An Algorithmic Framework for Strategic Fair Division

We study the paradigmatic fair division problem of allocating a divisible good among agents with heterogeneous preferences, commonly known as cake cutting. Classical cake cutting protocols are susceptible to manipulation. Do their strategic outcomes still guarantee fairness? To address this question we adopt a novel algorithmic approach, by designing a concrete computational framework for fair division---the class of Generalized Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic properties of algorithms that operate in this model. The class of GCC protocols includes the most important discrete cake cutting protocols, and turns out to be compatible with the study of fair division among strategic agents. In particular, GCC protocols are guaranteed to have approximate subgame perfect Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule is flexible. We further observe that the (approximate) equilibria of proportional GCC protocols---which guarantee each of the $n$ agents a $1/n$-fraction of the cake---must be (approximately) proportional. Finally, we design a protocol in this framework with the property that its Nash equilibrium allocations coincide with the set of (contiguous) envy-free allocations

Democratic Fair Allocation of Indivisible Goods

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.Comment: Appears in the 27th International Joint Conference on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence (IJCAI-ECAI), 201

Community Enforcement of Informal Contracts: Jewish Diamond Merchants in New York

The diamond industry is home to many unusual features: the predominance of an ethnically homogeneous community of merchants, the norm of intergenerational family businesses, and a rejection of public courts in favor of private contract enforcement. This paper explains that the diamond industry\u27s unique attributes arise specifically to meet the particularly rigorous hazards of transacting in diamonds. Since diamonds are portable, easily concealable, and extremely valuable, the risk associated with a credit sale can be especially costly. However, the industry enjoys valuable organizational efficiencies if transactions occur on credit between independent, fully incentivized agents. Thus, an efficient system of exchange will find ways to induce merchants who purchase on credit to fulfill their payment obligations. The very features that give the diamond industry an unusual profile are responsible for providing institutions to support credit sales. A system of private arbitration spreads information regarding merchants\u27 past dealings, so a reputation mechanism to monitor merchants can take hold. Intergenerational legacies, though restricting entry only to those who can inherit good reputations from family members, resolve an end-game problem and induce merchants to deal honestly through their very last transaction. And the participation of Ultra-Orthodox Jews, for whom inclusion and participation in their communities is equally paramount to their material wealth, serve important value-added services as diamond cutters and brokers without posing the threat of theft and flight

Fair Divisions as Attracting Nash Equilibria of Simple Games

We consider the problem of allocating a finite number of divisible homogeneous goods to N = 2 individuals, in a way which is both envy-free and Pareto optimal. Building on Thomson (2005 Games and Economic Behavior), a new simple mechanism is presented here with the following properties: a) the mechanism fully implements the desired divisions, i.e. for each preference profile the set of equilibrium outcomes coincides with the set of fair divisions; b) the set of equilibria is a global attractor for the best-reply dynamics. Thus, players myopically adapting their strategies settle down in an fair division. The result holds even if mixed strategies are used.Fair divisions, envy-free, implementation, best reply dynamics

What (If Anything) Can Economics Say About Equity?

Does economics have anything to teach us about the meaning of fairness? The leading practitioners of law and economics disagree. Judge Richard Posner argues that economics is largely irrelevant to distributive issues. Posner maintains that the most useful economic measure of social welfare is cost-benefit analysis (which he calls wealth maximization). But, he observes, this economic measure ratifies and perfects an essentially arbitrary distribution of wealth. Given an ethically acceptable initial assignment of wealth, rules based on economic efficiency may have some claim to be considered fair. On the critical issue of distributional equity, however, Posner apparently believes that economics has little to say. In contrast, Professors Louis Kaplow and Steven Shavell believe that economics can teach us nearly everything about equity. In Fairness Versus Welfare, they argue that there is only one viable notion of equity: resources should be distributed so as to maximize overall social welfare. As we will see, the full import of this argument is ambiguous. On the one hand, Kaplow and Shaven expressly concede that multiple ways of calculating social welfare might exist, so Wy might have to look beyond economics to determine the right one. On the other hand, much of their argument is implicitly predicated on a specific social welfare function, and in a footnote they give the argument for adopting this function universally. If a unique social welfare function is given, economic analysis would completely resolve all equity issues under their approach. Thus, although they do not say so explicitly, the book can be read to endorse a singl� definition of equity based on economic analysis. This reading would completely eliminate any independent role for judgments about equity. At the least, however, Kaplow and Shaven believe that economics can restrict value judgments about equity to a single, sharply defined place in policy analysis: the choice of an appropriate social welfare function. Posner, in turn, sees only modest merit in the Kaplow and Shaven theory of social welfare, except to the extent that it reduces in practice to his own theory of wealth maximization