Previous work has failed to resolve the defenders dilemma of which strategy to select when the. Multifirm mergers with leaders and followers faculty of social. Example game where the stackelberg equilibrium is not a nash equilibrium. Stackelberg competition we solve the game using backward induction. The development contrasts with other existing extensions by demonstrating how the leaderfirms can utilize the true reaction curve of the followerfirms. In the stackelberg model of duopoly, one firm serves as the industry leader.
Pdf profitable mergers in cournot and stackelberg markets. Author links open overlay panel steffen huck a kai a. Stackelberg equilibrium 1 introduction numerous applications of the optimization theory in engineering and economics require the solution of coupled optimization equations. Judd hoover institution and national bureau of economic research may 1989 latest revision april 1996 i thank ray deneckere, avinash dixit, garth salonar, michael riordan, and michael whinston, and participants of seminars at the hoover institution, stanford university, northwest. While the first mover in a stackelberg duopoly earns more than a cournot. Then firm 1s problem is to maximize its profit by choosing its output level q1. In a linear cournot market, for example, two firms never have an incentive to merge while bilateral merger can be profitable if costs are. In this case, there is no supply function, you set either quantity or price.
As the industry leader, the firm is able to implement its decision before its rivals. You operate a monopolistically competitive business. However, in an asymmetric stackelberg market we obtain that some mergers. Mergers in stackelberg markets with efficiency gains. It is useful to compare the price cost margin in the stackelberg merger case with that prevailing in the initial cournot equilibrium. However, if a leader buys a follower this increases the joint payo. Mergers, merger profitability, merger paradox, stackelberg, leaders, followers. Nashbertrand competition in a duopoly with congestion kurt van dender department of economics university of california, irvine irvine, ca 926975100 tel. This paper investigates cournot and stackelberg equilibria in the akerlof model. What happens to the equilibrium price and quantity in such a market if one firm introduces a new, improved product. Openloop stackelberg learning solution for hierarchical.
Nash equilibrium is a set of strategies such that each player is doing the best given the actions of its opponents. Pdf in this paper, we examine the share rule for profitable mergers in the standard cournot and stackelberg. Apply nash equilibrium each chooses optimal p i given j no one has incentive to deviate if pricing above marginal cost, each has incentive to undercut competitor p i p j mc is not an equilibrium p i j mc is the only possible. Set up and solve a simple threefirm cournot model and then resolve the model assuming two of the firms merge leaving a twofirm duopoly.
Leader produces more than the cournot equilibrium output. The merger paradox and bertrand competition with equally. Suggested solutions to assignment 3 optional total marks. How to solve a stackelberg oligopoly problem youtube.
This goes through the following quantity leadership problem, also known as a stackelberg oligopoly. When firms choose output quantities, there is a firstmover advantage and when firms choose prices, there is a secondmover advantage. The stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. I study a merger model among symmetric cournot firms wherebefore a merger occursfirms choose output simultaneously and in which a merged entity acquires the market leadership. However, if the merged rm becomes a stackelberg leader, it can improve its position. Mathematical properties of a combined cournotstackelberg. They characterize the stackelberg equilibrium and investigate conditions under which channel coordination, i. The pre merger equilibrium price, quantities and profits are. This paper analyzes the profitability of mergers and their induced welfare effects in a setting where. Consider a cournot equilibrium in which each firm in an equilibrium in which a firms remain. Whether bertrand or stackelberg appears in equilibrium depends on the properties of demand functions crucially.
