This paper investigates the impacts of installing regulated wind and electricity storage on average price and price volatility in electricity markets. A stochastic bi-level optimization model is developed, which computes the optimal allocation of new wind and battery capacities, by minimizing a weighted sum of the average market price and price volatility. A fixed budget is allocated on wind and battery capacities in the upper-level problem. The operation of strategic/regulated generation, storage, and transmission players is simulated in the lower-level problem using a stochastic (Bayesian) Cournot-based game model. Australia's national electricity market, which is experiencing occasional price peaks, is considered as the case study. Our simulation results quantitatively illustrate that the regulated wind is more efficient than storage in reducing the average price, while the regulated storage more effectively reduces the price volatility. According to our numerical results, the storage-only solution reduces the average price at most by 9.4%, and the wind-only solution reduces the square root of price volatility at most by 39.3%. However, an optimal mixture of wind and storage can reduce the mean price by 17.6% and the square root of price volatility by 48.1%. It also increases the consumer surplus by 1.52%. Moreover, the optimal mixture of wind and storage is a profitable solution unlike the storage-only solution.