Bertrand and Cournot oligopolies when rivals' costs are unknown

We study Bertrand and Cournot oligopoly models with incomplete information about rivals’ costs, where the uncertainty is given by a uniform distribution. We compute the Bayesian- Nash equilibrium of both games, the ex-ante expected profits and the ex-post profits of each firm. We see that, in the price competition, even though only one firm produces in equilibrium, all firms have a positive ex-ante expected profit.

Simultaneous decisions or leadership in an international competition

In this paper, we study an international market with demand uncertainty. The model has two stages. In the first stage, the home government chooses an import tariff to maximize the revenue. Then, the firms engage in a Cournot or in a Stackelberg competition. The uncertainty is resolved between the decisions made by the home government and by the firms. We compare the results obtained in the three different ways of moving on the decision make of the firms.

Two-production-period in a duopoly with nonprofit and for-profit firms

We investigate endogenous roles in a competition between a nonprofit firm and a for-profit firm in a homogeneous goods market, by allowing two production periods. We find that the Cournot-type equilibrium and one Stackelberg-type equilibrium where the nonprofit firm becomes the follower exist; however, another tackelberg-type equilibrium where the nonprofit firm becomes the leader does not exist.

Maximum-revenue tariff with different roles in a price-setting competition

Published also at Lecture Notes in Engineering and Computer Science

A recursive process related to a partisan variation of Wythoff

Wythoff Queens is a classical combinatorial game related to very interesting mathematical results. An amazing one is the fact that the P-positions are given by (⌊├ φn⌋┤┤,├ ├ ⌊φ┤^2 n⌋) and (⌊├ φ^2 n⌋┤┤,├ ├ ⌊φ┤n⌋) where φ=(1+√5)/2. In this paper, we analyze a different version where one player (Left) plays with a chess bishop and the other (Right) plays with a chess knight. The new game (call it Chessfights) lacks a Beatty sequence structure in the P-positions as in Wythoff Queens. However, it is possible to formulate and prove some general results of a general recursive law which is a particular case of a Partizan Subtraction game.

Uncertainty in a mixed duopoly with quadratic costs

In this paper, we consider a mixed market with uncertain demand, involving one private firm and one public firm with quadratic costs. The model is a two-stage game in which players choose to make their output decisions either in stage 1 or stage 2. We assume that the demand is unknown until the end of the first stage. We compute the output levels at equilibrium in each possible role. We also determine ex-ante and ex-post firms’ payoff functions.

Desirable role in a price-setting international mixed duopoly

In this paper, we study the order of moves in a mixed international duopoly for differentiated goods, where firms choose whether to set prices sequentially or simultaneously. We discuss the desirable role of the public firm by comparing welfare among three games. We find that, in the three possible roles, the domestic public firm put a lower price, and then produces more than the foreign private firm.

Desirable role in an international duopoly model with tariffs

In this paper, we study an international market model in which the home government imposes a tariff on the imported goods. The model has two stages. In the first stage, the home government chooses an import tariff to maximize a function that cares about the home firm’s profit and the total revenue. Then, the firms engage in a Cournot or in a Stackelberg competition. We compare the results obtained in the three different ways of moving on the decision make of the firms.

Environmental and international tariffs in a mixed duopoly

In this paper, we study the effects of environmental and trade policies in an international mixed duopoly serving two markets, in which the public firm maximizes the sum of consumer surplus and its profit. We also analyse the effects of privatization. The model has two stages. In the first stage, governments choose environmental taxes and import tariffs, simultaneously. Then, the firms engage in a Cournot competition, choosing output levels for the domestic market and to export. We compare the results obtained in the three different ways of moving on the decision make of the firms.

Privatization in a mixed duopoly with environmental taxes

In this paper, we study the effects of environmental and privatization in a mixed duopoly, in which the public firm aims to maximize the social welfare. The model has two stages. In the first stage, the government sets the environmental tax. Then, the firms engage in a Cournot competition, choosing output and pollution abatement levels.

Licensing in an international triopoly

We study the effects of entry of two foreign firms on domestic welfare in the presence of licensing, when the incumbent is technologically superior to the entrants. We consider two different situations: (i) the cost-reducing innovation is licensed to both entrants; (ii) the cost- reducing innovation is licensed to just one of the entrants. We analyse three kind of license: (lump- sum) fixed-fee; (per-unit) royalty; and two-part tariff, that is a combination of a fixed-fee and a royalty. We prove that a two part tariff is never an optimal licensing scheme for the incumbent. Moreover, (i) when the technology is licensed to the two entrants, the optimal contract consists of a licensing with only output royalty; and (ii) when the technology is licensed to just one of the entrants, the optimal contract consists of a licensing with only a fixed-fee.

Privatization in an international mixed duopoly with environmental taxes

We study the effects of environmental and trade policies in an international duopoly serving two countries, with pollution abatement. This analysis is done in both mixed and privatized markets. The model has two stages: First, governments choose environmental taxes and import tariffs, simultaneously; then, the firms compete in the market by choosing output levels for the domestic market and to export and also abatement levels.

Privatization and social welfare in an international mixed Stackelberg duopoly

Competition between public and private firms exists in a range of industries like telecommunications, electricity, natural gas, airlines industries, as weel as services including hospitals, banking and education. Some authors studied mixed oligopolies under Cournot competition (firms move simultaneously) and some others considered Stackelberg models (firms move sequentially). Tomaru [1] analyzed, in a Cournot model, how decision-making upon cost-reducing R&D investment by a domestic public firm is affected by privatization when competing in the domestic market with a foreign firm. He shows that privatization of the domestic public firm lowers productive efficiency and deteriorates domestic social welfare. In this paper, we examine the same question but in a Stackelberg formulation instead of Cournot. The model is a three-stage game. In the first stage, the domestic firm chooses the amount of cost-reducing R&D investment. Then, the firms compete à la Stackelberg. Two cases are considered: (i) The domestic firm is the leader; (ii) The foreign firm is the leader. We show that the results obtained in [1] for Cournot competition are robust in the sence that they are also true when firms move sequentially.

Privatização num mercado misto com decisões sequenciais

Consideramos um mercado no qual competem uma empresa pública e uma empresa privada, decidindo, de forma sequencial, as quantidades a produzir. O governo impõe um imposto sobre as quantidades comercializadas, de acordo com uma função que consiste numa soma ponderada entre o bem-estar público e a receita total obtida pela aplicação desse imposto. O objetivo deste trabalho é estudar o efeito da privatização da empresa pública, (i) quando a empresa líder é a empresa pública; e (ii) quando a empresa líder é a empresa privada. Além disso, fazemos uma comparação entre os resultados obtidos nos dois modelos estudados.

Welfare effects of entry into international markets with licensing

We study the effects of entry of a foreign firm on domestic welfare in the presence of licensing, when the entrant is technologically inferior to the incumbent. We show that foreign entry increases domestic welfare for intermediate (respectively, sufficiently large) technological differences between the firms under licensing with fixed fee (respectively, output royalty).