Game Theoretic Models for Energy Production

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 competition with exhaustible resources. We trace the resulting theory of competitive equilibria and discuss some of the major emerging strands, including competition between renewable and exhaustible producers, endogenous market phase transitions, stochastic differential games with controlled jumps, and mean field games.