Stackelberg duopoly it was developed in 1934 by heinrich stackelberg in his market structure and equilibrium and represented a breaking point in the study of market structure, particularly the analysis of duopolies since it was a model based on different starting assumptions and gave different conclusions to those of the cournots and bertrands duopoly models. The stackelberg model of oligopoly with derivation. Stackelberg duopoly, also called stackelberg competition, is a model of imperfect competition based on a noncooperative game. Follower produces less than the cournot equilibrium output. Price competition in static oligopoly models we have seen how price and output are determined in perfectly competitive and monopoly markets. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival. The premerger equilibrium price, quantities and profits are. Changing the assumptions of how firms react to one another changes the decisionmaking process. Leader gets a c 2 4bn 1 each follower gets a c 2 4bn 12 premerger, the two rms gets. It was developed in 1934 by heinrich stackelberg in his market structure and equilibrium and represented a breaking point in the study of market structure, particularly the analysis of duopolies since it was a model based on different starting assumptions and. The reason is that at the end of period 2, after firm 2 has decided on q2, firm 1 would like to change its decision and produce the best response to q1, r 1q 2. This paper presents a new multiple leaderfollower model that is a consistent extension of stackelberg s leaderfollower duopoly. Suppose firm 1 takes firm 2s output choice q2 as given. On the equivalence of stackelberg equilibrium and static.
I find conditions under which a single or multiple mergers are profitable and solve the freeriding problem. Yasuhiro takarada abstract in this paper, we examine the share rule for pro. A stochastic multipleleader stackelberg model operations research 575, pp. Kabiraj and mukherjee 2001 also found that a bilateral merger is always profitable when a leader and a follower merge together and the merger firm behaves like a leader. This point can be extended to show that in this model, even if there are a lot of rms most of them 80% rule need to merge together for a merger to be pro table. Stackelberg equilibrium is attained if and only if firm 1 desires to be a leader and firm 2 a follower. Conclusion in this paper, we consider stackelberg equilibrium as a potentially better learning objective than nash equilibrium in. Faculty of policy studies, nanzan university kojun hamada faculty of economics, niigata university abstract in this paper, we examine which mergers are pro. A cournot stackelberg model of supply contracts with financial hedging ren e caldentey. In this case, there are two nash equilibriums, sweet,crispy and crispy,sweet. Most markets are oligopolistic, however, where more than one but less than many firms compete for consumer business.
Introduction to game theory this is the way modern economists model oligopoly. Two of the firms now merge and become a stackelberg leader such that there are from econ 4301 at carleton university. Stackelberg model differences between cournot and stackelberg. Once a firm announces a price, it is able to discount it but not raise it.
The cournot equilibrium is augustin cournots brilliant solution to the duopoly puzzle. Stackelberg with multiple followers and leaders in which a merger between two followers allows the. In cournot, firm 1 chooses its quantity given the quantity of firm 2 in stackelberg, firm 1 chooses its quantity given the reaction curve of firm 2 note. This paper analyses a sequential merger formation game in a setting where. It is shown that the stackelberg equilibrium may coincide with the cournot.
A stackelberg classroom experiment abstract the timing of moves can dramatically affect firm profits and market outcomes. Two of the firms now merge and become a stackelberg leader. Otherwise, one must change his pattern of behaviour and act as a leader before. Pushpull competition in a nonlife insurance market with. Industrial organizationmatilde machado stackelberg model 15 3. Keywordsbayesian games, game theory, leadership, nash equilibrium, normal form games, security games, stackelberg equilibrium, stackelberg. Stackelberg model of duopoly stackelberg s model of duopoly also has to do with companies trying to decide how much of a homogeneous good to produce. Pdf cournot and stackelberg equilibria in the akerlof. Horizontal mergersmerger paradox 3 will not be pro table. Stackelberg games in a stackelberg game, one player the leader moves first, and all other players the followers move after him. Stackelberg equilibrium, static equilibrium, multiplayers zerosum game.
This flexibility, however, would hurt firm 1 since firm 2 would anticipate. This video solves a standard stackelberg problem that is encountered when studying oligopoly models. Firms face a strategic setting in oligopoly markets. Under the stackelberg assumptions, the cournot solution is achieved if each desires to act as a follower, knowing that the other will also act as a follower. For this purpose, there is constructed a model of duopoly producers of highquality and lowquality products, which compete in conditions of information asymmetry. Merger analysis in the generalized hierarchical stackelberg model yasuhiro takarada. Stackelberg summary stackelberg model illustrates how commitment can enhance profits in strategic environments. Bertrand, cournot, stackelberg, linear hotelling, mergers 1 exercise 2. A cournotstackelberg model of supply contracts with.
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