Showing papers on "Stackelberg competition published in 2006"

Boiling Frogs: Pricing Strategies for a Manufacturer Adding a Direct Channel that Competes with the Traditional Channel

Abstract: We analyze a scenario where a manufacturer with a traditional channel partner opens up a direct channel in competition with the traditional channel. We first consider that in order to mitigate channel conflict the manufacturer, who chooses wholesale prices as a Stackelberg leader, commits to setting a direct channel retail price that matches the retailer’s price in the traditional channel. We find that the specific equal-pricing strategy that optimizes profits for the manufacturer is also preferred by the retailer and customers over other equal-pricing strategies. We next consider the implications of the equal-pricing constraint through a numerical experiment that indicates that the equal-pricing strategy is appropriate as long as the Internet channel is significantly less convenient than the traditional channel. If the Internet channel is of comparable convenience to the traditional channel, then the manufacturer has tremendous incentive to abandon the equal-pricing policy, at great peril to the traditional retailer.

Computing the optimal strategy to commit to

Abstract: In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models are synonymously referred to as leadership, commitment, or Stackelberg models, and optimal play in such models is often significantly different from optimal play in the model where strategies are selected simultaneously.The recent surge in interest in computing game-theoretic solutions has so far ignored leadership models (with the exception of the interest in mechanism design, where the designer is implicitly in a leadership position). In this paper, we study how to compute optimal strategies to commit to under both commitment to pure strategies and commitment to mixed strategies, in both normal-form and Bayesian games. We give both positive results (efficient algorithms) and negative results (NP-hardness results).

Self-enforcing international environmental agreements revisited

Abstract: In Barrett's (1994) paper on transboundary pollution abatement is shown that if the signatories of an international environmental agreement act in a Stackelberg fashion, then, depending on parameter values, a self-enforcing IEA can have any number of signatories between two and the grand coalition. Barrett obtains this result using numerical simulations and also ignoring the fact that emissions must be non-negative. Recent attempts to use analytical approaches and to explicitly recognize the non-negativity constraints have suggested that the number of signatories of a stable IEA may be very small. The way such papers have dealt with non-negativity constraints is to restrict parameter values to ensure interior solutions for emissions. We argue that a more appropriate approach is to use Kuhn-Tucker conditions to derive the equilibrium of the emissions game. When this is done we show, analytically, that the key results from Barrett's paper go through. Finally, we explain why his main conclusion is correct although his analysis can implicitly imply negative emissions.

Leader-Follower Equilibria for Electric Power and NO x Allowances Markets

Abstract: This paper investigates the ability of the largest producer in an electricity market to manipulate both the electricity and emission allowances markets to its advantage. A Stackelberg game to analyze this situation is constructed in which the largest firm plays the role of the leader, while the medium-sized firms are treated as Cournot followers with price-taking fringes that behave competitively in both markets. Since there is no explicit representation of the best-reply function for each follower, this Stackelberg game is formulated as a large-scale mathematical program with equilibrium constraints. The best-reply functions are implicitly represented by a set of nonlinear complementarity conditions. Analysis of the computed solution for the Pennsylvania–New Jersey–Maryland electricity market shows that the leader can gain substantial profits by withholding allowances and driving up NO x allowance costs for rival producers. The allowances price is higher than the corresponding price in the Nash–Cournot case, although the electricity prices are essentially the same.

The role of 4PL as the reverse logistics integrator

Abstract: Purpose – An effective return policy is used as an important competitive weapon in the marketplace to substantially influence product sales. However, return policy is also seen as a problem for all parties in the supply chain due to the headache in processing returned merchandise. While retailers are efficient in selling, they do not usually have the expertise in handling the reverse flow. The purpose of this paper is to propose the use of a fourth party logistics (4PL) as a return service provider, and develops optimal decision policies for both the seller and the 4PL.Design/methodology/approach – A profit‐maximization model is presented to jointly obtain optimal policies for the seller and the 4PL through the use of Stackelberg like game theory, where the seller acts as the leader and the 4PL acts as the follower.Findings – Optimal values for the seller's and the 4PL's decisions are presented. Conditions under which profits for the seller and 4PL both increase are shown.Practical implications – This pap...

