  In this paper, we establish a dynamic game to allocate CSR (Corporate Social
Responsibility) to the members of a supply chain. We propose a model of a
three-tier supply chain in a decentralized state which includes a supplier, a
manufacturer and a retailer. For analyzing supply chain performance in
decentralized state and the relationships between the members of the supply
chain, we use a Stackelberg game and consider in this paper a hierarchical
equilibrium solution for a two-level game. In particular, we formulate a model
that crosses through multi-periods with the help of a dynamic discrete
Stackelberg game. We obtain an equilibrium point at which both the profits of
members and the level of CSR taken up by supply chains is maximized.
