Public input competition, stackelberg equilibrium and optimality. Pdf in this chapter, we formulate and discuss a sensitivity based approach to solving stackelberg nashcournot snc equilibrium problems on a. Recursive methods for computing equilibria of general equilibrium dynamic stackelberg games. Noncompensatory consideration and compensatory choice. The stackelberg model of oligopoly with derivation microeconomics. 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. The graph below shows a monopolistically competitive firm in longrun equilibrium with zero profit. Entry, stackelberg equilibrium and reasonable conjectures. Existence theorems of equilibrium points in stackelberg. The advertising model of lanchester is used in a game where the relevant solution concept is feedback stackelberg equilibrium. Pdf stackelberg equilibrium in robot platooning jep ti. 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. 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. Stationary strong stackelberg equilibrium in discounted stochastic games.
Bertrand, cournot, stackelberg, linear hotelling, mergers 1 exercise 2. On the equivalence of stackelberg equilibrium and static. Stackelberg game for user clustering and power allocation. This paper explores a class of stackelberg differential games in which the openloop strategies of the leader satisfies time consistency. Cournot reaction function, then a consistent leaderfollower pair would be formed.
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. 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. Stackelberg equilibrium is attained if and only if firm 1 desires to be a leader. In the cournot equilibrium, firms choose quantities simultaneously. Firm b will now be the leader while firm a becomes the follower. The stackelberg model of oligopoly with derivation. Once a firm announces a price, it is able to discount it but not raise it. The weight determines the leaderfollower strategic relationship. We develop a broad class of game perturbation schemes that lead to them in the limit. We study stackelberg equilibria in finite sequential games or extensiveform games and provide new exact algorithms, approximate.
We define the weight on public signal about a followers estimation of uncertainty. In this paper, we introduce the axiomatic definition of quasiperfect stackelberg equilibrium. Download fulltext pdf download fulltext pdf download fulltext pdf download fulltext pdf. 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. Computation of stackelberg equilibria of finite sequential games. Stackelberg games and multiple equilibrium behaviors on networks. Mathematical properties of a combined cournotstackelberg. We show that in this class of games the openloop equilibrium coincides with the corresponding feedback equilibrium. Unlike standard models of choice, experimental evidence suggests that individuals avoid tradeoffs when choice problems are complex.
Existence theorems of equilibrium points are given when the reaction set of the follower to the strategy of the leader, is a singleton. Equilibrium of the cournot duopoly marketan alternative geometrical illustration. In this way two stackelberg equilibria were added to the. The stackelberg model is a quantity leadership model. On time consistency in stackelberg differential games. Whether bertrand or stackelberg appears in equilibrium depends on the properties of demand functions crucially. In the equilibrium, a leaders private signal becomes followers public signal. Our class of perturbation schemes strictly generalizes prior perturbation. A cournotstackelberg model of supply contracts with. 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. The stackelberg equilibrium strategy concept has wide applications in modeling of socioeconomic and large scale systems. Bertrand stackelberg cartels midterm 2 bring pencilpen, bluebook, pink scantron 8 mc questions, like last time important skills.
Gabriele farina quasiperfect stackelberg equilibrium. Pdf stackelberg leadership is understood as a stationary supply taking account of the followers cournot reaction function. In this paper, the joint design of user clustering and power allocation is investigated in a downlink nonorthogonal multiple accessbased millimeter wave mmwavenoma system. Buzacott and zhang2004 incorporate assetbased nancing in a deterministic multiperiod pro. Distributionally robust equilibrium for continuous games. B has a higher profit and the naive firm a has a lower profit as compared with the cournot equilibrium. 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. Download fulltext pdf download fulltext pdf download fulltext pdf download fulltext pdf stackelberg equilibrium in duopoly. And some comparisons with bertrand game with bounded rationality are also performed. The advertising model of lanchester is used in a game where the relevant solution concept is feedback stackelberg equilibrium, which is subgame perfect. Dynamic signaling games with quadratic criteria under nash. Pdf public input competition, stackelberg equilibrium. Stackelberg game for user clustering and power allocation in millimeter wavenoma systems abstract. In this figure, the straight line ab is the market demand curve 14.
Common models that explain oligopoly output and pricing decisions include cartel model, cournot model, stackelberg model, bertrand model and contestable market theory. 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. Oneleader and multiplefollower stackelberg games with. Its analytic difficulty, however, poses a main drawback. The graph will also be used to evaluate monopolistic competition with. Stackelberg games in a stackelberg game, one player the leader moves first, and all other players the followers. Pdf unifying cournot and stackelberg action researchgate. Pdf feedback stackelberg equilibria in a dynamic game of. The inverse demand function is p1q where q denotes total quantity and p is the price. Oligopoly models an oligopoly is a market structure characterized by significant interdependence. Stackelberg equilibria for discretetime dynamic games. 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. What is a qualitative solution to nplayer stackelberg.
This flexibility, however, would hurt firm 1 since firm 2 would anticipate. Cournot oligopolistic competition in spatially separated markets. We may now illustrate the equilibrium in the cournot duopoly market with the help of fig. Stackelberg equilibrium is an equilibrium in which one company acts as a leader and one another company as a follower. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. Stackelberg game is considered with constraints on the decision variables.
The classical stackelberg game is extended to boundedly rational price stackelberg game, and the dynamic duopoly game model is described in detail. Stackelberg equilibrium definition marketing dictionary. 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. Use the graph above and compare to longrun equilibriums in perfect competition and monopoly. 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. Stackelberg equilibrium, static equilibrium, multiplayers zerosum game. Feedback stackelberg equilibrium strategies when the.
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. The superiority of the stackelberg model over the mixed nash equilibrium model is the further improvement of system efficiency in. They characterize the stackelberg equilibrium and investigate conditions under which channel coordination, i. In the stackelberg equilibrium, one of the firms is sophisticated while the other is naive. Analysis of price stackelberg duopoly game with bounded. The analytical framework used in this paper involves the models examined by the several recent contributions to the time consistency issue as. The restricted stackelberg problem rsp considers a subset of the stackelberg strategy where the leader achieves his team cost. Stackelberg equilibria for discretetime dynamic games part i. We analyze oneleader and multiplefollower stackelberg games with uncertainty. Stackelberg equilibrium players have di erent roles in the stackelberg solution concept. The stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. The major insights by stackelberg are about duopoly dyopol in his jergon, but the modern reader will be extremely.
Research supported by nserc, canada, and fqrsc, quebec. How to differ nash equilibrium with stackelberg equilibrium. Stackelberg duopoly, also called stackelberg competition, is a model of imperfect competition based on a noncooperative game. On the inducibility of stackelberg equilibrium for security games. In this the leader firm moves first and the follower firm follows it later.
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