Showing papers on "Stackelberg competition published in 1992"

Econometric Analysisof Collusive Behaviorin a Soft‐Drink Market

Abstract: This paper proposes an empirical methodology for studying various (implicit or explicit) collusive behaviors on two strategic variables, which are price and advertising, in a differentiated market dominated by a duopoly. In addition to Nash or Stackelberg behaviors, we consider collusion on both variables, collusion on one variable and competition on the other, etc. Using data on the Coca-Cola and Pepsi-Cola markets from 1968 to 1986, full information maximum likelihood estimation of cost and demand functions are obtained allowing for various collusive behaviors. The collusive hypothesis is not rejected, and the best form of collusive behavior is selected via nonnested testing procedures. Using the best model, Lerner indices are computed for both duopolists to provide summary measures of market power. Finally, our approach is contrasted with the conjectural variation approach and is shown to give superior results.

Hierarchical optimization: an introduction

Abstract: Decision problems involving multiple agents invariably lead to conflict and gaming. In recent years, multi-agent systems have been analyzed using approaches that explicitly assign to each agent a unique objective function and set of decision variables; the system is defined by a set of common constraints that affect all agents. The decisions made by each agent in these approaches affect the decisions made by the others and their objectives. When strategies are selected simultaneously, in a noncooperative manner, solutions are defined as equilibrium points [13,51] so that at optimality no player can do better by unilaterally altering his choice. There are other types of noncooperative decision problems, though, where there is a hierarchical ordering of the agents, and one set has the authority to strongly influence the preferences of the other agents. Such situations are analyzed using a concept known as a Stackelberg strategy [13, 14,46]. The hierarchical optimization problem [11, 16, 23] conceptually extends the open-loop Stackelberg model toK players. In this paper, we provide a brief introduction and survey of recent work in the literature, and summarize the contributions of this volume. It should be noted that the survey is not meant to be exhaustive, but rather to place recent papers in context.

Pollution control: a differential game approach

Abstract: Transnational pollution is formulated as a differential game between two sovereign governments. The symmetric open loop Nash equilibrium is shown to yield more pollution than in a cooperative solution. A model of Stackelberg leadership in pollution control is also investigated. The possibility of limit cycles is illustrated, using bifurcation theory.

The Choice of Environmental Policy Instruments and Strategic International Trade

Abstract: In this paper I examine the question of the choice of environmental policy instruments in the context of a model of strategic international trade between countries, and I show that in such a model there is a preference for the use of standards rather than taxes as policy instruments The paper employs a simple model of two countries who are the sole producers of a commodity sold on the world market Production uses an input which is directly related to the emission of a pollutant, and each country has a fixed target for the emissions level it wishes to achieve If trade is modelled as a one—shot Cournot equilibrium, the countries are indifferent about policy choice If trade is modelled as a Stackelberg equilibrium, then both countries are better off (in terms of producer surplus) if the follower uses standards Finally, if trade is modelled as a two— stage Cournot game in capacity and output then the choice of standards by both countries is a Nash equilibrium, and Pareto dominates the choice of taxes by both countries These results arise from the superior commitment properties of standards

