Showing papers on "Stackelberg competition published in 2007"
TL;DR: It is shown that low supplier default correlations dampen competition among the suppliers, increasing the equilibrium wholesale prices, and the retailer prefers suppliers with highly correlated default events, despite the loss of diversification benefits.
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 setting 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 dampen 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.
391 citations
TL;DR: This paper studies a decentralized supply chain consisting of a supplier and a retailer facing price-and lead-time-sensitive demands and shows that before pursuing a coordination strategy with retailers, a supplier should first improve his or her own internal operations.
Abstract: This paper studies a decentralized supply chain consisting of a supplier and a retailer facing price-and lead-time-sensitive demands. A Stackelberg game is constructed to analyze the price and lead time decisions by the supplier as the leader and the retailer as the follower. The equilibrium strategies of the two players are obtained. Using the performance of the corresponding centralized system as a benchmark, we show that decentralized decisions in general are inefficient and lead to inferior performance due to the double marginalization effect. However, further analysis shows that the decision inefficiency is strongly influenced by market and operational factors, and if the operational factors are dominating, it may not be significant. This shows that before pursuing a coordination strategy with retailers, a supplier should first improve his or her own internal operations.
175 citations
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TL;DR: In this article, a unified analysis of the theoretical results on internalization of airport congestion can be found within a simple and unified framework, and the analysis is validated by the results of Brueckner and Daniel.
Abstract: The goal of this paper is to bring some unity to the theoretical side of the debate on internalization of airport congestion by showing that all the literature's theoretical results can be derived within one simple and unified framework. The analysis starts by replicating the results of Brueckner (2002), who showed that, because airlines behaving in Cournot fashion internalize congestion, they should be charged low congestion tolls. The analysis then validates the findings of Daniel (1995), who argued that larger atomistic tolls are required in a model where a Stackelberg leader interacts with competitive fringe airlines. However, it is shown that this result only holds approximately when the carriers' outputs are imperfect substitutes.
166 citations
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TL;DR: It is proved that the optimal performance of the decentralized channel for distribution-free buyback contracts depends only on the curvature of the deterministic demand part.
Abstract: This paper studies a buyback contract in the Stackelberg framework of a manufacturer (leader) selling to a price-setting, newsvendor retailer (follower). Using an analytical model that focuses on a multiplicative demand form, we generalize previous results and produce new structural insights. A novel transformation technique first enables us to establish the unimodality of the profit functions for both channel partners, under relatively mild assumptions. Further analysis identifies the necessary and su±cient condition under which the optimal contract for the manufacturer (wholesale and buyback prices) is distribution-free, i.e., independent of the uncertainty in customer demand. A specific instance of the above condition is also necessary and su±cient for a no-buyback contract to be optimal from the manufacturer's perspective. We then prove that the optimal performance of the decentralized channel for distribution-free buyback contracts depends only on the curvature of the deterministic demand part. In addition, some of the optimal decisions and relevant profit ratios for buyback contracts in our setting are shown to be identical to those for their deterministic price-only counterparts.
140 citations
22 Oct 2007
TL;DR: A game theoretical approach is suggested that allows master-slave cognitive radio pairs to update their transmission powers and frequencies simultaneously and a modification to the exact potential game discussed earlier that would allow a Stackelberg leader to charge a virtual price for communicating over a licensed channel is suggested.
Abstract: The ongoing growth in wireless communication continues to increase demand on the frequency spectrum. The current rigid frequency band allocation policy leads to a significant under-utilization of this scarce resource. However, recent policy changes by the Federal Communications Commission (FCC) and research directions suggested by the Defense Advanced Research Projects Agency (DARPA) have been focusing on wireless devices that can adaptively and intelligently adjust their transmission characteristics, which are known as cognitive radios. This paper suggests a game theoretical approach that allows master-slave cognitive radio pairs to update their transmission powers and frequencies simultaneously. This is shown to lead to an exact potential game, for which it is known that a particular update scheme converges to a Nash Equilibrium (NE). Next, a Stackelberg game model is presented for frequency bands where a licensed user has priority over opportunistic cognitive radios. We suggest a modification to the exact potential game discussed earlier that would allow a Stackelberg leader to charge a virtual price for communicating over a licensed channel. We investigate virtual price update algorithms for the leader and prove the convergence of a specific algorithm. Simulations performed in Matlab verify our convergence results and demonstrate the performance gains over alternative algorithms.
