Posted Content•
Monotone Comparative Statics in Games with both Strategic Complements and Strategic Substitutes
TL;DR: In this article, the authors analyzed games with both strategic substitutes and complements and provided natural conditions to guarantee monotone comparative statics, based on intuitive tradeoffs between direct parameter effects and indirect strategic effects.
Abstract: This paper analyzes games with both strategic substitutes and strategic complements. Such games may behave differently from either games with strategic complements or games with strategic substitutes. In such games, equilibria do not decrease as the parameter increases. Moreover, natural conditions are presented to guarantee that an increase in the parameter leads to an increase in the equilibrium: in other words, conditions to guarantee monotone comparative statics. These conditions are based on intuitive tradeoffs between direct parameter effects and indirect strategic effects. These conditions are needed only for players with strategic substitutes; no conditions are imposed on players with strategic complements. Several examples highlight the results.
Citations
More filters
01 Jan 1998
TL;DR: In this paper, the authors analyse a situation where firms differ in their R&D technologies in two distinct ways: they differ both in the costs of performing research activities and in the output obtained from such activities and find that the optimal firm-specific industrial policy is affected differently by the two sources of firm heterogeneity.
Abstract: Our concern is about a firm-specific industrial policy. When R&D subsidies or taxes are differentiated among firms, the question arises which firms in an industry should receive such support. We analyse a situation where firms differ in their R&D technologies in two distinct ways: they differ both in the costs of performing R&D activities and in the output obtained from such activities. The introduction of several domestic firms creates a corrective motive for government intervention with the firms' R&D activities in addition to Spencer and Brander's strategic motive. We find that the optimal firm-specific industrial policy is affected differently by the two sources of firm heterogeneity. Moreover, a change in a firm's R&D productivity has an ambiguous effect on the optimal policy towards the firm.
26 citations
TL;DR: In this paper, the authors revisited endogenous timing in a quantity-setting duopoly game and showed that given strong heterogeneity in consumers willingness to pay (WTP ) and a moderately small consumer segment with low WTP, sequential moving outcomes can appear in equilibrium with the follower enjoying second-mover advantage.
Abstract: I revisit endogenous timing in a quantity-setting duopoly game. In the basic model, I show that given strong heterogeneity in consumers willingness to pay ( WTP ) and a moderately small consumer segment with low WTP , sequential moving outcomes can appear in equilibrium with the follower enjoying second-mover advantage. Owing to consumer heterogeneity in WTP , there is a local property that a firm's aggressive behaviour may lead to a competitor responding more aggressively. Hence, the sequential moves can restrict firms total outputs to avoid a price collapse, and result in firms strategic choices that Pareto dominate those under the simultaneous move. I further generalize my results and show that although firms compete in quantity, under some conditions of the demand function, features of strategic complements can appear.
6 citations
TL;DR: In this article, the authors extend the LeChatelier-Samuelson principle to strategic environments and to shocks that affect more than one action directly, and they show that the principle holds for supermodular games (strategic complements), submodular game and strategic substitutes.
Abstract: The LeChatelier-Samuelson principle ("the principle") states that as a reaction to a shock, an agent's short-run adjustment of an action is smaller than the long-run adjustment of that action when the other related actions can also be adjusted. We extend the principle to strategic environments and to shocks that affect more than one action directly. We define long run as an adjustment that also includes the affected player adjusting its other actions and other players adjusting their strategies. We show that the principle holds for 1) supermodular games (strategic complements), 2) submodular games (strategic substitutes) for shocks that affect only one player's action directly and when the players' payoffs depend only on their own strategies and the sum of the rivals' strategies (for example, homogeneous Cournot oligopoly). We also provide other sufficient conditions for the principle to hold in games of strategic substitutes. Our results imply that when the principle holds a multiproduct oligopoly might have lower cost pass-through in the short run than in the long run. Hence, we argue that the principle might explain the empirical findings of overshifting of cost and unit tax by multiproduct firms.
4 citations
TL;DR: In this article, the authors extend the LeChatelier-Samuelson principle to games where the long-run adjustment also accounts for other players adjusting their strategies, and show that the principle holds for supermodular games satisfying monotone comparative statics.
3 citations
References
More filters
TL;DR: In fact, some common properties are shared by practically all legislation, and these properties form the subject matter of this essay as discussed by the authors, which is the basis for this essay. But, in spite of such diversity, some commonsense properties are not shared.