Conflicts and cooperation in managing environmental resources

Abstract: Editor's Introduction.- Editor's Introduction.- 1: International Dimensions.- 1 International Environmental Agreements as Games.- 1. Introduction.- 2. Reaching agreement.- 2.1. Identical countries.- 2.2. Cost differences.- 2.3. Benefit differences.- 2.4. Choice of a benchmark.- 2.5. Summary.- 3. Sustaining agreement.- References.- Comments by Henk Folmer.- 2 Emission Taxes in a Dynamic International Game of CO2 Emissions.- 1. Introduction.- 2. A static game.- 3. A dynamic game.- 4. The open loop equilibrium without taxes.- 5. The Markov perfect equilibrium without taxes.- 6. Other subgame perfect equilibria.- 7. Pigouvian taxes.- 8. Non-commitment and taxation.- References.- Comments by Otto Keck.- 3 Critical Loads and International Environmental Cooperation.- 1. Critical loads.- 2. Naive interpretations.- 3. Stock of pollutants - the case of one country.- 4. Stock of pollutants - several countries and the open loop equilibrium.- 5. Closed loop or feed back equilibria.- References.- Comments by Henry Tulkens.- 4 Environmental Conflicts and Strategic Commitment.- 1. Introduction.- 2. Analytical framework.- 3. Asymmetric players and endogenous strategic timing.- 4. N players and strategic team formation.- 5. Conclusion.- References.- Comments by Detlev Homann.- 5 The Choice of Environmental Policy Instruments and Strategic International Trade.- 1. Introduction.- 2. The model.- 3. Single stage Cournot model.- 4. Two stage Stackelberg model.- 5. Two stage Cournot model.- 6. Conclusions.- References.- Comments by Marji Lines.- 6 Economic Models of Optimal Energy Use under Global Environmental Constraints.- 1: The CO2 Problem in Basic Models of Optimal Use of Fossil Fuels.- 2. Background problem on climatic change and global environmental constraints.- 3. Economic studies on the CO2 problem.- 4. Preliminary definitions and the general model.- 5. A simplified model.- 5.1. Necessary conditions.- 5.2. Sufficient conditions.- 5.3. Definition and optimality of equilibrium.- 5.4. Illustration by a phase plane diagram.- 6. A discrete type impact of CO2 emissions.- 7. Further specification of the model.- 8. Discussion.- 2: Technical Change, International Co-operation, and Structural Uncertainty.- 10. A taxonomy of technical change.- 11. Neutral technical change in a general model.- 12. International co-operation.- 13. Structural uncertainty.- 13.1. Modelling uncertainty about critical CO2 levels as uncertainty about a critical, limited natural resource.- 13.2. Treating structural uncertainty.- 13.3. Numerical calculations.- 14. Conclusions and perspectives.- Appendix A: Existence and Uniqueness of the Optimal Solution.- Appendix B: Existence and Stability of Equilibrium.- References.- Comments by Oskar Von Dem Hagen.- Comments by Cees Withagen.- 2: Monitoring and Enforcement.- 7 Monitoring and Enforcement of Pollution Control Laws in Europe and the United States.- 1. Introduction.- 2. Differences among monitoring and enforcement problems and systems.- 3. Key dimensions of monitoring and enforcement systems.- 3.1. Probability of monitoring.- 3.2. Surprise.- 3.3. Definition of a violation.- 3.4. Penalties and other responses to violations.- 4. Some evidence on European & U.S. choices in monitoring & enforcement.- 5. A glimpse of the future? Recommendations from the U.K. (The "Kinnersley Report").- 6. Concluding comments.- References.- Comments by Heinz Welsch.- 8 The Economics of Negotiations on Water Quality - An Application of Principal Agent Theory.- 1. Introduction.- 2. The basic model structure of a modified LEN-model.- 3. The basic model with a beta-distribution of water quality depending on abatement intensity.- 4. Possible extensions.- References.- Comments by Gunther knieps.- 9 Monitoring the Emission of Pollutants by Means of the Inspector Leadership Method.- 1. Monitoring point sources of pollution.- 2. Decision theoretical formulation of the problem.- 3. Comparison of the solutions of the simple' simultaneous' and 'leadership' games.- 4. The general inspector leadership game and the Neyman -Pearson lemma.- 5. Application.- 6. Concluding remarks.- References.- Comments by Till Requate.- 10 Illegal Pollution and Monitoring of Unknown Quality - A Signaling Game Approach -.- 1. Introduction.- 1: Equilibrium Scenarios with Pooling and Signaling Behavior.- 2. The game model.- 3. A gallery of equilibrium scenarios.- 3.1. Pooled shirking and illegal waste disposal: 'polluter's paradise scenario'.- 3.2. Exploratory accidents and illegal waste disposal due to unqualified control: 'signaling scenarios'.- 3.3. Absence of illegal pollution due to efficient control: 'controller's paradise scenario'.- 3.4. Intermediate illegal pollution: 'constrained polluter's paradise scenario'.- 3.5. Equilibrium scenarios and the multiplicity of equilibria.- 2: Perfect Equilibria and (Unique) Solutions via Equilibrium Selection.- 4. Uniformly perfect pure strategy equilibria.- 5. Comparison of signaling and pooling equilibria.- 5.1. Cell and truncation consistency.- 5.2. Payoff dominance.- 5.3. Risk dominance.- 5.4. Solutions in the range (4.14).- 5.5. The solution in the range (4.15).- 5.6. Discussion of the solution.- 6. Conclusions.- References.- Comments by Aart de Zeeuw.