130 citations
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TL;DR: Stackelberg differential game models have been used to study sequential decision making in non-cooperative games in diverse fields as mentioned in this paper, where a common feature of these applications is the specification of the game structure: a decentralized channel composed of a manufacturer and independent retailers, and a sequential decision procedure with demand and supply dynamics.
Abstract: Stackelberg differential game models have been used to study sequential decision making in non-cooperative games in diverse fields. In this paper, we survey recent applications of Stackelberg differential game models to the supply chain management and marketing channels literatures. A common feature of these applications is the specification of the game structure: a decentralized channel composed of a manufacturer and independent retailers, and a sequential decision procedure with demand and supply dynamics and coordination issues. In supply chain management, Stackelberg differential games have been used to investigate inventory issues, wholesale and retail pricing strategies, and outsourcing in dynamic environments. The underlying demand typically has growth dynamics or seasonal variation. In marketing, Stackelberg differential games have been used to model cooperative advertising programs, store brand and national brand advertising strategies, shelf space allocation, and pricing and advertising decisions. The demand dynamics are usually extensions of the classical advertising capital models or sales-advertising response models. We begin by explaining the Stackelberg differential game solution methodology and then provide a description of the models and results reported in the literature.
128 citations
TL;DR: Stackelberg differential game models have been used to study sequential decision making in non-cooperative games in diverse fields as discussed by the authors, where a common feature of these applications is the specification of the game structure: a decentralized channel composed of a manufacturer and independent retailers.
Abstract: Stackelberg differential game models have been used to study sequential decision making in noncooperative games in diverse fields. In this paper, we survey recent applications of Stackelberg differential game models to the supply chain management and marketing channels literatures. A common feature of these applications is the specification of the game structure: a decentralized channel composed of a manufacturer and independent retailers, and a sequential decision procedure with demand and supply dynamics and coordination issues. In supply chain management, Stackelberg differential games have been used to investigate inventory issues, wholesale and retail pricing strategies, and outsourcing in dynamic environments. The underlying demand typically has growth dynamics or seasonal variation. In marketing, Stackelberg differential games have been used to model cooperative advertising programs, store brand and national brand advertising strategies, shelf space allocation, and pricing and advertising decisions. The demand dynamics are usually extensions of the classical advertising capital models or sales-advertising response models. We begin by explaining the Stackelberg differential game solution methodology and then provide a description of the models and results reported in the literature.
128 citations
07 Jan 2007
TL;DR: It is shown that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program.
Abstract: It is well known that in a network with arbitrary (convex) latency functions that are a function of edge traffic, the worst-case ratio, over all inputs, of the system delay caused due to selfish behavior versus the system delay of the optimal centralized solution may be unbounded even if the system consists of only two parallel links. This ratio is called the price of anarchy (PoA). In this paper, we investigate ways by which one can reduce the performance degradation due to selfish behavior. We investigate two primary methods (a) Stackelberg routing strategies, where a central authority, e.g., network manager, controls a fixed fraction of the flow, and can route this flow in any desired way so as to influence the flow of selfish users; and (b) network tolls, where tolls are imposed on the edges to modify the latencies of the edges, and thereby influence the induced Nash equilibrium. We obtain results demonstrating the effectiveness of both Stackelberg strategies and tolls in controlling the price of anarchy.For Stackelberg strategies, we obtain the first results for nonatomic routing in graphs more general than parallel-link graphs, and strengthen existing results for parallel-link graphs, (i) In series-parallel graphs, we show that Stackelberg routing reduces the PoA to a constant (depending on the fraction of flow controlled). (ii) For general graphs, we obtain latency-class specific bounds on the PoA with Stackelberg routing, which give a continuous trade-off between the fraction of flow controlled and the price of anarchy, (iii) In parallel-link graphs, we show that for any given class L of latency functions, Stackelberg routing reduces the PoA to at most α + (1 - α) · ρ(L), where α is the fraction of flow controlled and ρ(L) is the PoA of class L (when α = 0).For network tolls, motivated by the known strong results for nonatomic games, we consider the more general setting of atomic splittable routing games. We show that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program. Furthermore, we give a complete characterization of flows that can be induced via tolls. These are the first results on the effectiveness of tolls for atomic splittable games.
