Supplemental Information to the August 2008 Education Task Force Report, August 2008

The Rebuild Iowa Education Task Force is composed of Iowans with experience and expertise related to the impact of the tornadoes, storms, and floods of 2008 on the educational system in Iowa. The massive damage greatly impacted educational facilities and enrollment, resulting in thousands of displaced students and significant long-term rebuilding needs. In addition, the education system is a “community center,” and in many ways acts as a first responder to Iowans experiencing the disasters. It is important to also recognize this role and the need for “non-educational” (and often non-quantifiable) supports as a part of the overall recovery effort. There are a few parts of the state that sustained significant structural and other damage as a result of the disasters. However, many school districts and educational institutions throughout the state experienced damage that resulted in re-allocating building usage, enrollment issues (because of housing and relocation issues in the community), or use of school facilities to assist in the recovery efforts (by housing displaced community agencies and providing temporary shelter for displaced Iowans). At this time, damage estimates are only estimates and numbers are revised often. Estimates of damage are being developed by multiple agencies, including FEMA, the Iowa Department of Education, insurance companies, and schools themselves, since there are many different types of damage to be assessed and repaired. In addition to structural damage, educational institutions and communities are trying to find ways to quantify sometimes unquantifiable data, such as future revenue capabilities, population declines, and impact on mental health in the long-term. The data provided in this report is preliminary and as up to date as possible; information is updated on a regular basis as assessments continue and damage estimates are finalized. Supplemental Information to the August 2008 Education Task Force Report

Flood Plain Management & Hazard Mitigation Task Force Report, August 2008

The Flood Plain Management and Hazard Mitigation Task Force emphasizes the long-term benefits of mitigation and management to the entire state in preventing or reducing damages from floods and other hazards faced in Iowa. Investments in efforts to manage watershed areas and to mitigate any damages from floods or other disaster events benefit individuals, families, communities, agriculture, business and industry, and certainly public entities and infrastructure. The Task Force encourages the Rebuild Iowa Advisory Commission to balance the immediate needs for rebuilding to include the beginning of the investments required to effectively mitigate future damage and maintain effective policy in Iowa’s watersheds. The significance of the damage seen in Iowa from the tornadoes, storms, and floods of 2008 include the loss of eighteen Iowans in disaster-related events. This alone should inspire investment in mitigation efforts for all hazards. Much of the damage resulting from the disasters can be tied to floodplain management and hazard mitigation, pointing the way toward enhanced efforts and new initiatives to safeguard lives, property, and communities’ economic health. Even so, it must be recognized that the weather events throughout last winter and spring added impetus to the rains and storms that ultimately resulted in record flooding. Some perspective must be maintained as planning progresses and significant investments in mitigation are considered to meet a specific level of safety and protection from future threats. The Task Force identified a number of issues, and four were agreed-upon as those with the highest priority to be addressed by the Task Force through a set of recommendations.

Supplemental Information to the August 2008 Flood Plain Management & Hazard Mitigation Task Force Report, August 2008

The Flood Plain Management and Hazard Mitigation Task Force emphasizes the long-term benefits of mitigation and management to the entire state in preventing or reducing damages from floods and other hazards faced in Iowa. Investments in efforts to manage watershed areas and to mitigate any damages from floods or other disaster events benefit individuals, families, communities, agriculture, business and industry, and certainly public entities and infrastructure. The Task Force encourages the Rebuild Iowa Advisory Commission to balance the immediate needs for rebuilding to include the beginning of the investments required to effectively mitigate future damage and maintain effective policy in Iowa’s watersheds. The significance of the damage seen in Iowa from the tornadoes, storms, and floods of 2008 include the loss of eighteen Iowans in disaster-related events. This alone should inspire investment in mitigation efforts for all hazards. Much of the damage resulting from the disasters can be tied to floodplain management and hazard mitigation, pointing the way toward enhanced efforts and new initiatives to safeguard lives, property, and communities’ economic health. Even so, it must be recognized that the weather events throughout last winter and spring added impetus to the rains and storms that ultimately resulted in record flooding. Some perspective must be maintained as planning progresses and significant investments in mitigation are considered to meet a specific level of safety and protection from future threats. The Task Force identified a number of issues, and four were agreed-upon as those with the highest priority to be addressed by the Task Force through a set of recommendations. Supplemental Information to the August 2008

Housing Task Force Report, August 2008

Few disaster recovery initiatives are more important than those that house the people and assist them to repair or replace their homes. The widespread damage to housing from the tornadoes, storms, and floods in 2008 creates greater challenges in housing than the state has faced from previous disasters. The Housing Task Force gratefully submits its Report to the Rebuild Iowa Advisory Commission as an opportunity to place data, issues, priorities and recommendations before residents, communities, state officials, and policymakers at all levels for consideration of how best to guide, support, and resource these efforts. Quantifying the impact of the disasters on communities is daunting. The many personal accounts and sets of community statistics paint pictures of Iowans who have emerged from the rubble or muck of their homes with a determination and commitment to rebuild not just like they were previous to the disasters, but better and stronger. Damage statistics are telling.

