We develop a framework for the analysis of dynamic games that can be applied to the analysis of firm which compete in a market whose characteristics evolve over time as a probabilistic function of the actions of the firms competing in that market. Firm's chose their actions to maximize their perceptions of the discounted value of the returns that will accrue to them as a result of those actions. These returns depend on both their own states and their competitor's states. The firms know their own states, but only observe imprecise signals on the states of their competitors. Our goal is to provide a framework capable of analyzing the impact of policy or environmental changes in such a setting. Bayesian perfect Nash equilibria for environments that are rich enough to adequately approximate behavior have computational and informational demands that both; (i) make them impossible for applied researchers to use, and (ii) unlikely to be the best approximation to agent's actual behavior. So we introduce an alternative notion of equilibria which is less demanding of both agents and researchers, while still implying agents 'optimize' in a meaningful sense of that word. We show that: (i) there is an artificial intelligence algorithm that makes it relatively easy to compute (at least some of) the resultant equilibria, and (ii) it is relatively easy to use the properties of that equilibria to estimate any unknown parameters of the game. We use the analysis of a de-regulated electric utility market as an example. Two firms each own several generators and bid 'supply functions' into the market in every period (a quantity supplied as an increasing function of price). An independent system operator (an ISO) sums the supply curves horizontally and intersects the result with demand to determine the period's price and the quantities to be produced by each firm. The firm's cost of supplying electricity on each of its generators is increasing in the current quantity produced and stochastically increasing in the quantities produced since the last time the firm did maintenance on that generator. Firms do not know the current cost of their competitor's generators but realize that the returns they will earn from the bid on each of its generator will increase the less the quantity supplied by other generators (their own, as well as those of its competitors). This provides incentives for firms to simply shut down some generators without doing maintenance, and to implicitly co-ordinate shutdowns across firms. Consumers pay the price through the resultant increase in the price of electricity.
Joint work with Chaim Fershtman