Identifying reaction functions in differential oligopoly games

Identifying Reaction Functions in a Differential Oligopoly Game with Sticky Prices

We investigate the issue of strategic substitutability/complementarity in a Cournot differential game with sticky prices. We show that first order conditions do not produce instantaneous best reply functions. However, we identify negatively sloped reaction functions in steady state, with the open-loop best reply being flatter than its closed-loop counterpart. JEL classification: C73, D43, D92, ...

Hamiltonian potential functions for differential games

We introduce the concept of Hamiltonian potential function for noncooperative open-loop differential games and characterise necessary and sufficient conditions for its existence. We also identify a class of games admitting a Hamiltonian potential and illustrate appropriate examples pertaining to oligopoly games where price or quantity competition goes along with noncooperative investments eithe...

Convexity and the Shapley value in Bertrand oligopoly TU-games with Shubik's demand functions

The Bertrand Oligopoly situation with Shubik’s demand functions is modelled as a cooperative TU game. For that purpose two optimization problems are solved to arrive at the description of the worth of any coalition in the so-called Bertrand Oligopoly Game. Under certain circumstances, this Bertrand oligopoly game has clear affinities with the well-known notion in statistics called variance with...

Games with Exhaustible Resources

We study N -player continuous-time Cournot games in an oligopoly where firms choose production quantities. These are nonzero-sum differential games, whose value functions may be characterized by systems of nonlinear Hamilton-Jacobi partial differential equations. When resources are in finite supply, such as oil, exhaustibility enters as boundary conditions for the PDEs. We analyze the problem w...

A Differential Oligopoly Game with Sticky Prices and Environmental Externality