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We identify a natural counterpart of the standard GARP for demand data in which goods are all indivisible. We show that the new axiom (DARP, for "discrete axiom of revealed preference") is necessary and sufficient for the rationalization of the data by a well-behaved utility function. Our results complement the main finding of Polisson and Quah, Am. Econ. J.: Micro. 5(1) p.28-34 (2013), who rather minimally modify the original consumer problem with indivisible goods so that the standard GARP still applies.

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unani- mous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair allocations exist only for small groups. We introduce the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group. This concept is better suited to large groups such as cities or countries. We present protocols for democratic fair allocation among two or more arbitrarily large groups of agents with monotonic, additive, or binary valuations. Our protocols approximate both envy-freeness and maximin-share fairness. As an example, for two groups of agents with additive valuations, our protocol yields an allocation that is envy-free up to one good and gives at least half of the maximin share to at least half of the agents in each group.

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair allocations exist only for small groups. We introduce the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group. This concept is better suited to large groups such as cities or countries. We present protocols for democratic fair allocation among two or more arbitrarily large groups of agents with monotonic, additive, or binary valuations. For two groups with arbitrary monotonic valuations, we give an efficient protocol that guarantees envy-freeness up to one good for at least 1/2 of the agents in each group, and prove that the 1/2 fraction is optimal. We also present other protocols that make weaker fairness guarantees to more agents in each group, or to more groups. Our protocols combine techniques from different fields, including combinatorial game theory, cake cutting, and voting.

Focusing on the case of Jerusalem this article analyzes different types of "indivisibles" and explores a range of strategies for resolving conflicts over indivisibles through negotiations. The focus on Jerusalem as an ethnic conflict leads to an emphasis on mainstream Palestinian and Israeli views and proposals (among others the plan of Mayor Kollek), and on what these tend to see as the central aspects of the problem: sovereignty, municipal powers, and the Old City, including the holy places. (DÜI-Hns)

AbstractDisequilibrium trade can occur in a market lacking both recontracting and a computational system that maps utilities into prices. This paper studies disequilibrium trade in a large market for an indivisible good. We focus on the possible speed of adjustment when arbitrage among periods is feasible and the surplus loss. We find that incentive compatible sequential trade through a disequilibrium path is only compatible with sluggish price adjustments and sufficiently impatient agents. Thus, price adjustment does not depend on excess demand alone but on arbitrage opportunities and the willingness of agents to engage on them. We find that the upper bound on the speed of price adjustment involves a lower bound for the social surplus loss, whatever the kind of rationing. The reason is that even when the market price converges to the surplus maximizing value, as it happens when rationing is efficient, some pieces of surplus are not attainable at the current period due to arbitrage. Moreover, faster price adjustments do not imply less surplus loss, because the effect of price changes on transactions via arbitrage. Finally, under weaker-than-efficient rationing there is a one period incentive compatible trading procedure in which most of the surplus is destroyed. The procedure has the property that almost every agent in the market trades.