114 citations
TL;DR: The results suggest that the allocation of the shelf space depends on the quality of the private label, and the resulting Stackelberg equilibrium in terms of the amount of shelf space allocated to these brands as well as their prices.
112 citations
TL;DR: In this article, the Stackelberg game of network flow routing is formulated as a mathematical program with equilibrium constraints (MPEC), which is transformed into an equivalent, continuously differentiable single-level optimization problem, where the lower level VI is represented by a differentiable gap function constraint.
Abstract: The classical Wardropian principle assumes that users minimize either individual travel cost or overall system cost. Unlike the pure Wardropian equilibrium, there might be in reality both competition and cooperation among users, typically when there exist oligopoly Cournot-Nash (CN) firms. In this paper, we first formulate a mixed behavior network equilibrium model as variational inequalities (VI) that simultaneously describe the routing behaviors of user equilibrium (UE), system optimum (SO) and CN players, each player is presumed to make routing decision given knowledge of the routing strategies of other players. After examining the existence and uniqueness of solutions, the diagonalization approach is applied to find a mixed behavior equilibrium solution. We then present a Stackelberg routing game on the network in which the SO player is the leader and the UE and CN players are the followers. The UE and CN players route their flows in a mixed equilibrium behavior given the SO player’s routing strategy. In contrast, the SO player, realizing how the UE and CN players react to the given strategy, routes its flows to minimize total system travel cost. The Stackelberg game of network flow routing is formulated as a mathematical program with equilibrium constraints (MPEC). Using a marginal function approach, the MPEC is transformed into an equivalent, continuously differentiable single-level optimization problem, where the lower level VI is represented by a differentiable gap function constraint. The augmented Lagrangian method is then used to solve the resulting single-level optimization problem. Some numerical examples are presented to demonstrate the proposed models and algorithms.
108 citations
TL;DR: This paper investigates how opportunities to invest in demand enhancing services for a product line affect the interactions between a manufacturer and her dealer and finds that the equilibrium depends on which, if any, channel partner has the ability to act as a Stackelberg leader.
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TL;DR: In this article, the authors model the supply chain problem as a stochastic Stackelberg differential game and obtain the condition when offering co-op advertising is optimal, and compare the results with the advertising and price decisions of the vertically integrated channel, and suggest a method for coordinating the channel.
Abstract: Cooperative (co-op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co-op advertising policy, i.e., a participation rate that specifies the percentage of the retailer's advertising expenditure that it will provide. In addition, it also announces the wholesale price. In response, the retailer chooses its optimal advertising and pricing policies. We model this supply chain problem as a stochastic Stackelberg differential game whose dynamics follows Sethi's stochastic sales-advertising model. We obtain the condition when offering co-op advertising is optimal. We provide in feedback form the optimal advertising and pricing policies for the manufacturer and the retailer. We contrast the results with the advertising and price decisions of the vertically integrated channel, and suggest a method for coordinating the channel.
11 Jun 2007
TL;DR: This work considers the scenario where the network administrator wants the final solution to be (strictly) better than the Nash equilibrium, and finds the minimum fraction required to be centrally controlled to induce an optimum solution the Stackelberg threshold.
