Multiple access methods in a wireless network allow multiple nodes to share a set of available channels for data transmission. The nodes can either compete or cooperate with each other to access the channel(s) so that either an individual or a group objective can be achieved. Game theory, which is a mathematical tool developed to understand the interaction among rational entities, can be applied to model and to analyze individual or group behaviour of nodes for multiple access in wireless networks. Game theory also enables us to model the selfish/malicious behaviour of nodes, and subsequently design the punishment or defense mechanisms for robust multiple access in wireless networks. In addition, game models can provide distributed solutions to the multiple access problems, which are based on solid theoretical foundations. In this survey, we provide a comprehensive review of the game models (e.g., noncooperative/cooperative, static/dynamic, and complete/incomplete information) developed for different multiple access schemes (i.e., contention-free and contention-based random channel access) in wireless networks. We consider time-division multiple access (TDMA), frequency-division multiple access (FDMA), and codedivision multiple access (CDMA), ALOHA, and carrier sense multiple access (CSMA)-based wireless networks. In addition, game models for multiple access in dynamic spectrum accessbased cognitive radio networks are reviewed. The major findings from the game models used for these different access schemes are highlighted. To this end, several of the key open research directions are outlined.Index Terms-Wireless networks, game theory, multiple access, random access game, power and rate control game.