In this paper, the authors study the bargaining problem of allocating homogeneous goods or chores among participants having equal claim to a unit of the good or equal obligation to undertake a chore. Two sequential auctions with desirable properties for solving the problem are proposed. The paper consists of six sections and an appendix. Section 1 presents an introduction with a detailed overview of the paper and related literature. Section 2 describes the model and the two types of auctions. Section 3 is devoted to the equilibrium analysis and proves 6 propositions. More precisely, Proposition 1 presents necessary conditions for a symmetric Bayes Nash equilibrium of the chore auction in increasing and differentiable strategies, and shows that the necessary conditions are also sufficient. Proposition 2 provides the characterization of equilibrium for the chore and goods auctions with bidders being risk neutral. Proposition 3 shows that the expected payoff of risk neutral bidders in every efficient symmetric equilibrium of any symmetric budget balanced mechanism is the same. Hence, the core and goods auctions are payoff equivalent at efficient and symmetric equilibria (Corollary 1). Proposition 4 characterizes equilibrium in the chore and goods auctions with bidders having CARA preferences. Proposition 5 shows that risk aversion causes a bidder to demand less compensation in the goods auction and to offer more compensation in the chore auction. It also provides bounds on the equilibrium bid functions. Finally, Proposition 6 presents some comparative statics and shows that in both auctions bidders drop out earlier as they become more risk averse. Also, the chore and goods auctions have the same equilibrium bid function in the limit as bidders become infinitely risk averse. Section 4 concerns maxmin perfect strategies and shows that there is a unique maxmin perfect strategy for the chore and goods auctions which is the same for both auctions (Proposition 7). In Section 5, the equilibrium allocations resulting under maxmin perfect bidding in the chore and goods auctions are related to the strategic and normative Shapley value allocations, respectively (Proposition 8). As bidders become infinitely risk averse, the equilibrium allocation of the chore auction converges to the strategic Shapley value allocation and the equilibrium allocation of the goods auction approaches the normative Shapley value allocation (Corollary 2). Section 6 presents a discussion of three aspects of the results. It is shown that a uniform price auction cannot generate either strategic or normative Shapley value allocations. Moreover, the authors show that the strategic and normative Shapley values can be interpreted as fair shares of residual surpluses. Finally, they illustrate the convergence of equilibrium to the Shapley value allocation. The appendix shows the result analogous to Proposition 1 but for the goods auction and presents the proofs for the results on the core auctions. The supplemental appendix provides the symmetric proofs for the goods auctions.