Borrowing-proofness of the Lindahl rule in Kolm triangle economies

In the context of a simple model of public good provision, we study the requirement on an allocation rule that it be immune to manipulation by augmenting one's endowment through borrowing from the outside world. We call it open-economy borrowing-proofness (Thomson, 2009). We ask whether the Lindahl rule satisfies the property. The answer is yes on both the domain of quasi-linear economies and on the domain of homothetic economies. However, on the classical domain (when preferences are only required to be continuous, monotone, and convex), the answer is negative. We compare the manipulability of the rule through borrowing and its manipulability through withholding. We also asks whether the rule is immune to manipulation by borrowing from a fellow trader, closed-economy borrowing-proofness. We obtain a parallel set of answers. The negative results hold no matter how small the amount borrowed is constrained to be.Public good; Lindahl rule; Kolm triangle; borrowing-proofness; withholding-proofness.

Divide-and-Permute

We construct "simple" games implementing in Nash equilibria several solutions to the problem of fair division. These solutions are the no-envy solution, which selects the allocations such that no agent would prefer someone else's bundle to his own, and several variants of this solution. Components of strategies can be interpreted as allocations, consumption bundles, permutations, points in simplices of dimensionalities equal to the number of goods or to the number of agents, and integers. We also propose a simple game implementing the Pareto solution and games implementing the intersections of the Pareto solution with each of these solutions.Nash implementation. No-envy. Divide-and-permute.

On the Existence of Consistent Rules to Adjudicate Conflicting Claims: A Constructive Geometric Approach

For the problem of adjudicating conflicting claims, a rule is consistent if the choice it makes for each problem is always in agreement with the choice it makes for each "reduced problem" obtained by imagining that some claimants leave with their awards and reassessing the situation from the viewpoint of the remaining claimants. We develop a general technique to determine whether a given two-claimant rule admits a consistent extension to general populations, and to identify this extension if it exists. We apply the technique to a succession of examples. One application is to a one-parameter family of rules that offer a compromise between the constrained equal awards and constrained equal losses rules. We show that a consistent extension of such a rule exists only if all the weight is placed on the former or all the weight is placed on the latter. Another application is to a family of rules that provide a compromise between the constrained equal awards and proportional rules, and a dual family that provide a compromise between the constrained equal losses and proportional rules. In each case, we identify the restrictions implied by consistency.claims problems, consistent extensions, proportional rule, constrained equal awards rule, constrained equal losses rule.

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

Two families of rules for the adjudication of conflicting claims

We define two families of rules to adjudicate conflicting claims. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules. The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. In each case, we identify the subfamily of consistent rules.claims problems, constrained equal awards rule, constrained equal losses rule, Talmud rule, minimal overlap rule, ICI rules, CIC rules, consistency.

A Characterization of a Family of Rules for the Adjudication of Conflicting Claims

We consider the problem of adjudicating conflicting claims, and characterize the family of rules satisfying four standard invariance requirements, homogeneity, two composition properties, and consistency. It takes as point of departure the characterization of the family of two-claimant rules satisfying the first three requirements, and describes the restrictions imposed by consistency on this family and the further implications of this requirement for problems with three or more claimants. The proof, which is an alternative to Moulin's original proof (Econometrica, 2000), is based on a general method of constructing consistent extensions of two-claimant rules (Thomson, 2001), which exploits geometric properties of paths of awards, seen in their entirety.claims problems, consistent extensions, proportional rule, constrained equal awards rule, constrained equal losses rule.

Preserving Social Media: the Problem of Access

As the applications and services made possible through Web 2.0 continue to proliferate and influence the way individuals exchange information, the landscape of social science research, as well as research in the humanities and the arts, has the potential to change dramatically and to be enriched by a wealth of new, user-generated data. In response to this phenomenon, the UK Data Service have commissioned the Digital Preservation Coalition to undertake a 12-month study into the preservation of social media as part of the ‘Big Data Network’ programme funded by the Economic and Social Research Council (ESRC). The larger study focuses on the potential uses and accompanying challenges of data generated by social networking applications. This paper, ‘Preserving Social Media: the Problem of Access’, comprises an excerpt of that longer study, allowing the authors a space to explore in closer detail the issue of making social media archives accessible to researchers and students now and in the future. To do this, the paper addresses use cases that demonstrate the potential value of social media to academic social science. Furthermore, it examines how researchers and collecting institutions acquire and preserve social media data within a context of curatorial and legislative restrictions that may prove an even greater obstacle to access than any technical restrictions. Based on analysis of these obstacles, it will examine existing methods of curating and preserving social media archives, and second, make some recommendations for how collecting institutions might approach the long-term preservation of social media in a way that protects the individuals represented in the data and complies with the conditions of third party platforms. With the understanding that web-based communication technologies will continue to evolve, this paper will focus on the overarching properties of social media, analysing and comparing current methods of curation and preservation that provide sustainable solutions

On properties of division rules lifted by bilateral consistency

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is "lifted" if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic.claims problems, consistency, lifting, constrained equal awards rule, constrained equal losses rule

Convergence under Replication of Rules to Adjudicate Conflicting Claims

We study the behavior of rules for the adjudication of con°icting claims when there are a large number of claimants with small claims. We model such situations by replicating some basic problem. We show that under replication, the random arrival rule (O'Neill, 1982) behaves like the proportional rule, the rule that is the most often recommended in this context. Also, under replication, the minimal overlap rule (O'Neill, 1982) behaves like the constrained equal losses rule, the rule that selects a division at which all claimants experience equal losses subject to no-one receiving a negative amount.Claims problems, Replication, Random arrival rule, Proportional rule, Minimal overlap rule, Constrained equal losses rule.

A New Solution to the Problem of Adjudicating Conflicting Claims

For the problem of adjudicating conflicting claims, we consider the requirement that each agent should receive at least 1/n his claim truncated at the amount to divide, where n is the number of claimants (Moreno-Ternero and Villar, 2004a). We identify two families of rules satisfying this bound. We then formulate the requirement that for each problem, the awards vector should be obtainable in two equivalent ways, (i) directly or (ii) in two steps, first assigning to each claimant his lower bound and then applying the rule to the appropriately revised problem. We show that there is only one rule satisfying this requirement. We name it the "recursive rule", as it is obtained by a recursion. We then undertake a systematic investigation of the properties of the rule.claims problems, recursive rule.