Competition and Efficiency of Coalitions in Cournot Games with Uncertainty

TL;DR

This paper examines how coalition formation affects efficiency in Cournot markets under uncertainty, showing that optimal group sizes balance market power and risk reduction, with implications for electricity markets with renewable energy.

Contribution

It introduces a model analyzing the impact of coalition size on market efficiency under uncertainty and characterizes optimal group sizes for welfare and output in Cournot games.

Findings

Coalition formation can improve efficiency under uncertainty.

Optimal group sizes are proportional to the square root and two-thirds power of the number of firms.

Results are validated with real electricity market data.

Abstract

We investigate the impact of coalition formation on the efficiency of Cournot games where producers face uncertainties. In particular, we study a market model where firms must determine their output before an uncertain production capacity is realized. In contrast to standard Cournot models, we show that the game is not efficient when there are many small firms. Instead, producers tend to act conservatively to hedge against their risks. We show that in the presence of uncertainty, the game becomes efficient when firms are allowed to take advantage of diversity to form groups of certain sizes. We characterize the tradeoff between market power and uncertainty reduction as a function of group size. In particular, we compare the welfare and output obtained with coalitional competition, with the same benchmarks when output is controlled by a single system operator. We show when there are $N$ firms present, competition between groups of size $\Omega(\sqrt{N})$ results in equilibria that are socially optimal in terms of welfare and groups of size $\Omega(N^{2/3})$ are socially optimal in terms of production. We also extend our results to the case of uncertain demand by establishing an equivalency between Cournot oligopoly and Cournot Oligopsony. We demonstrate our results with real data from electricity markets with significant wind power penetration.