Corporate social responsibility (CSR) is defined as corporate activities and their 7 impacts on different social groups. In this paper, CSR is considered in a two-echelon supply 8 chain consisting of an upstream supplier and a downstream firm that are bound by a wholesale 9 price contract. CSR performance (the outcome of CSR conduct) of the whole supply chain is 10 gauged by a global variable and the associated cost of achieving this CSR performance is only 11 incurred by the supplier with an expectation of being shared with the downstream firm via the 12 wholesale price contract. As such, the key issue is to determine who should be allocated as the 13 responsibility holder with the right of offering the contract and how this right should be 14 appropriately restricted. Game-theoretical analyses are carried out on six games, resulting from 15 different interaction schemes between the supplier and the firm, to derive their corresponding 16 equilibriums. Comparative institutional analyses are then conducted to determine the optimal 17 social responsibility allocations based on both economic and CSR performance criteria. Main 18 results are furnished in a series of propositions and their implications to the real-world business 19 practice are discussed. The key findings are threefold: Under the current model settings, (1) the 20 optimal allocation scheme is to assign the supplier as the responsibility holder with appropriate 21 restrictions on the corresponding rights to determine the wholesale price; (2) Inherent conflict 22 exists between the economic and CSR performance criteria and, hence, the two maxima cannot 23 be achieved simultaneously; (3) Although integrative channel profit is not attainable, the system-24 wide profit will be improved by implementing optimal social responsibility allocation schemes. 25

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A polluted river network is populated with agents (e.g., firms, villages, municipalities, or countries) located upstream and downstream. This river network must be cleaned, the costs of which must be shared among the agents. We model this problem as a cost sharing problem on a tree network. Based on the two theories in international disputes, namely the Absolute Territorial Sovereignty (ATS) and the Unlimitted Territorial Integrity (UTI), we propose three different cost sharing methods for the problem. They are the Local Responsibility Sharing (LRS), the Upstream Equal Sharing (UES), and the Downstream Equal Sharing (DES), respectively. The LRS and the UES generalize Ni and Wang ("Sharing a polluted river", Games Econ. Behav., 60 (2007), 176-186) but the DES is new. The DES is based on a new interpretation of the UTI. We provide axiomatic characterizations for the three methods. We also show that they coincide with the Shapley values of the three different games that can be defined for the problem. Moreover, we show that they are in the cores of the three games, respectively. Our methods can shed light on pollution abatement of a river network with multiple sovereignties.JEL classification: C71, D61, D62.

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A polluted river network is populated with agents (e.g., firms, villages, municipalities, or countries) located upstream and downstream. This river network must be cleaned, the costs of which must be shared among the agents. We model this problem as a cost sharing problem on a tree network. Based on the two theories in international disputes, namely the Absolute Territorial Sovereignty (ATS) and the Unlimitted Territorial Integrity (UTI), we propose three different cost sharing methods for the problem. They are the Local Responsibility Sharing (LRS), the Upstream Equal Sharing (UES), and the Downstream Equal Sharing (DES), respectively. The LRS and the UES generalize Ni and Wang ("Sharing a polluted river", Games Econ. Behav., 60 (2007), 176-186) but the DES is new. The DES is based on a new interpretation of the UTI. We provide axiomatic characterizations for the three methods. We also show that they coincide with the Shapley values of the three different games that can be defined for the problem. Moreover, we show that they are in the cores of the three games, respectively. Our methods can shed light on pollution abatement of a river network with multiple sovereignties.JEL classification: C71, D61, D62.

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