The Equitable Bargaining Set

We define the equitable bargaining set for exchange economies. Our definition differs from that in Mas-Colell (1989) because it requires that objections and counterobjections must satisfy some equitability conditions. We show that the equitable bargaining set coincides with that of Mas-Colell when the underlying economy is atomless, but not in general. Then we provide two sets of conditions for economies with market imperfections that apply to finite economies and to mixed market economies. In the first case our conditions imply that the equitable bargaining set is a subset of the core, and so it converges to the set of competitive allocations if the economy is replicated. In the second case, we show that all allocations in the equitable bargaining set are competitive, extending the Walras-bargaining equivalence of Mas-Colell (1989) to the framework of mixed markets. All the conditions we use follow from wellestablished assumptions from the literature in finite and mixed market economies

On the Limit Points of an Infinitely Repeated Rational Expectations Equilibrium

We show that a symmetric information Rational Expectations Equilibrium (REE) exists universally (and not generically), it is Pareto efficient and obviously incentive compatible. Agents, in a repeated economy framework, can reach a symmetric information REE (i.e., an efficient and incentive compatible equilibrium outcome) by observing the past asymmetric REE and also by updating their private information. We also prove the converse result, i.e., given a symmetric information REE, we can construct a sequence of approximate asymmetric REE allocations that converges to the symmetric information REE. The approximate REE can be interpreted as the mistakes that agents make due to bounded rationality, nonetheless, in the limit an exact symmetric information REE is reached. In view of the above results, the symmetric information REE provides a rationalization for the asymmetric one

Market equilibrium via classifications of commodities

When a rich variety of available goods is classified into a smaller number of tradable commodities, we have a market economy that relies on a simplified representation. We study how the classification of goods into commodities affects the allocation of scarce resources among agents. We also consider a notion of decentralized equilibrium that is achieved merely by an appropriate classification of the goods, regardless of the presence of a price-based mechanism

A topological analysis of competitive economies

This thesis deals with some central issues in the theory of competitive economies and with the intrinsic topological nature that they exhibit. The topics discussed focus on economic models with a multitude of agents and many commodities and are divided in an extended introduction and four chapters. In Chapter 2 we prove a convexity result for the range of finitely-additive vector measures and correspondences with values in a locally convex space. These results are based on a new topological reformulation of the so-called saturation property which, in some form, generalizes the notion of non-atomicity of a measure space and plays an important role in many economic problems. Chapter 3 investigates what topological assumptions on the commodity space are essential to formulate and study the problem of existence of competitive equilibrium in a Walrasian competitive economy with many commodities. It includes a general theorem on the existence of equilibrium prices in abstract markets with infinite dimensional commodity spaces that is inspired by Nikaido's work of 1959. In Chapter 4 we study a coalitional model of an exchange economy in which coalitions are represented as the elements of a topological Boolean ring, allocations are finitely additive vector measures and the commodity space is an ordered locally convex space. In this general framework we will use the results of Chapter 2 to provide a topological condition for a perfectly competitive economy and use it to prove two extensions of classical theorems on the veto power of coalitions (Schmeidler 1972 and Vind 1972). This will allow us to conclude that the economic power of coalitions is an essentially topological property. Finally, Chapter 5 studies the competitive objection mechanism in a saturated economy with a separable Banach space of commodities whose positive cone has non-empty interior. By doing so we will provide a new characterization of Mas-Colell's bargaining set in the infinite dimensional setting. We will then introduce stronger notions of bargaining set that allow to extend our analysis to the case of markets with imperfections

