Pdf in this chapter, we formulate and discuss a sensitivity based approach to solving stackelberg nashcournot snc equilibrium problems on a. Firm b will now be the leader while firm a becomes the follower. 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. Mathematical properties of a combined cournotstackelberg. Stackelberg equilibrium, static equilibrium, multiplayers zerosum game. How to differ nash equilibrium with stackelberg equilibrium. Stackelberg games and multiple equilibrium behaviors on networks. Noncompensatory consideration and compensatory choice. Download fulltext pdf download fulltext pdf download fulltext pdf download fulltext pdf. Cournot oligopolistic competition in spatially separated markets. The properties of the stackelberg solution in static and dynamic nonzerosum twoplayer games are investigated, and necessary and sufficient conditions for its existence are derived.
It was developed in 1934 by heinrich stackelbelrg 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. Cournot reaction function, then a consistent leaderfollower pair would be formed. The weight determines the leaderfollower strategic relationship. In the equilibrium, a leaders private signal becomes followers public signal. The analytical framework used in this paper involves the models examined by the several recent contributions to the time consistency issue as. Its analytic difficulty, however, poses a main drawback. Whether bertrand or stackelberg appears in equilibrium depends on the properties of demand functions crucially. Author links open overlay panel yongchao liu a huifu xu b shujung sunny yang c. The classical stackelberg game is extended to boundedly rational price stackelberg game, and the dynamic duopoly game model is described in detail. Stackelberg equilibrium players have di erent roles in the stackelberg solution concept. Pdf unifying cournot and stackelberg action researchgate. Pdf public input competition, stackelberg equilibrium. In this way two stackelberg equilibria were added to the.
Several game problems, such as games where one of the two players does not know the others performance criterion or games with different speeds in computing the strategies, are best modeled and solved. On time consistency in stackelberg differential games. The inverse demand function is p1q where q denotes total quantity and p is the price. The graph will also be used to evaluate monopolistic competition with. This flexibility, however, would hurt firm 1 since firm 2 would anticipate.
On the equivalence of stackelberg equilibrium and static. Computation of stackelberg equilibria of finite sequential games. We show that in this class of games the openloop equilibrium coincides with the corresponding feedback equilibrium. Now suppose that player 1 can commit to an action and credibly communicate the action to which she has committed to player 2 before player 2. Gabriele farina quasiperfect stackelberg equilibrium. Stackelberg equilibrium is an equilibrium in which one company acts as a leader and one another company as a follower. The restricted stackelberg problem rsp considers a subset of the stackelberg strategy where the leader achieves his team cost.
In this paper, we introduce the axiomatic definition of quasiperfect stackelberg equilibrium. Distributionally robust equilibrium for continuous games. Our class of perturbation schemes strictly generalizes prior perturbation. If firm b is the sophisticated oligopolist, it will choose to produce x b, corresponding to point b on xs reaction curve, because this is the largest profit that b can achieve given his isoprofit map and as reaction curve.
Oligopoly models an oligopoly is a market structure characterized by significant interdependence. The graph below shows a monopolistically competitive firm in longrun equilibrium with zero profit. Oneleader and multiplefollower stackelberg games with. The stackelberg model of oligopoly with derivation.
Equilibrium of the cournot duopoly marketan alternative geometrical illustration. What is a qualitative solution to nplayer stackelberg. The advertising model of lanchester is used in a game where the relevant solution concept is feedback stackelberg equilibrium. Feedback stackelberg equilibrium strategies when the. Existence theorems of equilibrium points in stackelberg.
They characterize the stackelberg equilibrium and investigate conditions under which channel coordination, i. The stackelberg model of oligopoly with derivation microeconomics. Bertrand stackelberg cartels midterm 2 bring pencilpen, bluebook, pink scantron 8 mc questions, like last time important skills. Stackelberg games in a stackelberg game, one player the leader moves first, and all other players the followers. We define the weight on public signal about a followers estimation of uncertainty.
