The paper examines the issue of corporate social responsibility (CSR) from the perspective of constitutional economics, focusing on the distinction between a political community’s constitutional choice of the rules of the “market game,” and the market players’ sub-constitutional choice of strategies within these rules. Three versions of CSR-demands are identified and discussed, a “soft,” a “hard”, and a “radical” version. The soft version is concerned with the issue of how “socially responsible” corporations ought to play the market game within existing rules. The hard version is about how the rules of the market ought to be changed in order to induce “socially responsible” corporate behavior. And the radical version questions the compatibility of CSR and the logic of the market game, calling in effect for adopting some alternative economic regime.