Supplemental Information to the August 2008 Housing Task Force Report, August 2008

Few disaster recovery initiatives are more important than those that house the people and assist them to repair or replace their homes. The widespread damage to housing from the tornadoes, storms, and floods in 2008 creates greater challenges in housing than the state has faced from previous disasters. The Housing Task Force gratefully submits its Report to the Rebuild Iowa Advisory Commission as an opportunity to place data, issues, priorities and recommendations before residents, communities, state officials, and policymakers at all levels for consideration of how best to guide, support, and resource these efforts. Quantifying the impact of the disasters on communities is daunting. The many personal accounts and sets of community statistics paint pictures of Iowans who have emerged from the rubble or muck of their homes with a determination and commitment to rebuild not just like they were previous to the disasters, but better and stronger. Damage statistics are telling. Supplemental Information to the August 2008

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Multi-sided Böhm-Bawerk assignment markets: the nucleolus and the core-center

En aquest treball mostrem que, a diferència del cas bilateral, per als mercats multilaterals d'assignació coneguts amb el nom de Böhm-Bawerk assignment games, el nucleolus i el core-center, i. e. el centre de masses del core, no coincideixen en general. Per demostrar-ho provem que donant un m-sided Böhm-Bawerk assignment game les dues solucions anteriors poden obtenir-se respectivament del nucleolus i el core-center d'un joc convex definit en el conjunt format pels m sectors. Encara més, provem que per calcular el nucleolus d'aquest últim joc només les coalicions formades per un jugador o m-1 jugadors són importants. Aquests resultats simplifiquen el càlcul del nucleolus d'un multi-sided ¿¿ohm-Bawerk assignment market amb un número molt elevat d'agents.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

On the nucleolus of 2 x 2 assignment games

[spa] En este artículo hallamos fórmulas para el nucleolo de juegos de asignación arbitrarios con dos compradores y dos vendedores. Se analizan cinco casos distintos, dependiendo de las entradas en la matriz de asignación. Los resultados se extienden a los casos de juegos de asignación de tipo 2 x m o m x 2.

An axiomatization of the nucleolus of the assignment game

[cat] En el domini dels jocs bilaterals d’assignació, es presenta una axiomàtica del nucleolus com l´unica solució que compleix les propietats de consistència respecte del joc derivat definit per Owen (1992) i monotonia de les queixes dels sectors respecte de la seva cardinalitat. Com a conseqüència obtenim una caracterització geomètrica del nucleolus mitjançant una propietat de bisecció més forta que la que satisfan els punts del kernel (Maschler et al, 1979).

Symmetrically multilateral-bargained allocations in multi-sided assignment markets

[cat] Aquest treball tracta d’extendre la noció d’equilibri simètric de negociació bilateral introduït per Rochford (1983) a jocs d’assignació multilateral. Un pagament corresponent a un equilibri simètric de negociación multilateral (SMB) és una imputación del core que garanteix que qualsevol agent es troba en equilibri respecte a un procés de negociación entre tots els agents basat en allò que cadascun d’ells podria rebre -i fer servir com a amenaça- en un ’matching’ òptim diferent al que s’ha format. Es prova que, en el cas de jocs d’assignació multilaterals, el conjunt de SMB és sempre no buit i que, a diferència del cas bilateral, no sempre coincideix amb el kernel (Davis and Maschler, 1965). Finalment, responem una pregunta oberta per Rochford (1982) tot introduïnt un conjunt basat en la idea de kernel, que, conjuntament amb el core, ens permet caracteritzar el conjunt de SMB.

Complements and substitutes in multilateral assignment markets

[cat] En aquest treball provo que, en mercats d’assignació amb més de dos costats, agents de diferents sectors poden no ser complementaris mentre que agents del mateix sector poden no ser substituts. Shapley (1962) va provar que això mai pot succeïr quan el mercat d’assignació només té dos costats. No obstant, demostro que existeixen condicions suficients que garanteixen la substitutabilitat i la complementarietat entre agents en aquests tipus de mercats. A més, provo que, quan els béns al mercat son homogenis, el resultat de Shapley (1962) es manté.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered