Consistent Conjecture Research Articles

Rational conjectures and evolutionary beliefs in public goods games

AbstractThis paper applies conjectural variations (CVs) to a model of public good provision and shows that CVs are superior to Nash beliefs. In addition to imposing consistency, as Bresnahan, I show that consistent conjectures (CCs) are obtained from individual payoff maximization. CCs emerge as the unique subgame perfect Nash equilibrium (NE) in a two‐stage game in which beliefs are chosen in Stage 1 and quantities in Stage 2. There is an individual payoff advantage to non‐Nash behavior, generating a Prisoner's Dilemma in conjectures in addition to the usual free‐rider problem associated with public goods. The correct and payoff maximizing conjecture is the unique equilibrium in an evolutionary framework against a player with Nash conjectures. The consistent conjecture equilibrium is the unique evolutionary equilibrium when both players conjectures evolve. Hence, the NE prediction is too optimistic when players have rational conjectures.

Diverse Data Sets Can Yield Reliable Information through Mechanistic Modeling: Salicylic Acid Clearance.

This is a practical example of a powerful research strategy: putting together data from studies covering a diversity of conditions can yield a scientifically sound grasp of the phenomenon when the individual observations failed to provide definitive understanding. The rationale is that defining a realistic, quantitative, explanatory hypothesis for the whole set of studies, brings about a “consilience” of the often competing hypotheses considered for individual data sets. An internally consistent conjecture linking multiple data sets simultaneously provides stronger evidence on the characteristics of a system than does analysis of individual data sets limited to narrow ranges of conditions. Our example examines three very different data sets on the clearance of salicylic acid from humans: a high concentration set from aspirin overdoses; a set with medium concentrations from a research study on the influences of the route of administration and of sex on the clearance kinetics, and a set on low dose aspirin for cardiovascular health. Three models were tested: (1) a first order reaction, (2) a Michaelis-Menten (M-M) approach, and (3) an enzyme kinetic model with forward and backward reactions. The reaction rates found from model 1 were distinctly different for the three data sets, having no commonality. The M-M model 2 fitted each of the three data sets but gave a reliable estimates of the Michaelis constant only for the medium level data (Km = 24±5.4 mg/L); analyzing the three data sets together with model 2 gave Km = 18±2.6 mg/L. (Estimating parameters using larger numbers of data points in an optimization increases the degrees of freedom, constraining the range of the estimates). Using the enzyme kinetic model (3) increased the number of free parameters but nevertheless improved the goodness of fit to the combined data sets, giving tighter constraints, and a lower estimated Km = 14.6±2.9 mg/L, demonstrating that fitting diverse data sets with a single model improves confidence in the results. This modeling effort is also an example of reproducible science available at html://www.physiome.org/jsim/models/webmodel/NSR/SalicylicAcidClearance

Categorizing others in a large game

We study the efficiency of categorization of other agents as a way of saving cognitive resources in the settings of a large normal-form game. We assume that, when an agent categorizes (partitions) her opponents, she only has information about the average strategy in each category. A strategy profile is a conjectural categorical equilibrium (CCE) with respect to a given categorization profile if every player's strategy is a best response to some consistent conjecture about the strategies of her opponents. It is shown that, for a wide family of games and for a particular categorization profile, every CCE is an approximate Nash equilibrium when the number of players is large. This result demonstrates the potential of categorization as an efficient way to store information in complex environments. Although possessing a coarse description of their opponents' strategies, agents behave as if they see the full picture.

The evolution of consistent conjectures

In this paper we model the evolution of conjectures in an economy consisting of a large number of firms which meet in duopolies. The duopoly game is modelled by the conjectural variation (CV) model. An evolutionary process leads to more profitable conjectures becoming more common (payoff-monotonic dynamics). Under this class of selection dynamics, convergence occurs to a small set of serially undominated strategies containing the consistent conjecture. This set can be made arbitrarily small by appropriate choice of the strategy set. If the game is dominance solvable, then the dynamics converge globally to the unique attractor.

Selected Papers

Consistent conjectures applied to the food industries are investigated. This is a homogeneous-product, quantity-setting model with identical firms. When firm numbers are fixed, the consistent conjecture is monopolistic. When variable, consistency requires firm output to expand with exit and contract with entry, but no conjecture exists that is consistent with equilibrium.

