On Quantity Competition and Transmission Constraints in Electricity Market

In this paper we characterize equilibria in a quantity game where symmetric firms face a local demand together with an export-constrained demand. Firms have unlimited access to a local demand but a restricted access to a second market, like in the electricity network where generators compete to satisfy demand but competition is restricted by transmission capacity. We show the existence of an effective demand that is continuous but not differentiable due to the transmission constraint. Three types of equilibria emerge in this context, parametrized by capacity. First, a symmetric equilibrium (unique) when the access to the second market is constrained. Second, a set of continuous and asymmetric equilibria with a fully used link but not constrained; and finally, a symmetric and unique equilibrium in which the link is not fully used. We also show how multiplicity of equilibria tends to disappear as the number of competitors increaseelectricity markets, Cournot games, capacity constraints

Endogenous capacities and price competition: the role of demand uncertainty

This paper analyzes a model of capacity choice followed by price competition under demand uncertainty. Under various assumptions regarding the nature and timing of demand realizations, we obtain general predictions concerning the role of demand uncertainty on equilibrium outcomes. We show that it reduces the multiplicity of equilibria, it may rule out the existence of symmetric equilibria, and it leads to endogenous capacity asymmetries even though firms are ex-ante symmetric. Furthermore, as compared to the certainty equivalent game, demand uncertainty reduces prices and increases consumer surplus, but it also decreases total welfare because of the emergence of idle capacity. By relying on the analysis of firms' reaction functions as well as on the theory of submodular games, we are able to show that a subgame perfect equilibrium always exists and to fully characterize it

Tacit Collusion and Capacity Withholding in Repeated Uniform Price Auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this out-come. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factorAuction, Capacity, Collusion, Electricity Market, Supply Function

Tacit Collusion and Capacity Withholding in Repeated Uniform Price Auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this outcome. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor above which the perfectly collusive outcome with equal sharing is sustainable on a stationary path. Under the Market Clearing Price rule, only one step is required. That is, within the class of step bidding functions with a finite number of steps, maximal collusion is attained with simple price-quantity strategies exhibiting capacity withholding.Auction; Capacity; Collusion; Electricity Market; Supply Function