Mathematical Optimization and Economic Theory
Mathematical Optimization and Economic Theory
A differential game among sectors in a macroeconomy
Automatica (Journal of IFAC)
Brief paper: Nash strategies for M-person differential games with mixed information structures
Automatica (Journal of IFAC)
Coordinating static and dynamic supply chains with advertising through two-part tariffs
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
In this paper an application of differential game theory in the area of microeconomics is presented. The problem considered is that of a dynamic duopoly where two firms each limited by a maximum capacity of production, share the same market, and try simultaneously but independently to maximize their profits over a certain planning horizon. While the static duopoly theory does not address itself to the question of the process by which changes in the price are brought about, but only compares the prices before and after the change takes place, the dynamic market theory, considered in this paper, allows for an analysis of how the price changes with time and what trajectory it follows. Necessary conditions for the existence of a Nash equilibrium solution in the general case are discussed and more specific results for the special case of linear demand and quadratic cost functions are developed.