A novel policy for allocating reconfigurable fabric resources in multi-core processors is presented. The authors deploy a minority-game to maximize the efficient use of the reconfigurable fabric while meeting performance constraints of individual tasks running on the cores. As they will show, the Minority Game ensures a fair allocation of resources, e.g., no single core will monopolize the reconfigurable fabric. Rather, all cores receive a \"Fair\" share of the fabric, i.e., their tasks would miss their performance constraints by approximately the same margin, thus ensuring an overall graceful degradation. The policy is implemented on a Virtex-4 FPGA and evaluated for diverse applications ranging from security to multimedia domains.