Review Article: Psychological Effects of Functional Electrical Stimulation: A Review of the Literature

There has been considerable interest in utilizing functional electrical stimulation (FES) to help spinal cord injured individuals rebuild atrophied muscles and improve overall fitness and functioning. While most studies have addressed the physiological benefits accruing from FES training, there has been consistent conjecture that FES training leads to significant psychological benefits as well. In this report, the literature on the psychological effects of FES exercise training is reviewed. The studies that have examined the psychological effects of FES training have found improvements in self-esteem, mood factors, depression, and anxiety that parallel the changes noted in ablebodied individuals who exercise and in spinal cord injured individuals who participate in non-FES exercise programs. Some negative effects have also been reported, such as increased tension and anger and decreased motivation. In addition to these published findings, guidelines for more systematic research in this area are presented,...

Consistent Conjectures in a Value-Maximizing Duopoly

Recent literature on consistent conjectures has established that, under a variety of conditions, only competitive behavior is rational. Rationality or consistency is defined in this literature as the condition that the slope of a firm's profit-maximizing reaction function must equal the conjecture made about the firm's reactions by its rivals. This concept of consistency is due to Bresnahan [5], who uses it to select among the many possible conjectural equilibria in duopoly as defined by Bowley [3].' Perry [24] extends the duopoly analysis to the case of an arbitrary fixed number of identical firms, as well as to the case of free entry and exit. Both papers show that only the Bertrand conjecture, in which firms accommodate rivals' output changes by making equal and opposite changes, is consistent when marginal costs are constant. In addition, Perry shows that this result also holds when entry and exit are free. The Bertrand conjecture is identified with competitive behavior since it implies price taking and marginal cost pricing. The equivalence that both papers establish between consistent conjecture equilibrium (CCE) and competitive equilibrium under constant marginal cost may have important practical implications. Johnston summarizes his thorough survey of cost functions with the comment: Two major impressions, however, stand out clearly. The first is that the various short-run studies more often than not indicate constant marginal cost and declining average cost as the pattern that best seems to describe the data that have been analyzed [15, 168]. Therefore, the results of Bresnahan and Perry would seem to apply to a wide range of observed behavior, making a strong theoretical case that much economic activity is truly competitive regardless of the number of firms.2 Even when marginal costs are not constant and the number of firms is fixed, the implication of the consistent conjectures hypothesis for profit-maximizing firms is that behavior is more competitive than Coumot. This result in itself is important, since recent work has indicated that Cournot equilibrium approaches the competitive limit in the case of large economies; see for

Price reaction functions and conjectural variations

Price conjectural variations are estimated to measure the degree of price competition in a product differentiated oligopoly. The empirical model is a simultaneous equation system of product demand and price reaction functions. Own and cross price demand elasticities are estimated in conjunction with the price conjectural variations and price reaction function elasticities. The conjectural variations are estimated for pairs of ready-to-eat breakfast cereal products using brand price and quantity data. The empirical results reject competitive brand pricing behavior in favor of independent or collusive pricing. Further, the hypothesis of a unique consistent conjecture is rejected.

SPATIAL COMPETITION WITH CONSISTENT CONJECTURES*

ABSTRACT Equilibrium in spatial models invariably depends on firms' conjectures about how competitors will react to their price changes. This paper analyzes spatial price and location equilibrium when firms hold consistent (i.e. correct) conjectures. Most spatial models assume an exogenous conjecture. Consistent conjectures are one method, albeit a controversial one, for endogenizing the conjecture.We show that the consistent conjecture about a competitor's reaction to a price change in the simplest case is 1/3. When demand is elastic the consistent conjecture is a decreasing function of the radius. It is always below 1/3 and can be negative. In the third model, we show that the consistent conjecture declines as the number of dimensions and the number of competitors increases.

TARIFFS, QUOTAS, AND INTERNATIONAL OLIGOPOLY

This paper compares the effects of tariffs and quotas in the presence of quantity-setting international duopolists. With the Cournot-Nash case, a tariff is equivalent to a quota; but with the Stackelberg and consistent conjecture cases, a quota will induce a switching of the domestic conjectural variation and is found to be not equivalent to a tariff. Copyright 1989 by Royal Economic Society.

Consistent conjecture and free entry oligopoly: A general analysis

This paper shows that, in an oligopoly model that allows free entry, only competitive conjecture is consistent for any demand and cost functions and for any conjectural variation function that depends on the firm's own output and the outputs of the other firms.