Dynamic oligopoly pricing with reference-price effects

We analyze the strategic implications of consumers’ reference-price effects, either symmetric (for loss-neutral consumers) or asymmetric (for loss-averse consumers), in a differentiated oligopoly model where firms compete either in prices (à la Bertrand) or in quantities (à la Cournot) over an infinite time horizon. The dynamic game is specified in continuous time. The solution concept is Markov Perfect Equilibrium. We show how price dynamics in the presence of reference-price effects crucially depends on the nature of market competition. One of the main results of our analysis is that, with loss-averse consumers, there exists an interval of initial reference prices such that firms adopt the same constant-pricing strategy in both the Bertrand and the Cournot games, implying that the distinction between price and quantity competition has no impact on market conduct and performance.     

Continuous learning methods in two-buyer pricing problem

This paper presents continuous learning methods in a monopoly pricing problem where the firm has uncertainty about the buyers’ preferences. The firm designs a menu of quality-price bundles and adjusts them using only local information about the buyers’ preferences. The learning methods define different paths, and we compare how much profit the firm makes on these paths, how long it takes to learn the optimal tariff, and how the buyers’ utilities change during the learning period. We also present a way to compute the optimal path in terms of discounted profit with dynamic programming and complete information. Numerical examples show that the optimal path may involve jumps where the buyer types switch from one bundle to another, and this is a property which is difficult to include in the learning methods. The learning methods have, however, the benefit that they can be generalized to pricing problems with many buyers types and qualities.     

Reducing competitors in Cournot-Puu oligopoly

The aim of this paper is to investigate whether an oligopoly given by isoelastic demand function and constant marginal costs converges to a duopoly, that is, all the firms except for two of them will not produce anything in future.     

Study of unsteady oligopoly markets

Under study is some simulation model of an oligopolisticmarket in continuous time. For the suppliers (oligopolists) the two rules of behavior are defined by a system of ordinary differential equations. The scenario determines the strategy that is used by the supplier, including the possibility of changing it during the interaction. It is shown, that there are possible stationary states in the model when a supplier profitability can be tools to start using a new rule of his behavior. In result of changing strategy his profit rises as compared to the other participants.     

Mixed oligopoly with consistent conjectures

In this paper, we consider a model of mixed oligopoly with conjectural variations equilibrium (CVE). The agents’ conjectures concern the price variations depending upon their production output’s increase or decrease. We establish existence and uniqueness results for the conjectural variations equilibrium (called an exterior equilibrium) for any set of feasible conjectures. To introduce the notion of an interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as a CVE with consistent conjectures). To prepare the base for the extension of our results to the case of non-differentiable demand functions, we also investigate the behavior of the consistent conjectures in dependence upon a parameter representing the demand function’s derivative with respect to the market price.     

Spatial oligopoly as a noncooperative game

Equilibrium in spatial markets has been studied as a problem of monopolistic competition. The typical assumption is that firms charge mill prices and believe that other firms either keep prices constant or preserve their market areas. In this paper somewhat different assumptions are made. First, a system of delivered or c.i.f. prices is assumed. A second model considers different production costs. A third model examines the case of more than two firms, but only for the special case where all firms are spaced at equal distance. Throughout this paper it is assumed that collusion is illegal, the game is a noncooperative one.     

Price oligopoly as a cooperative game

We consider an oligopolistic market as follows. In the market, one good is traded for money. Each oligopolist is a price setter and has the same linear cost function. Each buyer is a price taker and buys the good from oligopolists setting the lowest price. We formulate this market as a cooperative game, and consider two kinds of solution concepts, the core and a bargaining set of the game. First we show that in the monopolistic market, the core gives the monopoly price, but in the oligopolistic market, the core is empty. Second, we obtain the bargaining set of the oligopolistic market.     

Cooperative oligopoly games with boundedly rational firms

We analyze cooperative Cournot games with boundedly rational firms. Due to cognitive constraints, the members of a coalition cannot accurately predict the coalitional structure of the non-members. Thus, they compute their value using simple heuristics. In particular, they assign various non-equilibrium probability distributions over the outsiders’ set of partitions. We construct the characteristic function of a coalition in such an environment and we analyze the core of the corresponding games. We show that the core is non-empty provided the number of firms in the market is sufficiently large. Moreover, we show that if two distributions over the set of partitions are related via first-order dominance, then the core of the game under the dominated distribution is a subset of the core under the dominant distribution.     

An oligopoly model of dynamic advertising competition

An oligopoly model is presented that allows the determination of feedback Nash equilibrium advertising strategies for an oligopoly. Analyses of symmetric and asymmetric oligopolies with the model show that unit contribution and advertising effectiveness have positive effects on a competitor’s own advertising and steady-state sales, while discount rate and decay rate have negative effects. An asymmetric analysis further shows that unit contribution and advertising effectiveness affect positively, and discount rate and decay rate negatively, a competitor’s rivals’ advertising, but have effects in opposite directions regarding rivals’ steady-state sales. The symmetric and asymmetric analyses also show that steady-state sales per competitor decline with the number of competitors in the oligopoly, while total oligopoly steady-state sales increase. The model is applied empirically to the triopolistic competition involving Anheuser-Busch, SABMiller, and Molson Coors in the beer industry.     

