Strategic bidding for multiple price-maker hydroelectric producers

In a market comprised of multiple price-maker firms, the payoff each firm receives depends not only on one's own actions but also on the actions of the other firms. This is the defining characteristic of a non-cooperative economic game. In this article, we ask: What is the revenue-maximizing production schedule for multiple price-maker hydroelectric producers competing in a deregulated, bid-based market? In every time stage, we seek a set of bids such that, given all other price-maker producers' bids, no price-maker can improve (increase) their revenue by changing their bid; i.e., a pure-strategy Nash-Cournot equilibrium. From a theoretical game theory perspective, the analysis on the underlying non-cooperative game is lacking. Specifically, existing approaches are not able to detect when multiple equilibria exist and consider any equilibrium found optimal. In our approach, we create interpolations for each price-maker's best response function using mixed-integer linear programming formulations within a dynamic programming framework. In the presence of multiple Nash equilibria, when one exists, our approach finds the equilibrium that is Pareto optimal. If a Pareto-optimal Nash equilibrium does not exist, we use a tailored bargaining algorithm to determine a unique solution. To illustrate some of the finer details of our method, we present three examples and a case study on an electricity market in Honduras.