Price and Capacity Competition

Abstract: We study the efficiency of oligopoly equilibria in a model where firms compete over capacities and prices. The motivating example is a communication network where service providers invest in capacities and then compete in prices. Our model economy corresponds to a two-stage game. First, firms (service providers) independently choose their capacity levels. Second, after the capacity levels are observed, they set prices. Given the capacities and prices, users (consumers) allocate their demands across the firms. We first establish the existence of pure strategy subgame perfect equilibria (oligopoly equilibria) and characterize the set of equilibria. These equilibria feature pure strategies along the equilibrium path, but off-the-equilibrium path they are supported by mixed strategies. We then investigate the efficiency properties of these equilibria, where "efficiency" is defined as the ratio of surplus in equilibrium relative to the first best. We show that efficiency in the worst oligopoly equilibria of this game can be arbitrarily low. However, if the best oligopoly equilibrium is selected (among multiple equilibria), the worst-case efficiency loss has a tight bound, approximately equal to 5/6 with 2 firms. This bound monotonically decreases towards zero when the number of firms increases. We also suggest a simple way of implementing the best oligopoly equilibrium. With two firms, this involves the lower-cost firm acting as a Stackelberg leader and choosing its capacity first. We show that in this Stackelberg game form, there exists a unique equilibrium corresponding to the best oligopoly equilibrium. We also show that an alternative game form where capacities and prices are chosen simultaneously always fails to have a pure strategy equilibrium. These results suggest that the timing of capacity and price choices in oligopolistic environments is important both for the existence of equilibrium and for the extent of efficiency losses in equilibrium.

One-Way Essential Complements

Abstract: While competition between firms producing substitutes is well understood, less is known about rivalry between complementors. We study the interaction between firms in markets with one-way essential complements. One good is essential to the use of the other but not vice versa, as arises with an operating system and applications. Our interest is in the division of surplus between the two goods and the related incentive for firms to create complements to an essential good. Formally, we study a two-good model where consumers value A alone, but can only enjoy B if they also purchase A. When one firm sells A and another sells B, the firm that sells B earns a majority of the value it creates. However, if the A firm were to buy the B firm, it would optimaly charge zero for B, provided marginal costs are zero and the average value of B is small relative to A. Hence, absent strong antitrust or intellectual property protections, the A firm can leverage its monopoly into B costlessly by producing a competing version of B and giving it away. For example, Microsoft provided Internet Explorer as a free substitute for Netscape; in our model, this maximizes Microsoft's joint monopoly profits. Furthermore, Microsoft has no incentive to raise prices, even if al browser competition exits. This may seem surprising since it runs counter to the traditional gains from price discrimination and versioning. We also show that an essential monopolist has no incentive to degrade rival complementary products, which suggests that a monopoly internet service provider will offer net neutrality. There are other means for the essential A monopolist to capture surplus from B. We consider the incentive to add a surcharge (or subsidy) to the price of B, or to act as a Stackelberg leader. We find a small gain from pricing first, but much greater profits from adding a surcharge to the price of B. The potential for A to capture B's surplus highlights the challenges facing a firm whose product depends on an essential good.

Competition and Diversification Effects in Supply Chains with Supplier Default Risk

Abstract: We study the effects of disruption risk in a supply chain where one retailer deals with competing risky suppliers who may default during their production lead-times. The suppliers, who compete for business with the retailer by establishing wholesale prices, are leaders in a Stackelberg game with the retailer. The retailer, facing uncertain future demand, chooses order quantities while weighing the benefits of procuring from the cheapest supplier against the advantages of order diversification. For the model with two suppliers we show that low supplier default correlations dampens competition among the suppliers, increasing the equilibrium wholesale prices. Therefore, the retailer prefers suppliers with highly correlated default events, despite the loss of diversification benefits. In contrast, the suppliers and the channel prefer defaults that are negatively correlated. However, as the number of suppliers increases our model predicts that the retailer may be able to take advantage of both competition and diversification.