Abstract: Since the turn of the twentieth century, legislation in Western countries has expanded rapidly to reverse the brief dominance of laissez faire during the nineteenth century. The state no longer merely protects against violations of person and property through murder, rape, or burglary but also restricts ‘discrimination’ against certain minorities, collusive business arrangements, ‘jaywalking’, travel, the materials used in construction, and thousands of other activities. The activities restricted not only are numerous but also range widely, affecting persons in very different pursuits and of diverse social backgrounds, education levels, ages, races, etc. Moreover, the likelihood that an offender will be discovered and convicted and the nature and extent of punishments differ greatly from person to person and activity to activity. Yet, in spite of such diversity, some common properties are shared by practically all legislation, and these properties form the subject matter of this essay.
9,613 citations
TL;DR: A firm's actions in one market can change competitors' strategies in a second market by affecting its own marginal costs in that other market as mentioned in this paper, and whether the action provides costs or benefits in the second market depends on whether it increases or decreases marginal costs.
Abstract: A firm's actions in one market can change competitors' strategies in a second market by affecting its own marginal costs in that other market. Whether the action provides costs or benefits in the second market depends on (a) whether it increases or decreases marginal costs in the second market and (b) whether competitors' products are strategic substitutes or strategic complements. The latter distinction is determined by whether more "aggressive" play (e.g., lower price or higher quantity) by one firm in a market lowers or raises competing firms' marginal profitabilities in that market. Many recent results in oligopoly theory can be most easily understood in terms of strategic substitutes and complements.
2,588 citations
TL;DR: The authors analyzes the duality of prices and quantities in a differentiated duopoly and shows that if firms can only make two types of binding contracts with consumers, the price contract and the quantity contract, it is a dominant strategy for each firm to choose the quantity (price) contract, provided the goods are substitutes (complements).
Abstract: This article analyzes the duality of prices and quantities in a differentiated duopoly. It is shown that if firms can only make two types of binding contracts with consumers, the price contract and the quantity contract, it is a dominant strategy for each firm to choose the quantity (price) contract, provided the goods are substitutes (complements).
2,516 citations
TL;DR: In this article, a rich class of non-cooperative games, including models of oligopoly competition, macroeconomic coordination failures, arms races, bank runs, technology adoption and diffusion, R&D competition, pretrial bargaining, coordination in teams, and many others, are studied.
Abstract: We study a rich class of noncooperative games that includes models of oligopoly competition, macroeconomic coordination failures, arms races, bank runs, technology adoption and diffusion, R&D competition, pretrial bargaining, coordination in teams, and many others. For all these games, the sets of pure strategy Nash equilibria, correlated equilibria, and rationalizable strategies have identical bounds. Also, for a class of models of dynamic adaptive choice behavior that encompasses both best-response dynamics and Bayesian learning, the players' choices lie eventually within the same bounds. These bounds are shown to vary monotonically with certain exogenous parameters. WE STUDY THE CLASS of (noncooperative) supermodular games introduced by Topkis (1979) and further analyzed by Vives (1985, 1989), who also pointed out the importance of these games in industrial economics. Supermodular games are games in which each player's strategy set is partially ordered, the marginal returns to increasing one's strategy rise with increases in the competitors' strategies (so that the game exhibits "strategic complementarity"2) and, if a player's strategies are multidimensional, marginal returns to any one com- ponent of the player's strategy rise with increases in the other components. This class turns out to encompass many of the most important economic applications of noncooperative game theory. In macroeconomics, Diamond's (1982) search model and Bryant's (1983, 1984) rational expectations models can be represented as supermodular games. In each of these models, more activity by some members of the economy raises the returns to increased levels of activity by others. In oligopoly theory, some models of Bertrand oligopoly with differentiated products qualify as supermodu- lar games. In these games, when a firm's competitors raise their prices, the marginal profitability of the firm's own price increase rises. A similar structure is present in games of new technology adoption such as those of Dybvig and Spatt (1983), Farrell and Saloner (1986), and Katz and Shapiro (1986). When more users hook into a communication system or more manufacturers adopt an interface standard, the marginal return to others of doing the same often rises. Similarly, in some specifications of the bank runs model introduced by Diamond and Dybvig (1983), when more depositors withdraw their funds from a bank, it is more worthwhile for other depositors to do the same. In the warrant exercise
1,795 citations
TL;DR: In this article, the authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem, and develop practical methods for checking the condition.
Abstract: The authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem. In addition, they develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm, the monopolist, the Bertrand oligopolist, consumer and growth theory, game theory, and general equilibrium analysis. Copyright 1994 by The Econometric Society.
1,526 citations