Stability and fairness in models with a multiple membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are in- divisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness on metric environments with indivisible projects. To do so, we explore, among other things, the performance of several well-known solutions (such as the Shapley value, the nucleolus, or the Dutta-Ray value) in these environments.stability, fairness, membership, coalition formation

A non-cooperative foundation for the continuous Raiffa solution

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes

Evolutionary cooperative games

This thesis proposes a new approach to deriving cooperative solution concepts from dynamic interactive learning models. For different classes of cooperative games, the procedures implement the core. Within the core, tendencies towards equity are revealed and equitable outcomes are favoured in the long run

Essays on egalitarianism-based solution concepts for cooperative TU-games

Per a una classe de jocs reduïts, satisfent una propietat de monotonia, introduim una família de solucions conjustistes fonamentades en consideracions igualitàries i en principis de consistència, i estudiem la seva relació amb el core. Demostrem que la intersecció entre cadascuna d'aquestes solucions i el core és el conjunt buit o bé la "lexmax solution" d'Arin et al. (2003). Aquest resultat indueix un procediment per calcular la "lexmax solution" per a una classe de jocs, que conté jocs amb "large core" Sharkey (1982). Utilitzant la noció d'antidualitat d'un joc (Oishi and Nakayama, 2009), estenem l'anàlisi anterior trobant resultats paral·lels per a la lexmin solution (Arin and Iñarra, 2001; Yanovskaya, 1995). Introduim una classe de jocs equilibrats anomenats "exact partition games". En aquesta classe, es mostra que la solució igualitària de Dutta and Ray (1989) es comporta com en la classe dels jocs convexos. A més a més, aportem caracteritzacions utilitzant propietats de consistència, racionalitat coalicional i d'equitat à la Lorenz. Fruït d'això, obtenenim caracteritzacions alternatives de la solució igualitària en els jocs convexos. Utilitzant la noció d'axioma antidual (Oishi et al. 2016), obtenim axiomatitzacions addicionals de la solució igualitària en el domini dels "exact partition game" i també en el domini dels jocs convexos. En el domini dels jocs equilibrats, trobem noves caracteritzacions axiomatiques del "Lorenz maximal core". Definim el conjunt "Lorenz stable" i aportem una caracterització axiomàtica en termes de consistència projectada i d'igualitarianisme sobre jocs de dos agents. En el domini de tots els jocs cooperatius d'utilitat transferible, trobem que aquesta solució connecta la "weak constrained egalitarian solution" (Dutta and Ray, 1989) amb la "strong constrained egalitarian solution" (Dutta and Ray, 1991).Para una clase de juegos reducidos, satisfaciendo una propiedad de monotonía, introducimos una familia de soluciones conjustistas basadas en consideraciones igualitarias y en principios de consistencia, y estudiamos su relación con el core. Demostramos que la intersección entre cada una de estas soluciones y el core es el conjunto vacío o bien la "lexmax solution" de Arin et. al. (2003). Este resultado induce un procedimiento para calcular la "lexmax solution" para una clase de juegos, que contiene juegos con "large core" Sharkey(1982). Utilitzando la noción de antidualidad de un juego (Oishi and Nakayama, 2009), extendemos el anàlisis anterior encontrando resultados paralelos para la lexmin solution (Arin and Iñarra, 2001; Yanovskaya, 1995). Introducimos una clase de juegos equilibrados llamados "exact partition games". En esta clase, se muestra que la solución igualitaria de Dutta and Ray (1989) se comporta como en la clase de los juegos convexos. Además, aportamos caracterizaciones utilizando propiedades de consistencia, racionalidad coalicional y de equidad à la Lorenz. En consecuencia, obtenemos caracterizaciones alternativas de la solución igualitaria en los juegos convexos. Utilitzando la noción de axioma antidual (Oishi et al. 2016), obtenemos axiomatitzaciones adicionals de la solución igualitaria en el dominio de los "exact partition game" y también en el dominio de los juegos convexos. En el dominio de los juegos equilibrados, encontramos nuevas caracterizaciones axiomáticas del "Lorenz maximal core". Definimos el conjunto "Lorenz stable" y aportamos una caracterización axiomática en términos de consistencia proyectada y de igualitarianismo sobre juegos de dos agentes. En el dominio de todos los juegos cooperativos de utilidad transferible, encontramos que esta solución conecta la "weak constrainedegalitarian solution" (Dutta and Ray, 1989) con la "strong constrained egalitarian solution"(Dutta and Ray, 1991).For a class of reduced games satisfying a monotonicity property, we introduce a family of set-valued solution concepts based on egalitarian considerations and consistency principles, and study its relation with the core. Regardless of the reduction operation we consider, the intersection between both sets is either empty or a singleton containing the lexmax solution (Arin et al., 2003). This result induces a procedure for computing the lexmax solution for a class of games that contains games with large core (Sharkey,1982). We extend the previous analysis making use of the notion of anti-dual game (Oishi and Nakayama, 2009), finding parallel results for the lexmin solution. A class of balanced games, called exact partition games, is introduced. Within this class, it is shown that the egalitarian solution of Dutta and Ray (1989) behaves as in the class of convex games. Moreover, we provide axiomatic characterizations by means of suitable properties such as consistency, rationality and Lorenz-fairness. As a by-product, alternative characterizations of the egalitarian solution over the class of convex games are obtained. Using the notion of anti-duality to axioms (Oishi et al. 2016), we obtain additional axiomatizations of the egalitarian solution on the domain of exact partition games but also on the domain of convex games. On the domain of balanced games, new axiomatic characterizations of the Lorenz maximal core are obtained. We introduce the Lorenz stable set and provide an axiomatic characterization in terms of constrained egalitarianism and projection consistency. On the domain of all coalitional games, we find that this solution connects the weak constrained egalitarian solution (Dutta and Ray, 1989) with their strong counterpart (Dutta and Ray, 1991)

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

An Overview of Coalition & Network Formation Models for Economic Applications

This paper presents synthetically some recent developments in the theory of coalition and network formation. For this purpose, some major equilibrium concepts recently introduced to model the formation of coalition structures and networks among players are briefly reviewed and discussed. A few economic applications are also illustrated to give a flavour of the type of predictions such models are able to provide.Coalitions, Networks, Core, Games with Externalities, Endogenous Coalition Formation, Pairwise stability, Stable Networks, Link Formation

Relational Contracting, Repeated Negotiations, and Hold-Up

We propose a unified framework to study relational contracting and hold-up problems in infinite horizon stochastic games. We first illustrate that with respect to long run decisions, the common formulation of relational contracts as Pareto-optimal public perfect equilibria is in stark contrast to fundamental assumptions of hold-up models. We develop a model in which relational contracts are repeatedly newly negotiated during relationships. Negotiations take place with positive probability and cause bygones to be bygones. Traditional relational contracting and hold-up formulations are nested as opposite corner cases. Allowing for intermediate cases yields very intuitive results and sheds light on many plausible trade-offs that do not arise in these corner cases. We establish a general existence result and a tractable characterization for stochastic games in which money can be transferred. This paper formulates a theory of relational contracting in dynamic games. A crucial feature is that existing relational contracts can depreciate and ensuing negotiations then treat previous informal agreements as bygones. The model nests the traditional formulation of relational contracts as Pareto-optimal equilibria as a special case. In repeated games both formulations are always mathematically equivalent. We provide ample illustrations that in dynamic games the traditional formulation is restrictive in so far that it rules out by assumption many plausible hold-up problems - even for small discount factors. Our model provides a framework that naturally unifies the analysis of relational contracting and hold-up problems