Sharing Supermodular Costs

We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations; in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron—a problem that often arises in combinatorial optimization—has supermodular optimal costs. In addition, we examine the computational complexity of the least core and least core value of supermodular cost cooperative games. We show that the problem of computing the least core value of these games is strongly NP-hard and, in fact, is inapproximable within a factor strictly less than 17/16 unless P = NP. For a particular class of supermodular cost cooperative games that arises from a scheduling problem, we show that the Shapley value—which, in this case, is computable in polynomial time—is in the least core, while computing the least core value is NP-hard.National Science Foundation (U.S.) (DMI-0426686

Approximating the least core value and least core of cooperative games with supermodular costs

We study the approximation of the least core value and the least core of supermodular cost cooperative games. We provide a framework for approximation based on oracles that approximately determine maximally violated constraints. This framework yields a 3-approximation algorithm for computing the least core value of supermodular cost cooperative games, and a polynomial-time algorithm for computing a cost allocation in the 2-approximate least core of these games. This approximation framework extends naturally to submodular profit cooperative games. For scheduling games, a special class of supermodular cost cooperative games, we give a fully polynomial-time approximation scheme for computing the least core value. For matroid profit games, a special class of submodular profit cooperative games, we give exact polynomial-time algorithms for computing the least core value as well as a least core cost allocation.National Science Foundation (U.S.) (DMI-0426686

Institutions and Development Processes: the Role of Strategic Complementarities. A Review of main Literature

This survey is an overview on the literature that investigates the relationship between the institutions and development processes. The attention it has been focus, in sequence, on the ways in which it has been performed the empirical and the theoretical analysis of the relationship between the economic development and the role of institutions. As it is clear the first difficulty is the definition of what an institution is, so the survey gives dig relevance to the different manners to conceptualize the notion of institution. Another difficulty arises from the perplexity about how the efficiency of the institutions can be evaluated. This problem is related to the necessity to close off in the right way the weight and the influence of the institutions respect to the other variables on the economic development. The analysis of the complementarities involved in the development processes, can be a useful way to explain some kinds of relationship between institutions and development processes especially in the short run. The use of more elaborated indices to measure the in�uence of institutions in the economic system and of the coentegration models can improve the reliability of the empirical analysis. In the same manner the supermodularity and the supermodular games can efficiently explain the mechanism of the strategic complementarity between di¤erent kinds of institution generating virtuous development processes from a theoretical point of view. Necessarily, in the future, both the analysis must be integrated but, for the time being, the state of art in the two approaches represent a very good starting point for new outcomes related to the investigation on these type of kind of economic phenomena.Institutions, Complementarities, Development Process

Algorithmic and game-theoretic perspectives on scheduling

This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2008.Includes bibliographical references (p. 103-110).(cont.) Second, for almost all 0-1 bipartite instances, we give a lower bound on the integrality gap of various linear programming relaxations of this problem. Finally, we show that for almost all 0-1 bipartite instances, all feasible schedules are arbitrarily close to optimal. Finally, we consider the problem of minimizing the sum of weighted completion times in a concurrent open shop environment. We present some interesting properties of various linear programming relaxations for this problem, and give a combinatorial primal-dual 2-approximation algorithm.In this thesis, we study three problems related to various algorithmic and game-theoretic aspects of scheduling. First, we apply ideas from cooperative game theory to study situations in which a set of agents faces super modular costs. These situations appear in a variety of scheduling contexts, as well as in some settings related to facility location and network design. Although cooperation is unlikely when costs are super modular, in some situations, the failure to cooperate may give rise to negative externalities. We study the least core value of a cooperative game -- the minimum penalty we need to charge a coalition for acting independently that ensures the existence of an efficient and stable cost allocation -- as a means of encouraging cooperation. We show that computing the least core value of supermodular cost cooperative games is strongly NP-hard, and design an approximation framework for this problem that in the end, yields a (3 + [epsilon])-approximation algorithm. We also apply our approximation framework to obtain better results for two special cases of supermodular cost cooperative games that arise from scheduling and matroid optimization. Second, we focus on the classic precedence- constrained single-machine scheduling problem with the weighted sum of completion times objective. We focus on so-called 0-1 bipartite instances of this problem, a deceptively simple class of instances that has virtually the same approximability behavior as arbitrary instances. In the hope of improving our understanding of these instances, we use models from random graph theory to look at these instances with a probabilistic lens. First, we show that for almost all 0-1 bipartite instances, the decomposition technique of Sidney (1975) does not yield a non-trivial decomposition.by Nelson A. Uhan.Ph.D

The Theory of Human Capital Revisited: On the Interaction of General and Specific Investments

Human capital theory distinguishes between training in general-usage and firm-specific skills. In his seminal work, Becker (1964) argues that employers will not be willing to invest in general training when labor markets are competitive. However, they are willing to invest in specific training because it cannot be transferred to outside firms. The paper reconsiders Becker’s theory. We show that there exists an incentive complementarity between employersponsored general and specific investments: the possibility to provide specific training leads the employer to invest in general human capital. Conversely, the latter reduces the hold-up problem that arises with respect to the provision of firm-specific training. We also consider the virtues of long-term contracting and discuss some empirical observations that could be explained by the model.human capital formation, general and specific training, hold-up problem.

Institutions and Development Processes: the Role of Strategic Complementarities. A Review of main Literature

This survey is an overview on the literature that investigates the relationship between the institutions and development processes. The attention it has been focus, in sequence, on the ways in which it has been performed the empirical and the theoretical analysis of the relationship between the economic development and the role of institutions. As it is clear the first difficulty is the definition of what an institution is, so the survey gives dig relevance to the different manners to conceptualize the notion of institution. Another difficulty arises from the perplexity about how the efficiency of the institutions can be evaluated. This problem is related to the necessity to close off in the right way the weight and the influence of the institutions respect to the other variables on the economic development. The analysis of the complementarities involved in the development processes, can be a useful way to explain some kinds of relationship between institutions and development processes especially in the short run. The use of more elaborated indices to measure the in�uence of institutions in the economic system and of the coentegration models can improve the reliability of the empirical analysis. In the same manner the supermodularity and the supermodular games can efficiently explain the mechanism of the strategic complementarity between di¤erent kinds of institution generating virtuous development processes from a theoretical point of view. Necessarily, in the future, both the analysis must be integrated but, for the time being, the state of art in the two approaches represent a very good starting point for new outcomes related to the investigation on these type of kind of economic phenomena

Four essays in behavioral economics

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economic