On Hierarchical Spatial Competition

Abstract: In this paper we consider a hierarchical model of spatial electoral competition with two dominant players (incumbents) and one entrant. The incumbents engage in a non-cooperative game against each other and act as Stackelberg leaders with respect to a vote-maximizing entrant. We prove that the equilibrium of this game, called a hierarchical equilibrium, exists and is unique for an arbitrary single-peaked distribution of voters' ideal points. Moreover, we fully characterize the set of equilibrium strategies and show its equivalence to the set of strategies generated by a perfect-foresight equilibrium. Most of the recently developed models of entry in oligopolistic markets and the theory of political competition deal with the case of dominant firms or parties which face a threat of potential entry. These models possess a number of features on which they may be compared and contrasted. The most important of these features are the ways in which the existing parties or firms compete against each other for votes or profits, and types of expectations the incumbents have about the responses of potential entrants to changes in their decisions. In most of the cases an electoral or oligopolistic competition is represented by some type of a non-cooperative game played by parties or firms. In this paper we also consider a non-cooperative model of electoral race where the established parties (incumbents) compete against each other by offering positions ("ideologies") to the population of voters. Given the profile of voters' preferences over the space of "ideologies" (or, issue space), each of the established parties attempts to maximize its vote share. In making their choices, the incumbents, however, anticipate that a new party (an entrant) will join the electoral race. Consistent with the other parties' objectives, the entrant is assumed to maximize its share of voters while taking the incumbents' choices as given. The resulting non-cooperative game possesses, therefore, a structural hierarchy: the established parties behave as Nash players with respect to each other, whereas acting as Stackelberg leaders with respect to the entrant and correctly anticipating its vote-maximizing response to their choices in the issue space. The main purpose of this paper is to study the properties of the game we described and, in particular, to characterize its equilibrium, which we will call "hierarchical equilibrium". Naturally, some assumptions are needed in order to guarantee the existence of the equilibrium. We assume that there are two established parties, the issue space I is the uni-dimensional interval, all voters have symmetric single peaked-peaked preferences over I and the distribution of the voters' ideal points is represented by a quasi-concave continuous density function. Under these rather mild assumptions, we are able to prove the existence and uniqueness of the hierarchical equilibrium and to completely

A game theoretic perspective to flow control in telecommunication networks

Abstract: Multiple classes of traffic with differing and often conflicting requirements arise in an integrated telecommunications environment as users share the limited existing resources. In this paper, a game theoretic perspective is presented and analysed as the appropriate framework for the study of the flow control problem. Using the notion of power as the performance criterion, we compare a network—Pareto optimal solution—with two user optimal solutions—Nash and Stackelberg equilibria. The appropriateness of each solution is discussed given the operating characteristics of the system. A proposed greedy algorithm is shown to converge to the Nash equilibrium.

