Resource-Monotonicity for House Allocation Problems

We study a simple model of assigning indivisible objects (e.g., houses, jobs, offices, etc.) to agents. Each agent receives at most one object and monetary compensations are not possible. We completely describe all rules satisfying efficiency and resource-monotonicity. The characterized rules assign the objects in a sequence of steps such that at each step there is either a dictator or two agents who “trade” objects from their hierarchically specified “endowments.”

Resource-monotonicity for house allocation problems

We study a simple model of assigning indivisible objects (e.g., houses, jobs, offices, etc.) to agents. Each agent receives at most one object and monetary compensations are not possible. We completely describe all rules satisfying efficiency and resource-monotonicity. The characterized rules assign the objects in a sequence of steps such that at each step there is either a dictator or two agents "trade" objects from their hierarchically specified "endowments."

Review of the Primary Schools' General Allocation Model

The allocation of additional teaching resources to schools under the terms of the General Allocation Model (GAM) was intended to make possible the development of inclusive primary schools; ensure that primary schools have a means of providing additional teaching support to pupils with learning difficulties and special educational needs arising from high incidence disabilities without recourse to making applications on behalf of individual pupils and included additional teaching time that was previously allocated for learning-support teaching as well as an allocation of additional teaching time for what was termed resource teaching for pupils with special educational needs arising from high incidence disabilities.

Solving Large Location-Allocation problems by Clustering and Simulated Annealing

Globalization involves several facility location problems that need to be handled at large scale. Location Allocation (LA) is a combinatorial problem in which the distance among points in the data space matter. Precisely, taking advantage of the distance property of the domain we exploit the capability of clustering techniques to partition the data space in order to convert an initial large LA problem into several simpler LA problems. Particularly, our motivation problem involves a huge geographical area that can be partitioned under overall conditions. We present different types of clustering techniques and then we perform a cluster analysis over our dataset in order to partition it. After that, we solve the LA problem applying simulated annealing algorithm to the clustered and non-clustered data in order to work out how profitable is the clustering and which of the presented methods is the most suitable

Sequential decisions in allocation problems

[eng] In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequentia decision problem. In each step of process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentally compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersections of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantagenous properties for the first player

Sequential decisions in allocation problems

[eng] In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequentia decision problem. In each step of process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentally compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersections of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantagenous properties for the first player

Robustness on resource allocation problems

En problemes d'assignació de recursos, normalment s'han de tenir en compte les incerteses que poden provocar canvis en les dades inicials. Aquests canvis dificulten l'aplicabilitat de les planificacions que s'hagin fet inicialment. Aquesta tesi se centra en l'elaboració de tècniques que consideren la incertesa alhora de cercar solucions robustes, és a dir solucions que puguin continuar essent vàlides encara que hi hagi canvis en l'entorn. Particularment, introduïm el concepte de robustesa basat en reparabilitat, on una solució robusta és una que pot ser reparada fàcilment en cas que hi hagi incidències. La nostra aproximació es basa en lògica proposicional, codificant el problema en una fórmula de satisfactibilitat Booleana, i aplicant tècniques de reformulació per a la generació de solucions robustes. També presentem un mecanisme per a incorporar flexibilitat a les solucions robustes, de manera que es pugui establir fàcilment el grau desitjat entre robustesa i optimalitat de les solucions.

Switch allocation problems in power distribution systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Strategy-proofness and essentially single-valued cores revisited

We consider general allocation problems with indivisibilities where agents' preferences possibly exhibit externalities. In such contexts many different core notions were proposed. One is the gamma-core whereby blocking is only allowed via allocations where the non-blocking agents receive their endowment. We show that if there exists an allocation rule satisfying ‘individual rationality’, ‘efficiency’, and ‘strategy-proofness’, then for any problem for which the gamma-core is non-empty, the allocation rule must choose a gamma-core allocation and all agents are indifferent between all allocations in the gamma-core. We apply our result to housing markets, coalition formation and networks.

Equity considerations in health care: An axiomatic bargaining approach

The general issues of equity and efficiency are placed at the center of the analysis of resource allocation problems in health care. We examine them using axiomatic bargaining theory. We study different solutions that have been proposed and relate them to previous literature on health care allocation. In particular, we focus on the solutions based on axiomatic bargaining with claims and suggest that they may be particularly appealing as distributive criteria in health policy. Finally, we present the results of a survey that tries to elicit moral intuitions of people about resource allocation problems and their different solutions.

Allocation via Deferred-Acceptance under Responsive Priorities

In many economic environments - such as college admissions, student placements at public schools, and university housing allocation - indivisible objects with capacity constraints are assigned to a set of agents when each agent receives at most one object and monetary compensations are not allowed. In these important applications the agent-proposing deferred-acceptance algorithm with responsive priorities (called responsive DA-rule) performs well and economists have successfully implemented responsive DA-rules or slight variants thereof. First, for house allocation problems we characterize the class of responsive DA-rules by a set of basic and intuitive properties, namely, unavailable type invariance, individual rationality, weak non-wastefulness, resource-monotonicity, truncation invariance, and strategy-proofness. We extend this characterization to the full class of allocation problems with capacity constraints by replacing resource- monotonicity with two-agent consistent con ict resolution. An alternative characterization of responsive DA-rules is obtained using unassigned objects invariance, individual rationality, weak non-wastefulness, weak consistency, and strategy-proofness. Various characterizations of the class of "acyclic" responsive DA-rules are obtained by using the properties efficiency, group strategy-proofness, and consistency.

Strategy-proof tie-breaking

We study a general class of priority-based allocation problems with weak priority orders and identify conditions under which there exists a strategy-proof mechanism which always chooses an agent-optimal stable, or constrained efficient, matching. A priority structure for which these two requirements are compatible is called solvable. For the general class of priority-based allocation problems with weak priority orders,we introduce three simple necessary conditions on the priority structure. We show that these conditions completely characterize solvable environments within the class of indifferences at the bottom (IB) environments, where ties occur only at the bottom of the priority structure. This generalizes and unifies previously known results on solvable and unsolvable environments established in school choice, housing markets and house allocation with existing tenants. We show how the previously known solvable cases can be viewed as extreme cases of solvable environments. For sufficiency of our conditions we introduce a version of the agent-proposing deferred acceptance algorithm with exogenous and preference-based tie-breaking.

Centralized allocation in multiple markets

We study the problem of centralized allocation of indivisible objects in multiple markets. We show that the set of allocation rules that are group strategy-proof and Pareto-efficient are sequential dictatorships. Therefore, the solution of the joint al-location in multiple markets is significantly narrower than in the single-market case. Our result also applies to dynamic allocation problems. Finally, we provide conditions under which the solution of the single-market allocation coincides with the multiple-market case, and we apply this result to the study of the school choice problem with sibling priorities.