2019. Differential Game of Demand and Supply in Cobweb Dynamics
Invited abstract in session TC-53: New Trends in Game Theory VI, stream Game Theory and Mathematical Economics.
Tuesday, 12:30-14:00Room: Liberty Moot Court
Authors (first author is the speaker)
| 1. | PREM PRAKASH MISHRA
|
| Mathematics, National Institute of Technology Nagaland |
Abstract
The demand and supply of agro-products at any time is a part of cobweb dynamics. We study about dynamic game of supply of inventory and its non-linear demand. The demand function constitutes with inventory-level as state variable and time dependent price as control variable. In contrary, the supply function constitutes with state variable as previous price and inventory level at current time as a control variable. Hence, we construct the system of Integral, differential equations and its corresponding Hamilton Bellman Jacobi Equations. The Lagrange’s method and Volterra` Integral equation solution techniques are employed to determine maximum value of demand and maximum value of supply of products at a particular time. In this consequence, we also get the optimum trajectory of price with its associated inventory level and optimum trajectory of inventory level with associated price of product.
Keywords
- Economic Modeling
- Dynamical Systems
- Game Theory
Status: accepted
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