Abstract: Noncooperative network routing games are a natural model of userstrying to selfishly route flow through a network in order to minimize their own delays. It is well known that the solution resulting from this selfish routing (called the Nash equilibrium) can have social cost strictly higher than the cost of the optimum solution. One way to improve the quality of the resulting solution is to centrally control a fraction of the flow. A natural problem for the network administrator then is to route the centrally controlled flow in such a way that the overall cost of the solution is minimized after the remaining fraction has routed itself selfishl.This problem falls in the class of well-studied Stackelberg routing games. We consider the scenario where the network administrator wants the final solution to be (strictly) better than the Nash equilibrium. In other words, she wants to control enough flow such that the cost of the resulting solution is strictly less than the cost of the Nash equilibrium.We call the minimum fraction of users that must be centrally routed to improve the quality of the resulting solution the Stackelberg threshold. We give a closed form expression for the Stackelberg threshold for parallel links networks with linear latency functions. The expression is in terms of Nash equilibrium flows and optimum flows. It turns out that the Stackelberg threshold is the minimum of Nash flows on links which have more optimum flow than Nash flow.Using our approach to characterize the Stackelberg thresholds, we are able to give a simpler proof of an earlier result which finds the minimum fraction required to be centrally controlled to induce an optimum solution.
TL;DR: The problem is analyzed as a Stackelberg game in which the manufacturer declares quantity discount pricing schemes to the retailer and then the retailer follows by selecting the retail price and associated quantity.
TL;DR: It is proved that the problem is APX-hard even if there are only two different red costs, and an approximation algorithm is given whose approximation ratio is at most min {k,1+ln’b,1-ln W}, where k is the number of distinct red Costs, b is thenumber of blue edges, and W is the maximum ratio between red costs.
Abstract: We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST.
The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game.
We analyze the complexity and approximability of the first player's best strategy in StackMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most $\min \{k,1+\ln b,1+\ln W\}$, where $k$ is the number of distinct red costs, $b$ is the number of blue edges, and $W$ is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm.
TL;DR: This paper considers the problem of dynamic congestion pricing that determines optimal time-varying tolls for a pre-specified subset of arcs with bottleneck on a congested general traffic network with the assumption that the underlying information structure is open loop.
Abstract: This paper considers the problem of dynamic congestion pricing that determines optimal time-varying tolls for a pre-specified subset of arcs with bottleneck on a congested general traffic network. A two-person nonzero-sum dynamic Stackelberg game model is formulated with the assumption that the underlying information structure is open loop. Characteristics of the Stackelberg equilibrium solution are analyzed. The Hooke–Jeeves algorithm that obviates an evaluation of the gradient vector of the objective function is presented with a numerical example. The paper concludes with its future extensions.
TL;DR: In this article, the Stackelberg model is used to study the question under which circumstances a firm with a first-mover advantage may get leapfrogged by a follower, and they find that there is a unique equilibrium in which both firms invest in process R&D, only the follower delegates, and the follower can overcome the first mover advantage of the quantity leader and obtain a higher profit than the leader.
Abstract: In this paper we are studying the question under which circumstances a firm with a first-mover advantage may get leapfrogged by a follower. At the market stage we assume a Stackelberg structure, i.e. the leader commits to a quantity and the follower then reacts to it. It is well-known that the leader has a first-mover advantage. In our model, we additionally allow the owners of both firms to select the internal organization and the production technology before quantities are determined and produced. That is, leader and follower can additionally use two other commitment strategies alternatively or in combination: investing in (process) R&D and delegating quantity decisions to managers. Despite the symmetry of options for the two firms, we find that there is a unique equilibrium in which both firms invest in process R&D, only the follower delegates, and the follower can overcome the first-mover advantage of the quantity leader and obtain a higher profit than the leader. Although seemingly similar, our analysis reveals that there are some important differences between the two commitment devices "cost-reducing R&D" and "delegation to managers".
TL;DR: In this article, the authors investigated the possibility of excess entry in the absence of scale economies and showed that with free entry, more firms than is socially optimal typically enter provided there are economies of scale.
