Search results for "Mathematical Economics"

Les followers ont-ils vraiment de l'importance dans le modèle de Stackelberg?

2011

In this paper, we consider a T-stage linear model of Stackelberg oligopoly. First, we show geometrically and analytically that under the two conditions of linear market demand and identical constant marginal costs, the T-stage Stackelberg model reduces to a model where T oligopolies exploit residual demand sequentially. At any stage, leaders behave as if followers did not matter. Second, we study social welfare and convergence toward competitive equilibrium. Especially, we consider the velocity of convergence as the number of firms increases. The convergence is faster when reallocating firms from the most to the less populated cohort until equalizing the size of all cohorts.

Stackelberg equilibrium with multiple firms and setup costs

2017

Abstract I provide conditions that guarantee that a Stackelberg game with a setup cost and an integer number of identical leaders and followers has an equilibrium in pure strategies. The main feature of the game is that when the marginal follower leaves the market the price jumps up, so that a leader’s payoff is neither continuous nor quasiconcave. To show existence I check that a leader’s value function satisfies the following single crossing condition: When the other leaders produce more the leader never accommodates entry of more followers. If demand is strictly logconcave, and if marginal costs are both non decreasing and not flatter than average costs, then a Stackelberg equilibrium ex…

Beyond Viner: Smoothed Cost Curves and Co-Detetermination of Output and Production Capacity

2017

We address two problems of traditional cost functions: the discontinuity caused by the production capacity (the marginal cost abruptly becomes infinite when production capacity is reached) and the production capacity is artificially exogenous. So, we introduce a smoothed form of marginal cost function. It progressively tends to infinity when it approaches to the production capacity. Then, we prove that it is perfectly possible to determine directly output, fixed costs and production capacity simultaneously, even if this could lead to a system of equations that is not so elementary to solve because it includes a Lambert function. We also show that the smoothed cost function prevails in both …

Testing the Form of a Decision-maker's Multiattribute Value Function Based on Pairwise Preference Information

1989

In a recent paper we presented a test, based on pairwise preference information, to identify to which class of functions (linear, quasi-concave, or neither) a decision-maker's (implicit) value function belongs. In this note we investigate the power of the test. Some improvements to the test are also suggested.

A Decision Model for the Multiple Criteria Group Secretary Problem: Theoretical Considerations

1996

A decision model is developed for solving the discrete multiple criteria group secretary problem. The model extends the single decision-maker progressive algorithm by Korhonen, Moskowitz and Wallenius to group contexts. As the original progressive algorithm, it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision-maker's preference structure (value function). The decision-makers are requested to settle on a compromise, if possible. The model then proceeds with determining the likelihood of finding possibly/surely better settlements (compromises). Linear value functions, linear prospect theory-type value functions, and quasiconca…

Dynamics in stochastic evolutionary models

2016

We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict, and illustrate the theory with the fall of the Qing dynasty and the rise of communism in China.

An appraisal of Piero Sraffa's 'The Laws of Returns under Competitive Conditions'

2001

The paper proposes a new interpretation of Sraffa's 1926 Economic Journal article, ‘The Laws of Returns under Competitive Conditions’, according to which the latter derives from the same strategy of research which underlies its 1925 Italian precursor, ‘Sulle relazioni fra costo e quantità prodotta’. Sraffa tested the explanatory power of a Marshallian monopolistic partial equilibrium model and concluded that that model is able to treat one source of variable returns (firm-internal economies); but this articulation of Marshall‘s theory does not substantially improve on the trade-off between logical consistency and empirical relevance which afflicted the theory in its whole. © 2001, Taylor & …

Equivalence Revisited: Polish Perspectives on the Topic

2019

Dynamic Coalitional TU Games: Distributed Bargaining among Players' Neighbors

2013

We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. The game differs from other ones in the literature on dynamic, stochastic or interval valued TU games as it combines dynamics of the game with an allocation protocol for the players that dynamically interact with each other. The protocol is an iterative and decentralized algorithm that offers a paradigmatic mathematical description of negotiation and bargaining processes. The first part of the paper contributes to the definition of a robust (coalitional) TU game and the development of a distributed bargaining protoc…

Continuous-time portfolio optimization under terminal wealth constraints

1995

Typically portfolio analysis is based on the expected utility or the mean-variance approach. Although the expected utility approach is the more general one, practitioners still appreciate the mean-variance approach. We give a common framework including both types of selection criteria as special cases by considering portfolio problems with terminal wealth constraints. Moreover, we propose a solution method for such constrained problems.