Game-theoretic modeling and equilibrium analysis have provided valuable insights into the design of robust local control rules for the individual agents in multi-agent systems, e.g., Internet congestion control, road transportation networks, etc. In this paper, we introduce a non-cooperative MAC (Medium Access Control) game for wireless networks and propose new fully-distributed CSMA (Carrier Sense Multiple Access) learning algorithms that are probably optimal in the sense that their long-term throughputs converge to the optimal solution of a utility maximization problem over the maximum throughput region. The most significant part of our approach lies in introducing a novel cost function in agents' utilities so that the proposed game admits an ordinal potential function with (asymptotically) no price-of-anarchy. The game formulation naturally leads to known game-based learning rules to find a Nash equilibrium, but they are computationally inefficient and often require global information. Towards our goal of fully-distributed operation, we propose new fully-distributed learning algorithms by utilizing a unique property of CSMA that enables each link to estimate its temporary link throughput without message passing for the applied CSMA parameters. The proposed algorithms can be thought as `stochastic approximations' to the standard learning rules, which is a new feature in our work, not prevalent in other traditional game-theoretic approaches. We show that they converge to a Nash equilibrium, which is a utility-optimal point, numerically evaluate their performance to support our theoretical findings and further examine various features such as convergence speed and its tradeoff with efficiency.