Stanley S. Reynolds

Capacity Investment, Preemption and Commitment in an Infinite Horizon Model

The commitment value of capacity is analyzed in an infinite horizon duopoly model. The paper focuses on the role of alternative behavioral assumptions about the ability of firms to commit to investment paths. Each firms investment strategy in a feedback Nash equilibrium is shown to be a decreasing function of its rivals current capacity. This creates an incentive for a firm to expand its capacity to preempt subsequent rival investment. In a precommitment equilibrium there are no incentives to invest preemptively. As a consequence, steady state capacity levels are greater in a feedback Nash equilibrium than in a precommitment equilibrium. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Adaptation And Convergence Of Behavior In Repeated Experimental Cournot Games

This research examines results from laboratory experiments in which five human subjects participate as sellers in a Cournot oligopoly environment. The central issue is whether repeated play among a group of privately informed subjects will lead to convergence to a unique, static, noncooperative Nash equilibrium. The experiments were designed so that the implications of different hypotheses about adaptation and convergence, such as the best response dynamic and fictitious play, could be distinguished. The results provide, at best, only partial support for the hypothesis that behavior of privately informed subjects will converge to the static Nash equilibrium when play is repeated. Total output averaged over time periods and across experiments is greater than, but still close to, predicted equilibrium total output. However, observed intertemporal variation in total output and heterogeneity in individual choices are inconsistent with convergence to the static Nash equilibrium.

Bertrand-Edgeworth Competition, Demand Uncertainty, and Asymmetric Outcomes

Abstract We analyze investment and pricing incentives in a symmetric Bertrand– Edgeworth framework with uncertain demand. Firms choose production capacities before observing demand. Prices are chosen after demand is observed. If the extent of demand variation exceeds a threshold level then a symmetric equilibrium in pure strategies for capacities does not exist. A smaller firm has no incentive (ex ante) to expand its capacity because capacity expansion would reduce its expected revenue in the event that demand is lower than expected. Output prices are predicted to have positive variance when demand is low and zero variance when demand is high. Journal of Economic Literature Classification Numbers: D43, L13.

Bertrand-Edgeworth competition in experimental markets

The Bertrand-Edgeworth (BE) model describes competition among a group of price setting sellers, each of whom faces a production capacity constraint. We report on laboratory experiments that were designed so as to capture essential features of BE competition. These experiments permit us to evaluate different theories of BE competition: Competitive equilibrium (CE) pricing, Edgeworth cycles in prices, mixed strategy Nash equilibrium (NE) in prices, and tacit collusion. The experimental results indicate that while each of the theories helps to explain some aspects of the data, none of these theories are completely consistent with the data. In relative terms, the Edgeworth cycle theory provides better predictions than the other three theories. Most sellers adjusted their prices partially to their predicted Edgeworth price. The Edgeworth cycle theory is the only theory that predicts the kind of time dependence and cycling that was observed in most experiments.

Dynamic oligopoly with capacity adjustment costs

Abstract The literature on strategic investment emphasized the case of completely irreversible investment. This paper considers an oligopoly model in which investment is reversible and capacity is subject to adjustment costs. An n -player, linear-quadratic differential game is analyzed. Existence and characterization results for perfect equilibrium feedback strategies are provided. Feedback strategies provide incentives for each player to invest strategically so as to preempt subsequent expansion by rivals. A larger set of perfect equilibria is constructed by using memory-dependent trigger strategies. Equilibria of this type are shown to support joint-value maximization (for some initial states) and asymmetric steady states.

Auctions with a buy price

AbstracteBay and Yahoo allow sellers to list their auctions with a buy price at which a bidder may purchase the item immediately. On eBay, the buy-now option disappears once a bid is placed, while on Yahoo the buy-now option remains in effect throughout the auction. We show that when bidders are risk averse, both types of auctions raise seller revenue for a wide range of buy prices. The Yahoo format raises more revenue than the eBay format when bidders have either CARA or DARA. Bidders with DARA prefer the eBay auction, while bidders with CARA are indifferent between the two.

Appropriability and Market Structure in a Stochastic Invention Model

This research examines in the laboratory a class of game-theoretic equilibrium models of private research and development (R&D). We formulate a stochastic model of R&D investment whose predictions can be examined by using laboratory experiments. The noncooperative Nash equilibrium of our operational model yields testable predictions about the effects of appropriability and market structure on R&D. The experimental results support the hypothesis that the degree of appropriability is inversely related to R&D spending. The results strongly support the hypothesis that an increase in group size yields greater aggregate R&D. The noncooperative Nash equilibrium is shown to be a good predictor of central tendencies in the experiments.

Schumpeterian competition in experimental markets

Abstract We report on a series of laboratory experiments that capture key elements of research and development (R&D) rivalry. The experimental environment has a small number of sellers who compete in terms of pricing and production decisions and in terms of cost-reducing R&D. Rewards for innovation depend on the profitability of product market competition. The experiments capture a kind of dynamic, Schumpeterian competition. There is a sharp contrast in experimental results between monopolies and four-seller (competitive) markets. Aggregate R&D is higher under competition than under monopoly and prices follow marginal cost reductions much more quickly under competition than under monopoly. The paper examines market performance in the experiments and the sources of market performance problems.

Durable-Goods Monopoly: Laboratory Market and Bargaining Experiments

Results from single-period monopoly experiments (nondurable environment) are compared with results from multiperiod experiments that have features of a durable-goods environment. Average prices were below the static monopoly benchmark price in all settings. Observed initial prices were higher in multiperiod experiments than in single-period experiments, in contrast to equilibrium predictions. Prices in multiperiod experiments tended to fall over time; there was less price cutting in market experiments than in bargaining experiments. There was substantial demand withholding by buyers in multiperiod experiments. A version of bounded rationality is a promising candidate for explaining deviations from equilibrium predictions.

Pivotal Suppliers and Market Power in Experimental Supply Function Competition

We use experiments to study market power with supply function competition, akin to the competition in electricity markets. Our treatments vary the distribution of demand levels as well as the amount and symmetry of the allocation of production capacity between different suppliers. We relate our results to a descriptive power index and to the predictions of two models: a supply function equilibrium (SFE) model and a multi-unit auction (MUA) model. Observed behaviour is consistent with the equilibria of the unrestricted SFE model and inconsistent with the unique equilibria of two refinements of the SFE model and of the MUA model.