Fabio Lamantia

Assessing non-additive utility for multicriteria decision aid

Abstract In the framework of Multi-Attribute Utility Theory (MAUT) several methods have been proposed to build a Decision-Makers (DM) utility function representing his/her preferences. Among such methods, the UTA method infers an additive utility function from a set of exemplary decisions using linear programming. However, the UTA method does not guarantee to find a utility function which is coherent with the available information. This drawback is due to the underlying utility model of UTA, viz. the additive one, which does not allow to include additional information such as an interaction among criteria. In this paper we present a methodology for building a non-additive utility function, in the framework of the so called fuzzy integrals, which permits to model preference structures with interaction between criteria. Like in the UTA method, we aim at searching a utility function representing the DMs preferences, but unlike UTA, the functional form is a specific fuzzy integral (Choquet integral). As a result, we obtain weights which can be interpreted as the “importance” of coalitions of criteria, exploiting the potential interaction between criteria, as already proposed by other authors. However, within the same framework, we obtain also the marginal utility functions relative to each one of the considered criteria, that are evaluated on a common scale, as a consequence of the implemented methodology. Finally, we illustrate our approach with an example.

Evolutionary Competition in a Mixed Market with Socially Concerned Firms

In this paper we study an oligopoly market where profit-maximizing firms and socially concerned firms compete in quantities. Confronting remarks by Milton Friedman and Gary Becker, we are using an evolutionary setting to investigate the endogenous choice of the proper objective of business firms and the influence of product differentiation on the long run survival of firms which pursue non-profit motives. We find that firms which consider a combination of profit and consumer welfare can indeed have larger market shares and profits than their profit-maximizing rivals. One insight is that it might pay off for shareholders to consider stakeholder welfare, but that the level of social concern should not be too high. Based on a strategy׳s profitability, we consider asynchronous evolutionary updating with firms selecting Nash quantities or choosing best replies to the expected market quantity. Here we observe that the consumers׳ willingness to pay a price premium for products is crucial for the long run survival of socially concerned firms. Depending on the degrees of product differentiation and social concern, long run outcomes consist either of both types of firms or only one type of firm. If the firms׳ propensity to switch between a social or a profit-maximizing strategy is sufficiently large, steady states are unstable and even complicated dynamics can occur.

Competition and Cooperation in Natural Resources Exploitation: An Evolutionary Game Approach

Since the pioneering work of Gordon (1954), many bioeconomic models for the description of the commercial exploitation of common property renewable resources, such as fisheries, have stressed the problem known as ‘the tragedy of the commons’ (Hardin, 1968; see also Clark, 1990). This problem can be basically identified with a prisoner’s dilemma (see for example, Mesterton-Gibbons, 1993) because the presence of firms playing their dominant strategy which maximizes their own profit (disregarding competitors’ profits) leads to severe depletion of the resource, and consequently to low profits for all. On the other hand if firms cooperate to maximize total profits, then sustainable exploitation is more likely to obtain, which implies higher profits for all in the long run. However, unilateral defection, that is, the decision of an agent to harvest intensively while the other players harvest moderately in order to preserve resources, may lead to very high profits for the defector, and consequently to severe profit loss for the cooperators. This is the essence of the tragedy of the commons, often advanced in order to support the introduction of sanctions against defectors and/or restrictions to open access to common property resources. Dynamic models based on Cournot oligopoly games have been proposed by Levhari and Mirman (1982) and, more recently, by Szidarovszky and Okuguchi (1998, 2000), to describe commercial fishing. In these models, strategic interaction among players is related not only to the selling price, determined by the total harvesting quantity through a given demand function, but also to a cost externality, since resource stock reductions, as a consequence of players’ harvesting, lead to higher unitary fishing costs (see also Bischi and Kopel, 2002). In Szidarovszky and Okuguchi (1998) every player is assumed to decide his/her harvesting activity by solving a profit

A prey-predator fishery model with endogenous switching of harvesting strategy

We propose a dynamic model to describe a fishery where both preys and predators are harvested by a population of fishermen who are allowed to catch only one of the two species at a time. According to the strategy currently employed by each agent, i.e. the harvested variety, at each time period the population of fishermen is partitioned into two groups, and an evolutionary mechanism regulates how agents dynamically switch from one strategy to the other in order to improve their profits. Among the various dynamic models proposed, the most realistic is a hybrid system formed by two ordinary differential equations, describing the dynamics of the interacting species under fishing pressure, and an impulsive variable that evolves in a discrete time scale, in order to describe the changes of the fraction of fishermen that harvest a given stock. The aim of the paper is to analyze the economic consequences of this kind of self-regulating fishery, as well as its biological sustainability, in comparison with other regulatory policies. Our analytic and numerical results give evidence that in some cases this kind of myopic, evolutionary self-regulation might ensure a satisfactory trade-off between profit maximization and resource conservation.

