This article uses the main tools of cooperative game theory, the core of a game and the Shapley value, to tackle the challenge posed by corporate tax harmonization in order to fight tax competition and profit shifting. These tools are applied to provide a counterfactual evaluation and to assess the credibility of Saez and Zucman (2019) proposal to establish a minimum rate at 25% at the G7/G20 level. Based on the empirical data of Tørsløv et al. (2020), our main results are the following. First, at the G7 level, the more countries involved in the agreement, the more efficient it would be. Second, stability of cooperation at the G7 level can be achieved without giving up fairness consideration in the distribution of the surplus. We then extend our application to the G20 and show that these results do not hold anymore. Third, from our original methodological approach, we confirm that not only the target rate matters in the perspective of international tax cooperation, but also the numbers of participants and their current effective rates.