A note on Cooperative advertising, game theory and manufacturer-retailer supply chains

Abstract: This note extends the results in the manufacturer-dominated game model of the paper by Li et al. (Omega 30 (2002) 347) to the case where the manufacturer’s marginal profit is not large enough. In such situations, the profit of the entire supply chain under the co-op advertising mode is higher than the one under the Stackelberg game, which is consistent with the results of the original paper. However, the advertising expenditures of the manufacturer and the retailer under the co-op advertising model are not always larger than those under the Stackelberg game, which is different from the results of the original paper. Furthermore, the results are also compared with the simultaneous move game of the paper by Huang and Li (Eur. J. Oper. Res. 135 (2001) 527). The manufacturer always prefers the leader–follower structure rather than the simultaneous move structure, which is consistent with the results of the original paper. However, the retailer always prefers the simultaneous move structure rather than the leader–follower structure, which differs from the results of the original paper. 2005 Elsevier Ltd. All rights reserved.

Endogenous Timing in Duopoly: Experimental Evidence

Abstract: In this paper we experimentally investigate Cournot duopolies with an extended timing game. The timing game has observable delay, that is, firms announce a production period (one out of two periods) and then they produce in the announced sequence. Theory predicts simultaneous production in the first period. With random matching we find that, given the actual experimental behavior in the subgames, subjects play a timing game more akin to a coordina- tion game with two symmetric equilibria rather than the predicted game with a dominant strategy to produce early. As a result, a substantial proportion of subjects choose the second period.

The Impact of Manufacturers' Wholesale Prices on a Retailer's Shelf-Space and Pricing Decisions ∗

Abstract: This article examines shelf-space allocation and pricing decisions in the marketing chan- nel as the results of a static game playedla Stackelberg between two manufacturers of competing brands and one retailer. The competing manufacturers act as leaders that play a simultaneous and noncooperative game. They fix their transfer prices by taking into account the shelf-space allocation and price-markup decisions of their common exclusive dealer. The results indicate that the wholesale prices of brands are strongly linked to their share of the shelf. The main results of our numerical simulations may be summarized as follows: first, the lower the unit cost and/or the greater the price elasticity, the greater the shelf space allocated to that brand. Second, the higher the shelf-space elasticity, the lower are the wholesale prices and the profits of all channel members.

On Coincidence of Feedback Nash Equilibria and Stackelberg Equilibria in Economic Applications of Differential Games

Abstract: The scope of the applicability of the feedback Stackelberg equilibrium concept in differential games is investigated. First, conditions for obtaining the coincidence between the stationary feedback Nash equilibrium and the stationary feedback Stackelberg equilibrium are given in terms of the instantaneous payoff functions of the players and the state equations of the game. Second, a class of differential games representing the underlying structure of a good number of economic applications of differential games is defined; for this class of differential games, it is shown that the stationary feedback Stackelberg equilibrium coincides with the stationary feedback Nash equilibrium. The conclusion is that the feedback Stackelberg solution is generally not useful to investigate leadership in the framework of a differential game, at least for a good number of economic applications

Leader–follower game in vendor-managed inventory system with limited production capacity considering wholesale and retail prices

Abstract: Vendor-managed inventory (VMI) is a widely used co-operative inventory policy in supply chains in which each enterprise has its autonomy in pricing. In this paper, a leader–follower Stackelberg game in a VMI supply chain is discussed where the manufacturer, as a leader, produces a single product with a limited production capacity and delivers it at a wholesale price to multiple different retailers, as the followers, who then sell the product in dispersed and independent markets at retail prices. An algorithm is then developed to determine the equilibrium of the Stackelberg game. Finally, a numerical study is conducted to understand the influence of the Stackelberg equilibrium and market-related parameters on the profits of the manufacturer and its retailers. Through a numerical example, our research demonstrates that: (a) the market-related parameters have significant influence on the manufacturer's and its retailers' profits; (b) a retailer's profit may not necessarily be lowered when it is charged with ...

A Note on Feedback Sequential Equilibria in a Lanchester Model with Empirical Application

Abstract: We study in this paper dynamic equilibrium advertising strategies in a duopoly with asymmetric information structure and sequential play. The advertising model of Lanchester is used in a game where the relevant solution concept is feedback Stackelberg equilibrium, which is subgame perfect. An algorithm is devised for the computation of this equilibrium, and numerical results are reported and discussed. Using a data set from the cola market, we obtain the resulting advertising strategies and provide a comparison with closed-loop and open-loop Nash equilibria.

