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To address coordination and complexity issues, we formulate a grid task allocation problem as a bargaining based self-adaptive auction and propose the BarSAA grid task-bundle allocation algorithm. During the auction, prices are iteratively negotiated and dynamically adjusted until market equilibrium is reached. The BarSAA algorithm features decentralized bidding decision making in a heterogeneous distributed environment so that scheduler can offload its duty onto participating computing nodes and significantly reduces scheduling overheads. When a BarSAA auction converges, the equilibrium point is Pareto Optimal and achieves social efficient outcome and double-sided revenue maximization. In addition, BarSAA promotes truthful behavior among selfish nodes. Through game theoretical analysis, we demonstrate that truthful revelation is beneficial to bidders in making bidding strategies. Extensive simulation results are presented to demonstrate the efficiency of the BarSAA strategy and validate several important analytical properties.