Publication

Modelling competition in demand-based optimization models

Michel Bierlaire
2018
Talks

Abstract

This paper discusses some methodological approaches to model competition in a demand-based optimization framework which is particularly suitable for oligopolistic markets. Such approaches allow us to analyze oligopolies from three perspectives: at a customer level, by using discrete choice models to take into account preference heterogeneity and to model individual decisions; at an operator level, by solving a mixed integer linear program that maximizes any relevant objective function; and at a market level, by investigating the concept of Nash equilibrium in the resulting non-cooperative multi-leader-follower game. At the latter level, in order to find equilibrium solutions for this type of problem, we propose an algorithmic approach based on the fixed-point iteration method and a mixed integer linear program that enumerates the pure strategy Nash equilibria of a finite game.

Official source

https://infoscience.epfl.ch/entities/publication/6a5392ed-490a-4d5e-9143-6e34061d0074

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Michel Bierlaire
2018
Talks

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6a5392ed-490a-4d5e-9143-6e34061d0074

About this result

Related concepts (32)

Nash equilibrium

In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.

Strategy (game theory)

In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends not only on their own actions but on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. A player's strategy will determine the action which the player will take at any stage of the game.

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Related publications (11)

Modelling competition in demand-based optimization models

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