The work analyses three key concepts frequently recalled and strictly correlated: contemporarity of dialogue, convergence of interests and collectivity of responsibilities. The continuous digital conversations between companies and customers are changing the value creation processes and leading to new positive convergence of customers and citizens at work. Convergence is driven by a renewed social sensitivity which is clearly influenced by collective responsibilities. After introducing the literature we bring logical arguments and empirical evidences to focus on the new convergence of market and society interests. Through a new Co-Value Model we measure the intensity of conversations contents: co-advertising contents show the highest level of consumer involvement, followed by co-planning, co-selling, co-use, co-post-sales, co-logistic and co-production. The metrics of the Co-Value Model are aimed to measure and reinforce the basic idea of convergence between the customer perspective- logic of money- and the citizen perspective -logic of gift-. Analyzing the continuous conversation between customer and companies within 21 international digital services, we demonstrate that a) the continuous digital conversations between companies and customers are changing definitively the value creation processes; b) the renewed social sensitivity gradually brings a new convergence between market and society interests which is evidenced by the high frequence of conversation focussed on social topics: c) the new convergence is driven by a renewed collective sense of co-responsibility. The findings show the robustness of the core concept of convergence: companies and customers maintain separate and complementary roles but their conversations are fundamentally remodelled both in content and in shape. Individuals are now called to play an economic role as prosumers, but at the same time, they have new opportunities as citizens for new forms of dialogue which reinforce their critical and social role. This is what we call convergence of interests. Market and society do not coincide, companies and customer act as counterparts and have different roles but their interests are converging. In many cases, prosumerism can generate a new loop between companies and consumers responsibility, and consumers can commit to this new social game of being customer and citizen at work. The model is applied to a large number of very recent case histories able to focus on the managerial implications of the new social game.