentive mechanism design and the combination of blockchain with other technologies.