Efficiency-Risk Tradeoffs in Dynamic Oligopoly Markets - with   application to electricity markets
  In this paper, we examine in an abstract framework, how a tradeoff between efficiency and robustness arises in different dynamic oligopolistic market architectures. We consider a market in which there is a monopolistic resource provider and agents that enter and exit the market following a random process. Self-interested and fully rational agents dynamically update their resource consumption decisions over a finite time horizon, under the constraint that the total resource consumption requirements are met before each individual's deadline. We then compare the statistics of the stationary aggregate demand processes induced by the non-cooperative and cooperative load scheduling schemes. We show that although the non-cooperative load scheduling scheme leads to an efficiency loss - widely known as the "price of anarchy" - the stationary distribution of the corresponding aggregate demand process has a smaller tail. This tail, which corresponds to rare and undesirable demand spikes, is important in many applications of interest. On the other hand, when the agents can cooperate with each other in optimizing their total cost, a higher market efficiency is achieved at the cost of a higher probability of demand spikes. We thus posit that the origins of endogenous risk in such systems may lie in the market architecture, which is an inherent characteristic of the system. 
Qingqing Huang, Mardavij Roozbehani, and Munther A Dahleh
cs.SY