This paper explores a class of stackelberg differential games in which the openloop strategies of the leader satisfies time consistency. As opposed to the weak stackelberg equilibrium wse, the sse assumes that the follower breaks ties in favor of the leader and this is widely. On the inducibility of stackelberg equilibrium for security games. The stackelberg model is a quantity leadership model.
Stackelberg duopoly, also called stackelberg competition, is a model of imperfect competition based on a noncooperative game. Stackelberg equilibria for discretetime dynamic games. In the stackelberg equilibrium, one of the firms is sophisticated while the other is naive. In the cournot equilibrium, firms choose quantities simultaneously.
The major insights by stackelberg are about duopoly dyopol in his jergon, but the modern reader will be extremely. Pdf feedback stackelberg equilibria in a dynamic game of. Use the graph above and compare to longrun equilibriums in perfect competition and monopoly. The superiority of the stackelberg model over the mixed nash equilibrium model is the further improvement of system efficiency in. Entry, stackelberg equilibrium and reasonable conjectures.
Stackelberg equilibria for discretetime dynamic games part i. Research supported by nserc, canada, and fqrsc, quebec. Buzacott and zhang2004 incorporate assetbased nancing in a deterministic multiperiod pro. Stackelberg equilibrium definition marketing dictionary. Recursive methods for computing equilibria of general equilibrium dynamic stackelberg games. Pdf stackelberg leadership is understood as a stationary supply taking account of the followers cournot reaction function. A cournotstackelberg model of supply contracts with.
We analyze oneleader and multiplefollower stackelberg games with uncertainty. The stackelberg equilibrium strategy concept has wide applications in modeling of socioeconomic and large scale systems. In this figure, the straight line ab is the market demand curve 14. The stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. Unlike standard models of choice, experimental evidence suggests that individuals avoid tradeoffs when choice problems are complex.
The advertising model of lanchester is used in a game where the relevant solution concept is feedback stackelberg equilibrium, which is subgame perfect. Pdf stackelberg equilibrium in robot platooning jep ti. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. 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. Public input competition, stackelberg equilibrium and optimality. I analyze the implications of consumers using noncompensatory choice heuristics in a simple stackelberg game in which firms offer menus of multiattribute alternatives and influence the attribute considered to be salient by consumers via marketing. Bertrand, cournot, stackelberg, linear hotelling, mergers 1 exercise 2. Oligopoly models cournot vs stackelberg vs bertrand. Stackelberg game for user clustering and power allocation. Stackelberg game is considered with constraints on the decision variables. Hello, i am trying to compute a stackelberg nash equilibrium of a game, where the leader gives signals to the followers whom tries to find a ne in a non cooperative game. Take as given the quantities chosen by all the firms other than n and solve for the best response of firm n as a function of these quantities. Analysis of price stackelberg duopoly game with bounded. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied.
Dynamic signaling games with quadratic criteria under nash. Stackelberg equilibrium is attained if and only if firm 1 desires to be a leader. Stationary strong stackelberg equilibrium in discounted stochastic games. We study stackelberg equilibria in finite sequential games or extensiveform games and provide new exact algorithms, approximate.
Download fulltext pdf download fulltext pdf download fulltext pdf download fulltext pdf stackelberg equilibrium in duopoly. Existence theorems of equilibrium points are given when the reaction set of the follower to the strategy of the leader, is a singleton. We may now illustrate the equilibrium in the cournot duopoly market with the help of fig. In this paper, the joint design of user clustering and power allocation is investigated in a downlink nonorthogonal multiple accessbased millimeter wave mmwavenoma system. In this the leader firm moves first and the follower firm follows it later. We develop a broad class of game perturbation schemes that lead to them in the limit. B has a higher profit and the naive firm a has a lower profit as compared with the cournot equilibrium.
And some comparisons with bertrand game with bounded rationality are also performed. Common models that explain oligopoly output and pricing decisions include cartel model, cournot model, stackelberg model, bertrand model and contestable market theory. On stackelberg mixed strategies 3 player 1 up down player 2 f ih 1 1 3 0 0 0 2 1 le t right ri g h t,, fig. Once a firm announces a price, it is able to discount it but not raise it.
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