Arsen Palestini

Minimax Multi-District Apportionments

The problem of seat apportionment in electoral systems turns out to be quite complex, since no apportionment method exists which succeeds in verifying all the principal fairness criteria. Gambarelli (1999) introduced an apportionment technique which is custom made for each case, respects Hare minimum, Hare maximum and Monotonicity and satisfies other criteria in order of preference. In this chapter a generalization of that method is proposed, in order to extend it to the multi-district election case, where criteria should be respected at a global as well as at a local level. An existence theorem and a generating algorithm are supplied.

Hamiltonian potential functions for differential games

We introduce the concept of Hamiltonian potential functions for noncooperative open-loop differential games and we characterise sufficient conditions for their existence. We identify a class of games admitting a Hamiltonian potential and illustrate the related properties of their dynamic structure. Then, we offer a preliminary exploration of the construction of potential functions for feedback games. As an illustration, we consider an asymmetric oligopoly game with process innovation.

On a Nonrenewable Resource Extraction Game Played by Asymmetric Firms

A differential game of extraction of a nonrenewable resource is taken into account, where two firms compete over time and their two terminal times of extraction are two different random variables. The winning firm will be the only one remaining in the game after the first one retires. We explicitly compute the Hamilton–Jacobi–Bellman equations of the model and solve them in an asymmetric game with logarithmic payoff structure and linear state dynamics.

Static and dynamic best-response potential functions for the non-linear Cournot game

We show that the Cournot oligopoly game with non-linear market demand can be reformulated as a best-response potential game where the best-response potential function is linear-quadratic in the special case where marginal cost is normalized to zero. We also propose a new approach to show that the open-loop differential game with Ramsey dynamics admits a best-response Hamiltonian potential corresponding to the sum of the best-response potential function of the static game plus the scalar product of transition functions multiplied by the fictitious costate variables. Unlike the original differential game, its best-response representation yields the map of the instantaneous best reply functions.

The Incentive to Invest in Environmental-Friendly Technologies: Dynamics Makes a Difference

The established view on oligopolistic competition with environmental externalities has it that, since firms neglect the external effect, their incentive to invest in R&D for pollution abatement is nil unless they are subject to some form of environmental taxation. We take a dynamic approach to this issue, using a simple differential game to show that the conclusion reached by the static literature is not robust, as the introduction of dynamics shows that firms do invest in R&D for environmental-friendly technologies throughout the game. Moreover, our setup also illustrates the existence of multiple equilibria, only one of which is identified by the corresponding static game.

Regulating Environmental Externalities Through Public Firms: A Differential Game

We investigate the possibility of using public firms to regulate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the Cournot-Nash game among profit-seeking firms; (ii) the Markov Perfect Nash equilibrium under social planning, where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) the Markov Perfect Nash equilibrium in a mixed setup where at least one firm is public, while the others remain profit-seeking agents. Our analysis identifies the conditions whereby having a mixed market as a regulatory instrument suffices to drive the industry to the same output, externality and social welfare as under planning, both along the optimal path and in steady state.

The Leitmann-Schmitendorf advertising game with n players and time discounting

Abstract The extension of the Leitmann–Schmitendorf advertising game to n players and positive time discounting is investigated. We show that the strong time consistency of the open-loop Nash equilibrium is preserved. As to optimal controls, while the boundary solution is unaffected by the number of firms as well as discounting, the inner solution depends on industry structure. The fully symmetric version of the game allows us to identify the parameter regions wherein both solutions are sustainable.

On the Optimal Number of Firms in the Commons: Cournot vs Bertrand

We revisit the debate on the optimal number of firms in the commons in a differential oligopoly game in which firms are either quantity- or price-setting agents. Production exploits a natural resource and involves a negative externality. We calculate the number of firms maximising industry profits, finding that it is larger in the Cournot case. While industry structure is always inefficient under Bertrand behaviour, it may or may not be so under Cournot behaviour, depending on parameter values. The comparison of private industry optima reveals that the Cournot steady state welfare level exceeds the corresponding Bertrand magnitude if the weight of the stock of pollution is large enough.

Dynamic Oligopoly with Capital Accumulation and Environmental Externality

We model the interplay between capital accumulation for production and environmental externalities in a differential oligopoly game with Ramsey dynamics. The external effect is determined, alternatively, by sales or production. While the externality does not affect the behaviour of profit-seeking firms, it may induce a benevolent planner to shrink sales as compared to the Cournot-Nash equilibrium because of a tradeoff between consumer surplus and the externality, if the latter is driven by sales. If instead it is determined by production, there emerges that the Ramsey golden rule is no longer socially optimal.

A Class of Best-Response Potential Games

We identify a class of noncooperative games in continuous strategies which are best-response potential games. We identify the conditions for the existence of a best-response potential function and characterize its construction, describing then the key properties of the equilibrium. The theoretical analysis is accompanied by applications to oligopoly and monetary policy games.