Equilibrium Vertical Foreclosure: Reply

Abstract: In Ordover, Saloner, and Salop (1990; hereafter OSS) we showed that a downstream duopolist may have an incentive to backward integrate in order to foreclose its downstream rival from a source of upstream supply. As a result of the vertical integration, the downstream rival's input price increases, giving the integrating firm a competitive advantage in the downstream market. Moreover, in equilibrium, the foreclosed downstream rival does not find it profitable to negate these effects by integrating itself. OSS considers a four-stage game involving two upstream firms, Ul and U2, and two downstream firms, Dl and D2. In the first stage, the downstream firms can bid to acquire Ul. If there is an acquisition, (say, Dl acquires Ul to form F1), upstream input prices are set in the second stage. In the third stage, knowing the input prices it faces, D2 can attempt to acquire U2. Finally, in the fourth stage, Dl and D2 compete 'a la Bertrand with differentiated products. In his comment, David Reiffen (1992) makes three distinct points. First, he notes that once Dl has acquired Ul, the equilibrium of the subsequent subgame depends critically on how upstream prices are set in the second stage. He argues that our results depend on the ability of Fl to commit to a high upstream price. This criticism previously has been made by Oliver Hart and Jean Tirole (1990). We show below that the results in OSS do not depend on the ability of Fl to commit. Instead, our main result stems from the fact that vertical integration changes the firm's incentives to engage in price-cutting in the input market. The notion that vertically integrated firms behave differently from unintegrated ones in supplying inputs to downstream rivals would strike a businessperson, if not an economist, as common sense.1 We show that there is theoretical merit to that common-sense view. Second, Reiffen argues that the game considered by OSS is similar to a game in which there is no vertical integration but, rather, where a nonintegrated Dl has a first-mover advantage in the downstream market. In such a game, Dl benefits from the ability to commit to the price that its "Stackelberg leadership" position gives it. Reiffen considers this to be additional evidence in support of the claim that OSS depends critically on Fl's ability to commit, not on vertical integration. We explain why the mechanism by which Dl is able to raise its profits in the sequential one-shot game considered by Reiffen is conceptually quite different from the mechanism by which Dl profits from vertical integration in OSS. Third, Reiffen argues that our results depend on there being only two upstream firms. This is correct in the symmetric Bertrand model analyzed. However, as we discuss below, our results do obtain as long as the upstream price is decreasing in the number of firms, as occurs in many oligopoly models, particularly when costs vary across firms. The next section summarizes the conceptual problems pertaining to upstream pricing. These problems are resolved in Section II by means of simple and natural price * Ordover: Department of Economics, New York University, 269 Mercer St., 7th Floor, New York, NY 10003; Saloner: Graduate School of Business, Stanford University, Stanford, CA 94305; Salop: Georgetown University Law Center, 600 New Jersey Avenue NW, Washington, DC 20001. We have benefited greatly from several discussions with Faruk Gul. Research support from the National Science Foundation (grant 8813943-IRI), the Sloan Foundation, and the C. V. Starr Center for Applied Economics at NYU is gratefully acknowledged. 'For example, the Japan-U.S. Strategic Impediments Initiative is predicated on the proposition that the loosely linked Japanese firms that form the various keiretsu do discriminate against nonaffiliated firms.

Note on the open-loop von Stackelberg equilibrium in the cartel versus fringe model

Abstract: One of the ways to model the supply side of the world oil market is by means of the cartel versus fringe model and to employ the open-loop von Stackelberg equilibrium concept. This note shows that the equilibrium as presented in the literature does not satisfy the optimality conditions for the open-loop equilibrium. The authors show, furthermore, that in contrast with the prevailing view, the equilibrium can display discontinuous price trajectories. Copyright 1992 by Royal Economic Society.

Supplier-customer interaction in quality control

Abstract: We develop a game theoretic model of joint quality control in a single sourcing environment which integrates supplier and customer decisions. In this model, both parties behave strategically and take each other's incentives into account when deciding on their respective sampling plans. The specific sampling plans considered are of the “single sample fraction defective with rectifying inspection” type. A method to find the optimal sampling plans for both supplier and customer in two different informational setups is constructed. The resulting models lead to examination of Stackelberg and Nash equilibria. Numerical examples of such equilibria are presented, indicating how optimal strategies depend on the parameters of the problem.

Uniqueness results and algorithm for Stackelberg-Cournot-Nash equilibria

Abstract: This paper uses recently developed theory of sensitivity analysis to explore the reaction of a Cournot-Nash equilibrium to a Stackelberg firm, and to analyze the effect of this reaction on the uniqueness of the Stackelberg-Cournot-Nash equilibrium. Some of the results presented are not new, but the methods used provide simpler proofs and a different perspective. More importantly, the methods used here allow the development of new conditions for a unique Stackelberg-Cournot-Nash equilibrium that extends those previously known. The methods used also provide for the development of an efficient algorithm for finding the equilibrium.

Econometric Analysis of Collusive Behavior in a Soft Drink Market

Abstract: This paper proposes an empirical methodology for studying various (implicit or explicit) collusive behaviors on two strategic variables, which are price and advertising, in a differentiated market dominated by a duopoly. In addition to Nash or Stackelberg behaviors, we consider collusion on both variables, collusion on one variable and competition on the other, etc. Using data on the Coca-Cola and Pepsi-Cola markets from 1968 to 1986, full information maximum likelihood estimation of cost and demand functions are obtained allowing for various collusive behaviors. The collusive hypothesis is not rejected, and the best form of collusive behavior is selected via nonnested testing procedures. Using the best model, Lerner indices are computed for both duopolists to provide summary measures of market power. Finally, our approach is contrasted with the conjectural variation approach and is shown to give superior results.