Abstract: It is well-known that with free entry, more firms than is socially optimal typically enter provided there are economies of scale. This paper investigates the possibility of excess entry in the absence of scale economies
01 Jan 2007
TL;DR: In this article, the authors introduced the concept of nonlinear pricing within the context of their previous Stackelberg network game model and view the Internet Service Provider's (ISP) policy as an incentive policy, and the underlying game as a reverse Stackeckberg game.
Abstract: We introduce the concept of nonlinear pricing within the context of our previous Stackelberg network game model and view the Internet Service Provider’s (ISP’s) policy as an incentive policy, and the underlying game as a reverse Stackelberg game We study this incentive-design problem under complete information as well as incomplete information In both cases, we show that the game is not generally incentive controllable (that is, there may not exist pricing policies that would lead to attainment of a Pareto-optimal solution), but it is ɛ-incentive controllable (that is, the ISP can induce a behavior on the users that is arbitrarily close to a Pareto-optimal solution) The paper also includes a comparative study of the solutions under linear and nonlinear pricing policies, illustrated by numerical computations
TL;DR: In this article, a two-stage supply chain consisting of a capacitated supplier and a retailer that faces a stationary random demand is investigated, where all unsatisfied demand is backlogged and the customer backorder cost is shared between the supplier and the retailer.
Abstract: This paper investigates a two-stage supply chain consisting of a capacitated supplier and a retailer that faces a stationary random demand. Both the supplier and the retailer employ base stock policies for inventory replenishment. All unsatisfied demand is backlogged and the customer backorder cost is shared between the supplier and the retailer. We investigate the determination of decentralized inventory decisions when the two parties optimize their individual inventory-related costs in a noncooperative manner. We explicitly characterize the Nash equilibrium inventory strategies and identify the causes of inefficiency in the decentralized operation. We then study a set of simple linear contracts to see whether these inefficiencies can be overcome. Finally, we investigate Stackelberg games where one of the parties is assumed to be dominating.
TL;DR: In this article, the authors characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices, and show that the player with the lowest cost has a positive payoff in any equilibrium.
Abstract: We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts ‘early’ and a group of players who choose ‘late’. Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses ‘late’, whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost.
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TL;DR: In this article, the authors show why social learning gives rise to the Walrasian equilibrium and why, in a general setup, individual learning can effectively yield convergence to the Cournot equilibrium.
Abstract: Convergence to the Nash equilibrium in a Cournot oligopoly is a question that recurrently arises as a subject of controversy in economics. The development of evolutionary game theory has provided an equilibrium concept more directly connected with adjustment dynamics, and the evolutionary stability of the equilibria of the Cournot game has been extensively studied in the literature. Sev- eral articles show that the Walrasian equilibrium is the stable ESS of the Cournot game. But no general result has been established for the difficult case of simultaneous heterogenous mutations. Authors propose specific selection dynamics to analyze this case. Vriend (2000) proposes using a genetic algorithm for studying learning dynamics in this game and obtains convergence to Cournot equilibrium with individual learning. The resulting convergence has been questioned by Arifovic and Maschek (2006). The aim of this article is to clarify this controversy. It analyzes the mechanisms that are behind these contradictory results and underlines the specific role of the spite effect. We show why social learning gives rise to the Walrasian equilibrium and why, in a general setup, individual learning can effectively yield convergence to the Cournot equilibrium. We also illustrate these general results by systematic computational experiments.
TL;DR: This work presents conditions under which the leader's profit does not improve from (i) to (ii), and proposes a solution to this problem.
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TL;DR: In this article, it was shown that sufficient cost convexity in a Stackelberg model generates profitable mergers between two leaders and between two followers, and that the degree of convexities required for leaders to merge is generally far smaller than that required for followers.
Abstract: We are the first to confirm that sufficient cost convexity in a Stackelberg model generates profitable mergers between two leaders and between two followers. Moreover, the degree of convexity required for leaders to merge is generally far smaller than that required for followers. Most importantly, the structure of the stage game means that the convexity required for either two followers or two leaders to merge is less than that required for two Cournot competitors.
