The concept of differential privacy (DP) can quantitatively measure privacy loss by observing the changes in the distribution caused by the inclusion of individuals in the target dataset. The DP, which is generally used as a constraint, has been prominent in safeguarding datasets in machine learning in industry giants like Apple and Google. A common methodology for guaranteeing DP is incorporating appropriate noise into query outputs, thereby establishing statistical defense systems against privacy attacks such as membership inference and linkage attacks. However, especially for small datasets, existing DP mechanisms occasionally add excessive amount of noise to query output, thereby discarding data utility. This is because the traditional DP computes privacy loss based on the worst-case scenario, i.e., statistical outliers. In this work, to tackle this challenge, we utilize per-instance DP (pDP) as a constraint, measuring privacy loss for each data instance and optimizing noise tailored to individual instances. In a nutshell, we propose a per-instance noise variance optimization (NVO) game, framed as a common interest sequential game, and show that the Nash equilibrium (NE) points of it inherently guarantee pDP for all data instances. Through extensive experiments, our proposed pDP algorithm demonstrated an average performance improvement of up to 99.53% compared to the conventional DP algorithm in terms of KL divergence.