One-Way Essential Complements

Abstract: While competition between firms producing substitutes is well understood, less is known about rivalry between complementors. We study the interaction between firms in markets with one-way essential complements. One good is essential to the use of the other but not vice versa, as arises with an operating system and applications. Our interest is in the division of surplus between the two goods and the related incentive for firms to create complements to an essential good. Formally, we study a two-good model where consumers value A alone, but can only enjoy B if they also purchase A. When one firm sells A and another sells B, the firm that sells B earns a majority of the value it creates. However, if the A firm were to buy the B firm, it would optimally charge zero for B, provided marginal costs are zero and the average value of B is small relative to A. Hence, absent strong antitrust or intellectual property protections, the A firm can leverage its monopoly into B costlessly by producing a competing version of B and giving it away. For example, Microsoft provided Internet Explorer as a free substitute for Netscape; in our model, this maximizes Microsoft's joint monopoly profits. Furthermore, Microsoft has no incentive to raise prices, even if all browser competition exits. This may seem surprising since it runs counter to the traditional gains from price discrimination and versioning. We also show that a essential monopolist has no incentive to degrade rival complementary products, which suggests that a monopoly internet service provider will offer net neutrality. There are other means for the essential A monopolist to capture surplus from B. We consider the incentive to add a surcharge (or subsidy) to the price of B, or to act as a Stackelberg leader. We find a small gain from pricing first, but much greater profits from adding a surcharge to the price of B. The potential for A to capture B's surplus highlights the challenges facing a firm whose product depends on an essential good.

WLC41-4: Stackelberg Game for Distributed Resource Allocation over Multiuser Cooperative Communication Networks

Abstract: In this paper, we propose a Stackelberg game theoretic framework for distributive resource allocation over multiuser cooperative communication networks to improve the system performance and stimulate cooperation. Two questions of who should relay and how much power for relaying are answered, by employing a two-level game to jointly consider the benefits of source nodes as buyers and relay nodes as sellers in cooperative communication. From the derived results, the proposed game not only helps the source smartly find relays at relatively better locations but also helps the competing relays ask reasonable prices to maximize their own utilities. From the simulation results, the relays in good locations or good channel conditions can play more important roles in increasing source node's utility, so the source would like to buy power from these preferred relays. On the other hand, because of competition from other relays and selections from the source, the relays have to set proper prices to attract the source's buying so as to optimize their utility values.

The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions

Abstract: Let M be a single s-t network of parallel links with load dependent latency functions shared by an infinite number of selfish users. This may yield a Nash equilibrium with unbounded Coordination Ratio [12, 26]. A Leader can decrease the coordination ratio by assigning flow αr on M, and then all Followers assign selfishly the (1 - α)r remaining flow. This is a Stackelberg Scheduling Instance (M,r,α), 0 ≤ α ≤ 1. It was shown [23] that it is weakly NP-hard to compute the optimal Leader's strategy.For any such network M we efficiently compute the minimum portion βM of flow r needed by a Leader to induce M's optimum cost, as well as his optimal strategy.Unfortunately, Stackelberg routing in more general nets can be arbitrarily hard. Roughgarden presented a modification of Braess's Paradox graph, such that no strategy controlling αr flow can induce ≤ 1α times the optimum cost. However, we show that our main result also applies to any s-t net G. We take care of the Braess's graph explicitly, as a convincing example.

The Value of Commitment in Stackelberg Games with Observation Costs

Abstract: We study Stackelberg games in which the follower faces a cost for observing the leader's action. We show that, irrespective of the size of the cost, the leader's value of commitment is lost completely in all pure-strategy equilibria. However, there also exists a mixed-strategy equilibrium that fully preserves the first-mover advantage. In this type of equilibrium, the probability that the follower looks at the leader's action is independent of the cost of looking.