A dynamic model of oligopoly with R&D externalities along networks. Part II

In Bischi and Lamantia [4] a two-stage oligopoly game has been proposed to describe networks of firms that invest in cost-reducing R&D activity with the possibility of sharing R&D results with partner firms as well as gaining knowledge for free through spillovers, and an adaptive dynamic mechanism is proposed to describe how firms repeatedly update their R&D efforts over time. In that paper existence and stability of equilibria have been analyzed given a fixed structure of the collaboration network, divided into sub-networks. In this paper we analyze the influences of the degree of collaboration and spillovers on profits, social welfare and, more generally, on overall efficiency. We first consider two relevant benchmark cases, for which analytical results are provided, and then numerical experiments are performed to stress the role of the level of connectivity (i.e. the collaboration attitude) inside networks as well as the effects of involuntary knowledge spillovers inside each network and among different competing networks.

Original Articles: A dynamic model of oligopoly with R&D externalities along networks. Part I.

This paper formulates and analyzes a two-stage oligopoly game where firms can invest in cost-reducing R&D activity with the possibility of sharing R&D results with partner firms as well as gaining knowledge for free through spillovers. Firms are arranged within networks (or districts) inside which they can cooperate by bilateral agreements for sharing knowledge and compete in the market. An adaptive dynamic mechanism is proposed to describe how firms in a two-networks system repeatedly decide their R&D efforts over time. This adaptive adjustment may converge to a Nash equilibrium in the long run, or exhibit more complex dynamic behaviors. Analytical results about stability of equilibrium points are given, as well as numerical simulations to show global dynamical properties, including coexistence of attractors and complicated structures of their basins. In a second paper (Part II) some analytical results will be given for some relevant benchmark cases, together with numerical experiments that stress the role of the level of connectivity (i.e. the collaboration attitude) inside networks, as well as the effects of involuntary knowledge spillovers inside each network and among different competing networks.

Chaos Synchronization and Intermittency in a Duopoly Game with Spillover Effects

Discrete-time dynamic oligopoly games which exhibit chaotic time patters of the competitors’ strategic choices are at the center of a flourishing literature, including the seminal paper by Rand (1978) and several papers after it (see e.g. Dana and Montrucchio, 1986, Puu, 1991, Kopel, 1996), where simple microeconomic situations have been proposed which lead to duopoly games with chaotic dynamics. The main concern, in this stream of literature, is to emphasize the features of the duopoly games which are responsible for the transition from regular to chaotic dynamics and to analyze the bifurcations which cause the loss of stability of the equilibria and the appearance of more complex attractors (see e.g. Bischi et al., 2000).

Moment based approaches to value the risk of contingent claim portfolios

Abstract In this paper we describe and apply the estimating function methodology to value the risk of asset derivative portfolios. We first implement the Li’s model based on the first four moments and then we show the limits of this model in forecasting the maximum loss of contingent claims. In addition, we show that four moments are not enough to describe the behavior of the lower percentiles of derivatives. Finally, we propose a model that considers the first six moments and we compare the performances of these models proposing a backtest analysis on several historical and truncated asset derivative portfolios.

Coexisting Attractors and Complex Basins in Discrete-time Economic Models

In this lesson we consider discrete time dynamical systems with coexisting attractors, and we analyze the problem of the structure of the boundaries that separate their basins of attraction. This problem may become particularly challenging when the discrete dynamical system is represented by the iteration of a noninvertible map, because in this case nonconnected basins can be obtained, formed by several (even infinitely many) disjoint portions. Measure theoretic attractors, known as Milnor attractors, are also described, together with riddled basins, an extreme form of complex basin’s structure that can be observed in the presence of such attractors. Some tools for the study of global bifurcations that lead to the creation of complex structures of the basins are described, as well as some applications in discrete time models taken from economic dynamics.

Evolutionary technology adoption in an oligopoly market with forward-looking firms

In this paper, we propose an evolutionary oligopoly game of technology adoption in a market with isoelastic demand and two possible (linear) production technologies. While one technology is characterized by lower marginal costs, the magnitude of fixed costs entails that a technology does not necessarily dominate the other. Firms are forward-looking as they assess the profitability of employing either technology according to the corresponding expected profits. The dynamics of the system is studied through a piecewise-smooth map, for which we present a local stability analysis of equilibria and show the occurrence of smooth and border collision bifurcations. Global analysis of the model is also presented to show coexistence of attractors and its economic significance. This investigation reveals that firms can fail to learn to adopt the more efficient technology.