TL;DR: In this article, an optimal strategy based on knowledge discovery is proposed to improve the performance of the supply chain with one supplier and multiple retailers under deterministic price-sensitive customer demand.
TL;DR: In this article, a dynamic facility location model for a firm locating on a discrete network is proposed, which is based on sensitivity analysis of variational inequalities within a hierachical mathematical programming approach.
Abstract: We formulate a dynamic facility location model for a firm locating on a discrete network. It is assumed that this locating firm will act as the leader firm in an industry characterized by Stackelberg leader–follower competition. The firm’s I competitors are assumed to act as Cournot firms and are each assumed to operate under the assumption of zero conjectural variation with respect to their I–1 Cournot competitors. Using sensitivity analysis of variational inequalities within a hierachical mathematical programming approach, we develop reaction function based dynamic models to optimize the Stackelberg firm’s location decision. In the second half of this paper, we use these models to illustrate through a numerical example the insights yielded by our approach.
TL;DR: In this article, the authors consider network games with atomic players and show bounds on the inefficiency of the solutions that arise when the leader uses a heuristic that approximate its optimal strategy.
Abstract: We consider network games with atomic players, which indicates that some players control a positive amount of flow. Instead of studying Nash equilibria as previous work has done, we consider that players with considerable market power will make decisions before the others because they can predict the decisions of players without market power. This description fits the framework of Stackelberg games, where those with market power are leaders and the rest are price-taking followers. As Stackelberg equilibria are difficult to characterize, we prove bounds on the inefficiency of the solutions that arise when the leader uses a heuristic that approximate its optimal strategy.
TL;DR: In this article, the competition between a central securities depository (CSD) and a custodian bank is analyzed in a Stackelberg model, and it is shown that the CSD's equilibrium market share is higher than socially optimal.
01 Jan 2007
TL;DR: In this article, a dynamic game model of international terrorism is presented, where the time horizon is finite, about the size of one presidency, or infinite, and the game is played for brief periods of time.
Abstract: This paper presents a dynamic game model of international terrorism. The time horizon is finite, about the size of one presidency, or infinite. Quantitative and qualitative analyses of incentive Stackelberg strategies for both decisionmakers of the game (“theWest” and “International Terror Organization”) allow statements about the possibilities and limitations of terror control interventions. Recurrent behavior is excluded with monotonic variation in the frequency of terror attacks whose direction depends on when the terror organization launches its terror war. Even optimal pacing of terror control operations does not greatly alter the equilibrium of the infinite horizon game, but outcomes from theWest’s perspective can be greatly improved if the game is only “played” for brief periods of time and if certain parameters can be influenced, notably those pertaining to the terror organization’s ability to recruit replacements.
TL;DR: In this article, a decentralized assembly system is considered, where n suppliers sell complementary components to a downstream assembler, who faces a price-sensitive deterministic demand, using a two-stage approach.
Abstract: In this paper, we study dynamic supplier alliances in a decentralized assembly system. We examine a supply chain where n suppliers sell complementary components to a downstream assembler, who faces a price-sensitive deterministic demand. We analyze alliance/coalition formation between suppliers, using a two stage approach. In Stage 1, suppliers form coalitions that each agree to sell a kit of products to the assembler. In Stage 2, coalitions make wholesale price decisions, while the assembler buys the components (kits) from the coalitions and sets the selling price of the product. Stage 2 is modeled as a competitive game, in which the primary competition is vertical (i.e., supplier coalitions compete against the downstream assembler), and the secondary competition is horizontal, in that coalitions compete against each other. Here, we consider three cases - Supplier Stackelberg, Vertical Nash, and Assembler Stackelberg models - which correspond to different power structures in the market. In Stage 1, we analyze the stability of coalition structures. We assume that suppliers are farsighted, that is, each coalition considers the possibility that once it acts, another coalition may react, and a third coalition might in turn react, and so on. Using this framework, we predict the structure of possible supplier alliances, as a function of the power structure in the market, the market size, and the structure of the demand.