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

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

Endogenous Rationing, Price Dispersion, and Collusion in Capacity Constrained Supergames.

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival’s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with successful collusion, it may be a requirement of successful collusion.Bertrand-Edgeworth ; Supergame ; Collusion ; Capacity

Caps on Bidding in All-Pay Auctions: Comments on the Experiments of A. Rapoport and W. Amaldoss.

In an article published in this journal, Rapoport and Amaldoss (2000, Journal of Economic Behavior and Organization, 42, 483-521) analyze symmetric and asymmetric investment games similar to two-player all-pay auctions with bid caps. In this note, we correct an error in their characterization of the set of Nash Equilibria of their symmetric investment game. In particular, we find Equilibria that Rapoport and Amaldoss (2000) fail to identify. Taking these Equilibria into account has important implications for the analysis of data from Rapoport and Amaldoss’s experiments.All-Pay Auction ; Mixed strategies ; Discrete strategy space ; Bid caps ; Experiments

Shirking, Sharing Risk, and Shelving: The Role of University License Contracts

In this paper, we develop a theoretical model of university licensing to explain why university license contracts often include payment types that differ from the fixed fees and royalties typically examined by economists. Our findings suggest that milestone payments and annual payments are common because moral hazard, risk sharing, and adverse selection all play a role when embryonic inventions are licensed. Milestones address inventor moral hazard without the inefficiency inherent in royalties. The potential for a licensee to shelve inventions is an adverse selection problem which can be addressed by annual fees if shelving is unintentional, but may require an upfront fee if the firm licenses an invention with the intention to shelve it. Whether the licensing contract prevents shelving depends in part on the university credibly threatening to take the license back from a shelving firm. This supports the rationale for Bayh-Dole march-in rights but also shows the need for the exercise of these rights can be obviated by contracts.

A Comment on “David and Goliath: An Analysis on Asymmetric Mixed-Strategy Games and Experimental Evidence”.

In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Amaldoss and Jain (Management Science, 48(8), August 2002, pp. 972-991). Contrary to Amaldoss and Jain’s (2002) claim, we show that the equilibrium is not always unique and that the set of Equilibria is non-robust to changes in the (discrete) set of available strategies. In some Equilibria, the qualitative results are the reverse of those in the only equilibrium Amaldoss and Jain identify. Our findings have important implications for the analysis of the data from Amaldoss and Jain’s experiments, as well as other experiments appearing in the literature.All-Pay Auction ; Contests ; Experimental Economics ; Competitive Strategy ; R&D

On the use of graph theory to interpret the output results from a Monte-Carlo depletion code

The analysis of the results of a depletion code is often considered a tedious and delicate task for it requires both the processing of large volume of information (the time dependent composition of up to thousands isomeric states) and an extensive experience of nuclear reactions and associated nuclear data. From these observations, dedicated developments have been integrated to the upcoming version of the Monte Carlo depletion code VESTA 2.2, in order to implement an innovative representation of depletion problems. The aim is to provide user with an adapted and efficient framework to ease the analysis of the results of the code and facilitate their interpretation. This effort ultimately culminated in the development of the representation of the isotope evolution of a given system as a directed graph. In this paper, it is shown that the Bateman equation encoded in the VESTA code indeed possesses a natural interpretation in terms of directed cyclic graph and it is proposed to explore some of the insight one can gain from the graph representation of a depletion problem. Starting from the new capabilities of the code, it is shown how one can build on the wealth of existing methods of graph theory in order to gain useful information about the nuclear reactions taking place in a material under irradiation. The graph representation of a depletion problem being especially simple in activation problems, for then only a limited number of nuclides and reactions are involved, the graph representation and its associated tools will be used to study the evolution of the structure materials of a simplifed model of the ITER fusion reactor

Appropriability and Commercialization: Evidence from MIT Inventions

At least since Arrow (1962), the effects of appropriability on invention have been well studied, but there has been little analysis of the effect of appropriability on the commercialization of existing inventions. Exploiting a database of 805 attempts by private firms to commercialize inventions licensed from MIT between 1980 and 1996, we explore the influence of several appropriability mechanisms on the commercialization and termination of projects to develop products based on university inventions. We construct a theoretical model in which the licensee faces technical and market uncertainty, and anticipates that its products will be imitated. We characterize the hazards of commercialization and termination as functions of appropriability mechanisms, including patent scope and the effectiveness of patents as well as learning, lead time, and secrecy in attaining competitive advantage. The model is tested using a competing risks framework that allows for non-parametric unobserved heterogeneity and correlated risks. In our sample, patent strength and secrecy influence termination decisions, while learning, patent scope and lead time influence commercialization decisions.hazard rates, innovation, optimal stopping problem, patent scope, university licensing, termination

Appropriability and the timing of innovation: Evidence from MIT inventions

At least since Arrow (1962), the effects of appropriability on invention have been well studied, but there has been little analysis of the effect of appropriability on the commercialization of existing inventions. Exploiting a database of 805 attempts by private firms to commercialize inventions licensed from MIT between 1980 and 1996, we explore the influence of several appropriability mechanisms on the commercialization and termination of projects to develop products based on university inventions. Our central hypothesis is that the relationship between a licensee's decision to either terminate or commercialize the invention is driven by the current market value of the invention, as well as the option value of delaying its commercialization. We use a competing risks framework that allows for non- parametric heterogeneity and correlated risks. We find that better appropriability in the sense of more effective patent strength and secrecy has a strong negative effect on the hazard of license termination. The effectiveness of learning has a strong positive effect on the hazard of technology commercialization, while lead time has a negative effect.

Percolation properties of the neutron population in nuclear reactors

Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled stochastic systems however require to define intermediate quantities (e.g. the temperature field), which are bridging the gap between the stochastic neutron field and the deterministic feedback. By interpreting the branching random walk of neutrons in fissile media under the influence of a feedback mechanism as a directed percolation process and by leveraging on the statistical field theory of birth death processes, we will build a stochastic model of neutron transport theory and of reactor physics. The critical exponents of this model, combined to the analysis of the resulting field equation involving a fractional Laplacian will show that the critical diffusion equation cannot adequately describe the spatial distribution of the neutron population and shifts instead to a critical super-diffusion equation. The analysis of this equation will reveal that non-negligible departure from mean field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.Comment: 15 pages, 2 figures, 1 tabl