Organizational strategy and tacit collusion in oligopoly with agency

We study a model that integrates organizational structure and agency withdynamic price competition in oligopoly. Workers in different levels of the organizational structure have asymmetric information and heterogeneous objectives; i.e., there are agency conflicts within the firm. The organizational strategy of the firm is to determinesequentially the decision power relating to price and non-price competition instruments at each level. We examine the equilibrium organizational and competitive strategy of firms in a duopoly, and characterize the extent of noncooperative tacit collusion (with respect to price and non-price competition) that is feasible. We identify two sets of sufficient conditions that guarantee, (i) the monopoly solution is sustainable at any discount factor (rate of impatience of the workers), or (ii) the monopoly solution is not sustainable for any level of the discount factor. Interestingly, tacit collusion may be feasible when either the agency problem is non-existentor very severe; i.e., firm profits in equilibrium may be non-monotone in the extent of the agency conflict. Our analysis indicates that intrafirm learning and agency will have a stronger impact on feasible tacit collusion in markets where non-price competition plays a strong role. Moreover, there is an intimate connection between the firm's organizational strategy and the extent of tacit collusion with the (industry) business cycle.     

Dynamics of the cournot oligopoly with multi-product firms

The stability of the Cournot equilibrium for a linear oligopoly with multiproduct firms is analyzed. Under certain conditions, the equilibrium is proven to be stable independently of the values of the adjustment coefficients in the case of a continuous time system. However, it is stable only in duopoly for a discrete system of adjustment.     

More on spatial oligopoly as a noncooperative game

This paper presents and solves another case of a problem posed byBeckmann [1973]. It considers a duopoly game of c.i.f. pricers selling to a population distributed on an interval. While Beckmann assumed equal transportation costs to sellers and consumers, we assume prohibitive ones to consumers. We also arrive at a mixed strategy solution, one that is somewhat more complicated. A brief extension ton-players oligopoly is carried out at the end.     

Chaos in duopoly pricing

The dynamics of two competing firms in a market is studied in terms of Cournot's duopoly theory. Assuming iso-elastic demand and constant unit production costs the iterative mapping

for the outputs of the two firms ensues. The two constants are the unit production costs. The fixed point, the Cournot equilibrium, has earlier been assumed to be the only interesting feature of this model. It is, however, shown that the model can produce persistent motion, periodic or chaotic.     

Computing equilibria of Cournot oligopoly models with mixed-integer quantities

We consider Cournot oligopoly models in which some variables represent indivisible quantities. These models can be addressed by computing equilibria of Nash equilibrium problems in which the players solve mixed-integer nonlinear problems. In the literature there are no methods to compute equilibria of this type of Nash games. We propose a Jacobi-type method for computing solutions of Nash equilibrium problems with mixed-integer variables. This algorithm is a generalization of a recently proposed method for the solution of discrete so-called “2-groups partitionable” Nash equilibrium problems. We prove that our algorithm converges in a finite number of iterations to approximate equilibria under reasonable conditions. Moreover, we give conditions for the existence of approximate equilibria. Finally, we give numerical results to show the effectiveness of the proposed method.     

Stochastic models for bidding strategies on oligopoly electricity market

In this paper we consider the forward/futures contracts and Asian-type call options for power delivery as important components of the bidding strategies of the players’ profits on the electricity market. We show how these derivatives can affect their profit. We use linear asymmetric supply function equilibrium (SFE) and Cournot models to develop firms’ optimal bidding strategies by including forward/futures contracts and Asian-type options. We extend the methodology proposed by Niu et al. (IEEE Trans Power Syst 20(4):1859–1867, 2005), where only forward contracts for power delivery were considered in the SFE model.     

A note on oligopoly exploitation of common-pool renewable resources

This note derives the linear Feedback Nash equilibrium of a differential oligopoly game of exploitation of a common-pool renewable resource, and compares and contrasts it with social optimum. The case of regulated entry by means of a license fee is also considered. Two main results are derived. First, the steady-state oligopoly price can be increasing in the (exogenously given) number of firms. Second, an optimal license fee exists that induces the (endogenously given) number of firms to behave efficiently.     

Optimal warranties,reliabilities and prices for durable goods in an oligopoly

This paper addresses the problem of durable goods manufacturers in an oligopoly seeking optimal values for three decision variables: product warranty, reliability and price. Each firm seeks a warranty-reliability-price combination that maximizes expected profit subject to quite general constraints on the firm's decision variables. Warranty serves as a signal of product reliability, which is not observable by consumers. We present a game-theoretic model of warranty-reliability-price competition in such a market and examine Nash equilibria for this game. We show that under fairly general assumptions each firm can optimally set its warranty and reliability independently of price and competitors' actions. In addition, we show that optimal warranties and reliabilities are complementary, and we explore the impact of different market factors on the optimal warranty and reliability. Finally, we show that optimal warranties are longer and products more reliable when consumers are risk averse.     

Option pricing in incomplete markets

Expected utility maximization is a very useful approach for pricing options in an incomplete market. The results from this approach contain many important features observed by practitioners. However, under this approach, the option prices are determined by a set of coupled nonlinear partial differential equations in high dimensions. Thus, it represents numerous significant difficulties in both theoretical analysis and numerical computations. In this paper, we present accurate approximate solutions for this set of equations.     

A dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.