Marketing-production decisions under independent and integrated channel structure

Abstract: The topic of channel structure has recently attracted much attention among researchers in the marketing and economics area. However, in a majority of the existing literature the cost considerations are extremely simplified with the major focus being pricing policy. What happens when cost incurring decisions are strongly connected with pricing policies? This is the theme we wish to explore in the present paper. The non-trivial costs considered are production, inventory, and retailer effort rate, i.e. we seek to explore the marketing-production channel. We have used the methodology of differential games. The open-loop Stackelberg solution concept has been used to solve the manufacturer and retailer's problem. The Pareto solution concept has been used to solve the problem of the vertically integrated firm. The production, pricing, and effort rate policies thus derived have been compared to obtain insights into the impact of channel structure on these policies. Also, to examine the relation between channel structure and the retailing operation requiring effort, we derive the Stackelberg and Pareto solutions with and without effort rate as a decision variable. We show that once the production rate becomes positive, it does not become zero again. This implies production smoothing. However, none of the gains of production smoothing are passed on to the retailer. The optimal production rate and the inventory policy are a linear combination of the nominal demand rate, the peak demand factor, the salvage value, and the initial inventory. Also, as opposed to some of the existing literature, the optimal policies need not necessarily be concave in nature. In the scenario where the relating operation does not require effort, the pricing policies of the manufacturer and the retailer, and the production policy of the manufacturer have a synergistic effect. However, in the scenario where the retailing operation does benefit from effort, the retailer's pricing policy need not necessarily be synergistic with other policies. With regard to channel structures, it seems that production smoothing will be done more efficiently in the integrated setup. Also, we show that the price paid by the consumer need not necessarily be lower in the integrated setup. But despite higher prices, the channel profits are higher in the integrated setup. This implies a conflict between the interests of the consumers and the firm. Also, this contradicts the results of some of the earlier papers that have used simple static models.

Network facility-location models in Stackelberg-Nash-Cournot spatial competition

Abstract: A hierarchical mathematical programming approach is combined with sensitivity analysis (of variational inequalities) to formulate a facility-location model for a firm competing on a discrete network. It is assumed that the locating firm will act as the leader firm in an industry characterized by Stackelberg leader-follower(s) oligopolistic competition. The othern competitors in this industry are assumed to act as Cournot firms that each operate under the Cournot assumption of zero conjectural variation with respect to theirn — 1 Cournot competitors. It is further assumed that then Cournot firms will react to the location/production/shipping activities of the Stackelberg firm. Therefore, when the Stackelberg firm makes its location, production, and shipping decisions it takes into account the reaction of then Cournot firms to its (the Stackelberg firm's) integrated location and distribution decisions. Specifically, a Cournot reaction function is developed and imbedded in the Stackelberg firm's profit-maximizing objective function to project the anticipated reaction of the Cournot firms to the Stackelberg firm's location decision.

Closed-loop Stackelberg strategies for linear-quadratic descriptor systems

Abstract: In this paper, we investigate the linear-quadratic closed-loop Stackelberg game for the descriptor system. It is different from the Stackelberg game in the state-space system in that there may exist a descriptor variable feedback closed-loop incentive strategy in the Stackelberg game for the descriptor system. Sufficient conditions for the existence of such an incentive strategy are derived for both the finite-time and infinite-time cases. In addition, since there are two different decision makers in the Stackelberg games, it is not logical to assume that these different decision makers adopt the same reduced-order transformation to deal with their problems. We show that, if the system considered by the follower has index one, which can be guaranteed by the leader's incentive strategy, then the fact that the two decision makers adopt different reduced-order transformations does not affect the solution of the problem.