Incentives for Retailer Promotion in a Marketing Channel

Abstract: This chapter analyzes a differential game model of a two-member marketing channel. A manufacturer invests in national advertising with the purpose of improving (or sustaining) the image of one of her brands, and her retailer makes local promotions for the brand. The game is played a la Stackelberg with the manufacturer as leader. We characterize and compare equilibria for two scenarios. In the first one, the manufacturer designs an incentive strategy to affect the retailer’s promotion strategy with the objective of maximizing the total channel profit. In the second, the manufacturer’s objective is the maximization of her own payoff.

Determining the Desired Amount of Parking Using Game Theory

Abstract: The problem of seeking an optimal parking policy is formulated here as a Stackelberg game between the government and the travelers. The government wishes to encourage transit ridership while keeping a strong urban center; unlike most existing tools that assist in determining parking policies, the proposed game includes an explicit quantitative formulation of the governmental objective. Each traveler wishes to gain a maximum utility from his choice of destination and transportation mode, and the choice distribution of all travelers is obtained by Logit model. A fundamental difference exists between Game Theory practice and common assumptions used in transportation modeling regarding the relationship between a single traveler’s utility and the choice distribution of all travelers. This difference is tackled here through the definition of the player that represents the travelers and its objective function. A simple version of the game is tested in 24 imaginary scenarios of transportation and urban conditions.

Cooperative advertising in a dual channel supply chain

Abstract: The focus of this study is cooperative (co-op) advertising and the impact it has on the dual channel supply chain. We obtain equilibrium pricing and co-op advertising policies under two different competitive scenarios: Bertrand and Stackelberg equilibrium. We also compare the profit gains under these two marketing games. Based on our results, we propose the optimal strategies that system members should adopt in a dual channel competition. We also illustrate that by strategically implementing a cooperative advertising strategy under different market structures, both the system players can effectively improve their overall profits in a dual channel supply chain management.

Sequential Formation of Coalitions Through Bilateral Agreements in a Cournot Setting

Abstract: We study a sequential protocol of endogenous coalition formation based on a process of bilateral agreements among the players. We apply the game to a Cournot environment with linear demand and constant average costs. We show that the final outcome of any subgame perfect equilibrium of the game is the grand coalition, provided the initial number of firms is high enough and they are sufficiently patient.

Price and Capacity Competition

Abstract: We study the efficiency of oligopoly equilibria in a model where firms compete over capacities and prices. The motivating example is a communication network where service providers invest in capacities and then compete in prices. Our model economy corresponds to a two-stage game. First, firms (service providers) independently choose their capacity levels. Second, after the capacity levels are observed, they set prices. Given the capacities and prices, users (consumers) allocate their demands across the firms. We first establish the existence of pure strategy subgame perfect equilibria (oligopoly equilibria) and characterize the set of equilibria. These equilibria feature pure strategies along the equilibrium path, but off-the-equilibrium path they are supported by mixed strategies. We then investigate the efficiency properties of these equilibria, where efficiency is defined as the ratio of surplus in equilibrium relative to the first best. We show that efficiency in the worst oligopoly equilibria of this game can be arbitrarily low. However, if the best oligopoly equilibrium is selected (among multiple equilibria), the worst-case efficiency loss has a tight bound, approximately equal to 5/6 with 2 firms. This bound monotonically decreases towards zero when the number of firms increases. We also suggest a simple way of implementing the best oligopoly equilibrium. With two firms, this involves the lower-cost firm acting as a Stackelberg leader and choosing its capacity first. We show that in this Stackelberg game form, there exists a unique equilibrium corresponding to the best oligopoly equilibrium. We also show that an alternative game form where capacities and prices are chosen simultaneously always fails to have a pure strategy equilibrium. These results suggest that the timing of capacity and price choices in oligopolistic environments is important both for the existence of equilibrium and for the extent of efficiency losses in equilibrium.

Allowing for Two Production Periods in the Cournot Duopoly: Experimental Evidence

Abstract: In this study behavior in a Cournot duopoly with two production periods (the market clears only after the second period) is compared to behavior in a standard one-period Cournot duopoly. Theory predicts the endogenous emergence of a Stackelberg outcome in the two-period market. The results of the experiments, however, reveal that in both markets (roughly) symmetric outcomes emerge and that, after a short adaptation phase, average industry output in the two-period markets is the same as in the standard one-period markets.