Strategic supply function competition with private information
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In this article, a Bayesian supply function equilibrium is characterized: the equilibrium is privately revealing and the incentives to rely on private signals are preserved, and a range of applications in product and financial markets is presented.Abstract:
A finite number of sellers (n) compete in schedules to supply an elastic demand. The cost of each seller is random, with common and private value components, and the seller receives a private signal about it. A Bayesian supply function equilibrium is characterized: The equilibrium is privately revealing and the incentives to rely on private signals are preserved. Supply functions are steeper with higher correlation among the cost parameters. For high (positive) correlation, supply functions are downward sloping, price is above the Cournot level, and as we approach the common value case, price tends to the collusive level. As correlation becomes maximally negative, we approach the competitive outcome. With positive correlation, private information coupled with strategic behavior induces additional distortionary market power above full information levels. Efficiency can be restored with appropriate subsidy schemes or with a precise enough public signal about the common value component. As the market grows large with the number of sellers, the equilibrium becomes price-taking, bid shading is on the order of 1/n, and the order of magnitude of welfare losses is 1/n2. The results extend to inelastic demand, demand uncertainty, and demand schedule competition. A range of applications in product and financial markets is presented.read more
Figures
Figure 2b. ( )cn nDWL / n ETS ETS / n≡ − as a function of 2εσ (with parameters 1β = λ = , 30θ = , 50α = , 2 1θσ = , and n = 10) 
Figure 2b. ( )cn nDWL / n ETS ETS / n≡ − as a function of 2εσ (with parameters 1β = λ = , 30θ = , 50α = , 2 1θσ = , and n = 10) 
Figure 4. Efficiency differential between supply function and Cournot equilibria as a 
Figure 3b. Efficiency differential between supply function and Cournot equilibria as a 
Figure 1. The LBSFE ( )X ,pθ as ρ goes from 0 to 1. 
Figure 3b. Efficiency differential between supply function and Cournot equilibria as a
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