Complementarities and fit strategy, structure, and organizational change in manufacturing

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

http://www.parisschoolofeconomics.eu/docs/guesnerie-roger/milgromroberts90.pdf

Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities

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.

Monotone comparative statics

A major challenge in the operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With the increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash (1951) equilibrium that is inefficient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e., to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system.

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Efficient power control via pricing in wireless data networks

The paper is a first attempt at modelling the idea of group reputation as an aggregate of individual reputations A member's current incentives are affected by his past behaviour and, because his track record is observed only with noise, by the group's past behaviour as well The paper thus studies the joint dynamics of individual and collective reputations and derives the existence of stereotypes from history dependence rather than from a multiplicity of equilibria or from the existence of a common trait as is usually done in the literature It shows that new members of an organization may suffer from an original sin of their elders long after the latter are gone, and it derives necessary and sufficient conditions under which group reputations can be rebuilt Last, the paper applies the theory to analyse when a large firm can maintain a reputation for quality 1 COLLECTIVE REPUTATIONS Collective reputations play an important role in economics and the social sciences Countries, ethnic, racial or religious groups are known to be hard-working, honest, corrupt, hospitable or belligerent Some firms enjoy substantial rents from their reputations for producing high-quality products Some departments are reported to treat their faculty or students fairly The paper is a first attempt at modelling the idea of group reputation as an aggregate of individual reputations A member's current incentives are affected by her past behaviour and, because her track record is observed only with noise, by the group's past behaviour as well The paper studies the joint dynamics of individual and collective reputations in a model in which current generations are progressively replaced by new ones, and derives the existence of stereotypes from history dependence rather than from a multiplicity of equilibria or from the existence of a common trait as is usually done in the literature (see Section 2 for a detailed comparison with the literature) It shows that new members of an organization may suffer from an original sin of their elders long after the latter are gone, and it derives necessary and sufficient conditions under which group reputations can be rebuilt Last, the paper applies the theory to analyse when a large firm can maintain a reputation for quality Let us spell out the building blocks of our theory in more detail: (a) A group's reputation is only as good as that of its members Each member is characterized by individual traits such as talent, diligence or honesty Past individual behaviour conveys information about these traits and generates individual reputations

/pdf/a-theory-of-collective-reputations-with-applications-to-the-vqbbuzfrc9.pdf

A Theory of Collective Reputations (with applications to the persistence of corruption and to firm quality)

A submodular game is a finite noncooperative game in which the set of feasible joint decisions is a sublattice and the cost function of each player has properties of submodularity and antitone differences. Examples of submodular games include 1) a game version of a system with complementary products; 2) an extension of the minimum cut problem to a situation where players choose from different sets of nodes and perceive different capacities, with special cases being a game with players choosing whether or not to participate in available economic activities and a game version of the selection problem; 3) the pricing problem of competitors producing substitute products; 4) a game version of the facility location problem; and 5) a game with players determining their optimal usage of available products. A fixed point approach establishes the existence of a pure equilibrium point for certain submodular games. Two algorithms which correspond to fictitious play in dynamic games generate sequences of feasible join...

Donald M. Topkis

Papers

Equilibrium Points in Nonzero-Sum n-Person Submodular Games