Standard intuitions for optimal gerrymandering involve concentrating one's extreme opponents in “unwinnable” districts (“packing”) and spreading one's supporters evenly over “winnable” districts (“cracking”). These intuitions come from models with either no uncertainty about voter preferences or only two voter types. In contrast, we characterize the solution to a problem in which a gerrymanderer observes a noisy signal of voter preferences from a continuous distribution and creates N districts of equal size to maximize the expected number of districts she wins. Under mild regularity conditions, we show that cracking is never optimal—one's most ardent supporters should be grouped together. Moreover, for sufficiently precise signals, the optimal solution involves creating a district that matches extreme “Republicans” with extreme “Democrats,” and then continuing to match toward the center of the signal distribution. (JEL D72)

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Sanford Grossman and Oliver Hart used the theory of incomplete contracts to develop answers to the question "What is a firm, and what determines its boundaries?" in their path-breaking paper on "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration" ( Journal of Political Economy , 1986, vol. 94, no. 4). Perhaps the central issue is that economic actors are only boundedly rational and cannot anticipate all possible contingencies. It might well be that certain states of nature or actions cannot be verified by third parties after they arise, like certain qualities of a good to be traded in the future, and thus cannot be written into an enforceable contract. When contracts are incomplete, and consequently not all uses of an asset can be specified in advance, any contract negotiated in advance must leave some discretion over the use of the assets; and the "owner" of the firm is the party to whom the residual rights of control have been allocated at the contracting stage. The optimal allocation of property rights—or governance structure—is one that minimizes efficiency losses. This produces a theory of ownership and vertical integration as well as a theory of the firm. First we spell out Grossman and Hart's argument using a simple numerical example. Then we show how the incomplete contracts approach can be used to analyze the firms' internal organization; the firms' financial decisions; the costs and benefits from privatization; and the organization of international trade between inter- and intrafirm trade. We discuss several criticisms of the incomplete contracts/property rights methodology and review recent developments of the incomplete contracts approach.

We consider the robustness of extensive form mechanisms to deviations from common knowledge about the state of nature, which we refer to as information perturbations . First, we show that even under arbitrarily small information perturbations the Moore-Repullo mechanism does not yield (even approximately) truthful revelation and that in addition the mechanism has sequential equilibria with undesirable outcomes. More generally, we prove that any extensive form mechanism is fragile in the sense that if a non-Maskin monotonic social objective can be implemented with this mechanism, then there are arbitrarily small information perturbations under which an undesirable sequential equilibrium also exists. Finally, we argue that outside options can help improve efficiency in asymmetric information environments, and that these options can be thought of as reflecting ownership of an asset.