Il ruolo del capitale umano nella transizione verso un'industria 4.0

Nata in Germania come iniziativa strategica, l'espressione "Industria 4.0" si è ormai diffusa a livello globale, denotando caratteristiche che richiamano una quarta rivoluzione industriale, in grado di migliorare le condizioni di lavoro e la qualità dei processi, nonché la produttività delle imprese. Dalla letteratura di riferimento emerge come, all'interno del più ampio processo di trasformazione digitale delle imprese, l'implementazione delle nuove tecnologie abilitanti stia cambiando radicalmente le modalità di progettazione del modello di business, la struttura organizzativa e l'attività d'innovazione. Al fine di affrontare con successo tale ondata tecnologica, sarà sempre più critica la combinazione di nuove capacità e competenze proprie del capitale umano aziendale, senza le quali l'implementazione delle tecnologie sarebbe vana: leadership, individual identity, interpersonal relating e technical skill diventeranno fattori critici di successo della fabbrica innovativa digital driven. Attraverso un'accurata analisi della letteratura scientifica sul tema, l'articolo propone un modello di riferimento che permette di mappare l'insieme delle capacità e competenze chiave che le imprese operanti nell'Industria 4.0 dovranno sviluppare nell'ambito del nuovo paradigma industriale (o Skill 4.0), nonché per sostenere le aziende nella formulazione di politiche di sviluppo del personale lungimiranti e al tempo stesso orientate al disegno-ridisegno dei ruoli organizzativi.Born in Germany as a strategic initiative, the label "Industry 4.0" has now spread globally, assuming the characteristics that recall a fourth industrial revolution, able to improve working conditions and the quality of the processes, as well as the productivity of companies. The relevant literature highlights how, within a broader process of digital transformation, the implementation of new enabling technologies is radically changing the organizational structure, the innovation process and the way the business model is working. In order to cope with this technological wave, a combination of new skills, such as leadership, individual identity, interpersonal relating and technical skill, is required for the implementation of Industry 4.0 as these skills are becoming critical success factors in innovative digital-driven businesses. Through a careful analysis of the relevant scientific literature, this paper aims at advancing a conceptual framework to map the set of key skills (also named Skills 4.0) that businesses should develop within the Industry 4.0 paradigm. Moreover, this framework is aimed to help businesses develop farsighted human resource development policies and design-redesign organizational roles

Generalized coalitions and bargaining sets

We introduce new notions of bargaining set for mixed economies which rest on the idea of generalized coalitions (Aubin, 1979) to define objections and counter-objections. We show that the bargaining set defined through generalized coalitions coincides with competitive allocations under assumptions which are weak and natural in the mixed market literature. As a further result, we identify some additional properties that a generalized coalition must satisfy to object an allocation

On the Limit Points of an Infinitely Repeated Rational Expectations Equilibrium

We show that a symmetric information Rational Expectations Equilibrium (REE) exists universally (and not generically), it is Pareto efficient and obviously incentive compatible. Agents, in a repeated economy framework, can reach a symmetric information REE (i.e., an efficient and incentive compatible equilibrium outcome) by observing the past asymmetric REE and also by updating their private information. We also prove the converse result, i.e., given a symmetric information REE, we can construct a sequence of approximate asymmetric REE allocations that converges to the symmetric information REE. The approximate REE can be interpreted as the mistakes that agents make due to bounded rationality, nonetheless, in the limit an exact symmetric information REE is reached. In view of the above results, the symmetric information REE provides a rationalization for the asymmetric one

The Equitable Bargaining Set

We define the equitable bargaining set for exchange economies. Our definition differs from that in Mas-Colell (1989) because it requires that objections and counterobjections must satisfy some equitability conditions. We show that the equitable bargaining set coincides with that of Mas-Colell when the underlying economy is atomless, but not in general. Then we provide two sets of conditions for economies with market imperfections that apply to finite economies and to mixed market economies. In the first case our conditions imply that the equitable bargaining set is a subset of the core, and so it converges to the set of competitive allocations if the economy is replicated. In the second case, we show that all allocations in the equitable bargaining set are competitive, extending the Walras-bargaining equivalence of Mas-Colell (1989) to the framework of mixed markets. All the conditions we use follow from wellestablished assumptions from the literature in finite and mixed market economies

A convexity result for the range of vector measures with applications to large economies

On a Boolean algebra we consider the topology u induced by a finitely additive measure μ with values in a locally convex space and formulate a condition on u that is sufficient to guarantee the convexity and weak compactness of the range of μ. This result à la Lyapunov extends those obtained in (Khan and Sagara 2013 [26]) to the finitely additive setting through a more direct and less involved proof. We will then give an economical interpretation of the topology u in the framework of coalitional large economies to tackle the problem of measuring the bargaining power of coalitions when the commodity space is infinite dimensional and locally convex. We will show that our condition on u plays the role of the ‘‘many more agents than commodities’’ condition introduced by Rustichini and Yannelis in (1991) [31]. As a consequence of the convexity theorem, we will obtain two straight generalizations of Schmeidler's and Vind's Theorems on the veto power of coalitions of arbitrary economic weight