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...

Oil prices remained relatively low but volatile in the 2015-17 period, largely due to declining and uncertain demand from China. This follows a prolonged decline from around $110 per barrel in June 2014 to below $30 in January 2016, due in large part to increased supply of shale oil in the US,...

We give a selective survey of oligopoly models for energy production which capture to varying degrees issues such as exhaustibility of fossil fuels, development of renewable sources, exploration and new technologies, and changing costs of production. Our main focus is on dynamic Cournot...

We study how continuous time Bertrand and Cournot competitions, in which firms producing similar goods compete with one another by setting prices or quantities respectively, can be analyzed as continuum dynamic mean field games.Interactions are of mean field type in the sense that the demand...

We study the stochastic effect of resource exploration in dynamic Cournot models of exhaustible resources, such as oil. We first treat the case of a monopolist who may undertake costly exploration to replenish his diminishing reserves. We then consider a stochastic game between such an...

The dramatic decline in oil prices, from around $110 per barrel in June 2014 to less than $50 in January 2015, highlights the importance of competition between different energy sources. Indeed, the sustained price drop has been primarily attributed to OPEC's strategic decision not to curb its...

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework to construct optimal trading strategies under market impact in a multi-player framework by introducing...

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact in a multi-player framework by introducing strategic...