The costs incurred by cloud providers towards operating their data centers are often determined in large part by their peak demands. The pricing schemes currently used by cloud providers to recoup these costs from their tenants, however, do not distinguish tenants based on their contributions to the cloud's overall peak demand. Using the concrete example of peak-based pricing as employed by many electric utility companies, we show that this 'gap' may lead to unfair attribution of costs to the tenants. Simple enhancements of existing cloud pricing (e.g., analogous to the coincident peak pricing (CPP) used by some electric utilities) do not adequately address these shortcomings and suffer from short-term unfairness and undesirable oscillatory price vs. demand relationship offered to tenants. To overcome these shortcomings, we define an alternative pricing scheme to more fairly distribute a cloud's costs among its tenants. Our approach to fair attribution of cloud's costs is inspired by the concept of Shapley values used to fairly divide revenue among participants of a financial coalition. We demonstrate the efficacy of our scheme under price-sensitive tenant demand response using a combination of (i) extensive empirical evaluation with recent workloads from commercial data centers operated by IBM, and (ii) analytical modeling through non-cooperative game theory for a special case of tenant demand model.