A wireless network allows multiple nodes to share a set of available resources for data transmission. The nodes can either compete or cooperate with each other to achieve their individual objectives or a group objective. Game theory is a mathematical tool developed to understand the situations of conflict among rational entities. In this article, we consider the applications of game theory to address the problem of distributed radio resource allocation in wireless networks under uncertainty, where an individual wireless node has to make a decision without having complete information about the other nodes in the network. In particular, a noncooperative game model with incomplete information is our focus. First, different approaches to solve the distributed radio resource allocation problem under uncertainty are reviewed. Then different game theoretic approaches to resource allocation in wireless networks and related work in the literature are presented. Application of a Bayesian game is then discussed to solve the distributed resource allocation problem. To this end, we provide an example to illustrate the application of a Bayesian game-theoretic model to solve the distributed bandwidth sharing problem among multiple mobile nodes competing for the shared bandwidth from a wireless access point. In this case, a mobile node is unable to completely observe other mobile nodes' behavior (e.g., speed of movement, bandwidth demand). A distributed algorithm is proposed to obtain the bidding strategy of the mobile nodes for bandwidth auction in this game model. The Bayesian Nash equilibrium is considered as the solution of this game.