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This paper addresses the collaborative linear- assignment problem (CLAP) for a class of allocation applications. CLAP entails using agents to seek a concurrent allocation of one different object for every agent, to optimize a linear sum efficiency function as their (soft) social goal. Anchoring in the standard framework of automated negotiation allows an original belief-desire-intention (BDI) negotiation model for CLAP to be conceptually separated into a BDI assignment protocol and an adopted strategy. Facilitated by this conceptual separation, the contributions of this paper are as follows: 1) providing a rigorous analysis of the protocol and demonstrating its salient properties and 2) formulating new strategies using a novel idea of cooperative concession. Four different strategies for a negotiation agent and the arbitration agent provide 16 arbitration-negotiation combinations running with the protocol, and these are empirically assessed for their performance profiles in negotiation speed and solution quality. Important findings, including the stability of the protocol in producing better than good enough global allocations and the strategic influence of cooperative concessions on performance, are examined. The significance and practicality of this paper in relation to existing work are also discussed.