Crowding levels and fare classes in public transport

Abstract: This paper investigates the correlation between crowding levels and fare classes on the railways. The study is restricted to fare class systems where there is no perceived difference between fare classes except for crowding levels. A two stage model is used. In the first stage, public transport management decides on a price and a capacity for each fare class. In the second stage, passengers decide which class they will use, anticipating each other's choices and therefore the crowding levels. This results in a Nash equilibrium: given the choice of all other passengers, no passenger can improve his lot by moving to another class. Public transport management acts as a Stackelberg leader since it can determine which Nash equilibrium will occur through its choice of prices and capacities. The model was used to simulate a situation with two types of passenger (rich and poor). In this situation quantitatively different crowding equilibria occur depending on the proportion of the population that is poor. The welfare implications of operating a two class system are discussed and compared to those of operating a one fare class system. It was found that whether a two class system is better from a welfare point of view than the one class system depends upon the percentage of the population that is poor. For the covering abstract of the conference see IRRD 851540.

Endogenous Stackelberg Leadership when Costs are Private Information

Abstract: Lately several authors have tried to explain the emergence of Stackelberg leadership as an endogenous feature of duopoly models. This article describes two models where assumptions of incomplete information about the rival firm’s marginal cost of production creates incentives for duopolistic firms to end up in a sequential choice situation. In the first model the duopolists can commit themselves to be a Stackelberg leader or follower at the time when they know the distributions, but not the actual values, of their own and the rival’s cost. The central result from this model is that under quantity (but not price) competition the duopolists may agree on who should be the leader and who should be the follower. In the second model the firms cannot commit to a specific role. In the quantity setting version of this model they must decide both when and how much to produce. It turns out that there can never be an equilibrium where they both always produce in the same period. However, there are equilibria where one firm produces in the first period and the other in the second, i.e. Stackelberg-type equilibria. Similar results are found in a price setting version of the model.

The Open-Loop von Stackelberg Equilibrium in the Cartel Versus Fringe Model: A Reply

Abstract: In some cases, the open-loop Stackelberg equilibrium for an oil cartel facing a competitive fringe can be constructed from simple principles, but these fail if the cartel supplies both before and after the fringe as reallocations between these two phases relocate the entire fringe price path. In such cases, the price path need not be continuous and downward jumps are possible and cannot be arbitraged away. Upward jumps can only be arbitraged if competitive agents can store oil at low cost. Such equilibria are dynamically inconsistent. Copyright 1992 by Royal Economic Society.

Asynchrony and Learning in Serial and Average Cost Pricing Mechanisms: An Experimental Study

Abstract: This paper reports the first experimental study of the serial and the average cost pricing mechanism under three different treatments: a complete information treatment and two treatments designed to simulate distributed systems like the Internet with extremely limited information, synchronous and asynchronous moves. Although both games are dominance-solvable and the proportion of equilibrium play is statistically indistinguishable under complete information, their performance does change dramatically in settings that resemble distributed systems: the serial mechanism performs robustly better than the average cost pricing mechanism both in terms of convergence to Nash/Stackelberg equilibrium and system efficiency. These results provide some support for Friedman and Shenker's (1997) new solution concepts for implementation on the Internet. Four payoff-based learning models are simulated in order to understand individual learning behavior in distributed systems. Under the serial mechanism the payoff-assessment learning model (Sarin and Vahid (1997)) provides the best fit to the data, followed by the experience-weighted attraction learning model (Camerer and Ho (1999)), which in turn, is followed by a simple reinforcement learning model and the responsive learning automata. Under the average cost pricing mechanism, both the experience-weighted attraction learning model and the reinforcement model track the data better than the responsive learning automata, however, other pair-wise rankings of the four models are statistically insignificant.

The discrete-time model of Bagchi's regional investment allocation problem

Abstract: The paper deals with the discrete-time version of Bagchi's regional investment allocation model as a two-level Stackelberg game where a leader is the central planning board and followers are regional authorities. Each regional saving rate is determined by a discrete maximum principle under inequality constraints, maximizing its intertemporal utility function, given a tax rate and an allocation parameter. On the other hand, the central planning board will select the allocation parameter, without disturbing the reaction function of each region, so as to minimize the difference between regional capital stocks per capita and to maximize total capital stocks as a whole in the final period. Relations among capital and co-state variables are analyzed in phase diagrams, and numerical examples provide feasible series of optimum solutions for both Cobb-Douglas and CES production function cases.