Limit-pricing as Bertrand equilibrium

Summary. We consider a Bertrand duopoly model with increasing returns to scale where one of the firms have a cost advantage and prices vary over a grid. We find that typically more than one equilibria exist. However, there are only two perfect equilibria. Moreover, as the size of the grid becomes small, both these equilibria converge to the limit-pricing outcome. Received: February 25, 2000; revised version: January 9, 2001     

Assignment models and reneging

Summary. We consider a non-cooperative assignment model where we show that any subgame perfect equilibrium is stable, and that an appropriate refinement criterion leads to the p-optimal outcome. We then consider a model with reneging and derive some interesting properties of this game. We show that in this case ‘unraveling’ may occur. Furthermore, the resulting outcome can be either stable, or unstable. Received: July 1, 1997; revised version: May 30, 1998     

Adoption of new technology and joint venture instability

We consider a joint venture between a local firm from a less developed country, and a foreign multinational. In a dynamic two period model, we demonstrate that the availability of new technology can trigger a joint venture breakdown, a result that is consistent with the empirical evidence. We find that such breakdown is more likely if the MNC is relatively patient, or, in contrast to the existing literature, there is an increase in the level of demand. Moreover, our results are robust to alternative assumptions regarding bargaining power and control.     

Public-private partnerships in micro-finance: Should NGO involvement be restricted?

This paper examines public–private partnerships in micro-finance, whereby NGOs can help in channelizing credit to the poor, both in borrower selection, as well as in project implementation. We argue that a distortion may arise out of the fact that the private partner, i.e. the NGO, is a motivated agent. We find that whenever the project is neither too productive, nor too unproductive, reducing such distortion requires unbundling borrower selection and project implementation, with the NGO being involved in borrower selection only. Further, we compare and contrast two alternative credit delivery mechanisms, the linkage mechanism (which is the focus of this paper), with the ‘Grameen’ one.     

Effects of foreign equity participation on recipient firm exports

We offer new evidence on the role of foreign investment in domestic firms’ export decisions, both at intensive and extensive margins, using balance sheet data from a panel of manufacturing firms in India. In contrast to the existing literature, we analyse the effect of foreign investment at different levels, where the levels correspond to percentages of foreign equity. We use a selection procedure to control for the potential self-selection of firms into export participation. Though we do find that foreign investment increases a domestic firm’s likelihood to export, firms with majority foreign equity are found to serve domestic market more, once the self-selection is accounted for.     

Quality cut-offs in procurement auctions

Recently the Government of India used procurement auction mechanisms with endogenously determined minimum quality. We find these auctions have no equilibrium in continuous symmetric monotonic pure strategies. This may substantiate the use of auction mechanisms with exogenously determined minimum quality.     

Generalized assignment models: with an applicationto technology transfer

Summary.  We consider a generalized assignment model where the payoffs depend on the number of matchings that take place. We formulate a simple non-cooperative game and look for subgame perfect equilibrium of this model. Existence is established for a wide class of games. We also look at a refinement criterion which, for the standard assignment model, selects the -optimal outcome as the unique equilibrium. We then apply these concepts to a model of technology transfer between domestic and foreign firms. Received: June 24, 1994; revised version October 12, 1995     

Inefficiencies in a Model of Team Formation

We consider a two period model with complete information involving three agents, two on one side of the market, and one on the other. The agents on the same side of the market bargain, among themselves, over whether to form a team or not, and also with the other agent, either singly or as a team, regarding the payoffs. We characterize the subgame perfect Nash equilibrium of this game. We find that the behavioral assumptions regarding the agents play a critical role in the outcome. If the agents are combative then the outcome is efficient. Whereas if the agents are peace loving, and the discount factor is large, then the outcome may involve delay, as well as (inefficient) team formation.     

FIRM SIZE AND PRICING POLICY

We relate pricing policy of firms to their size, where firm size is interpreted as the size of the clientele served by the concerned firm. We argue that a firm with a large clientele faces a more severe reputational backlash if it ‘reneges’, i.e., deviates from its earlier price offer. This allows the firm to effectively commit to its offers, leading to a unique equilibrium without delay. Interestingly, this equilibrium corresponds to the equilibrium of the related model that does not allow for reneging possibilities. For smaller firms, however, the reputational effects are much less intense, and consequently the equilibria may involve deviation possibilities. In this case, the equilibria are non‐unique and may involve delays as well.     

Coalition-proof Bertrand equilibria

Summary. This paper examines the coalition-proof Nash equilibria of a Bertrand model of price competition where firms supply all demand. When firms are asymmetric we prove existence and provide a sufficient condition for uniqueness. For symmetric firms, we show that an equilibrium is necessarily unique. We also examine whether this unique equilibrium outcome is implementable through a sequential move game where the firms take turns at announcing prices. Finally we examine the limiting property of such equilibria as the number of firms go to infinity.Received: 20 March 2002, Revised: 5 August 2003JEL Classification Numbers: D43, D41, L13.Correspondence to: Kunal SenguptaWe are deeply indebted to an anonymous referee for very helpful and incisive comments that led to substantial improvements in the paper. We also gratefully acknowledge the hospitality of the Department of Finance, Hong Kong University of Science and Technology where much of the work on this paper was carried out.