Cooperation vs. competition in R&D: The role of stability of equilibrium

We consider a model in which firms first choose process R&D expenditures and then compete in an output market. We show the symmetric equilibrium under R&D competition is sometimes unstable, in which case two asymmetric equilibria must also exist. For the latter, we find, in contrast to the literature that total profits are sometimes higher with R&D competition than with research joint venture cartelization (due to the cost asymmetry of the resulting duopoly in the noncooperative case). Furthermore, these equilibria provide another instance of R&D-induced firm heterogeneity.     

Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility

This paper presents a model of stochastic oligopoly with demand uncertainty where firms endogenously choose entry timing. We examine two extreme types of market structure and show that the equilibrium correspondence that connects them is continous. With two identically sized firms, there are symmetric, Cournot type equilibria where the probability of early entry declines with greater uncertainty, and for low uncertainty two asymmetric equilibria. With one large firm with a continuum of nonatomic firms, there is a unique Stackelberg equilibrium. We conclude that the behavior of a dominant firm with a finite fringe can be approximated by Stackelberg equilibrium.Journal of Economic LiteratureClassification Numbers?: D21, L11.     

Multiple equilibria in Tullock contests

We find the sufficient conditions for the existence of multiple equilibria in Tullock-type contests, and show that asymmetric equilibria arise even under symmetric prize and cost structures. We then present existing contests where multiple equilibria exist under reasonably weak conditions.     

Equilibrium Selection and Stability for the Groves Ledyard Mechanism

In their seminal paper Groves and Ledyard (1976) construct a balanced incentive compatible mechanism that solves the free rider problem. In subsequent research, Bergstrom, Simon, and Titus (1983) prove that there exist numerous asymmetric equilibria in addition to the symmetric equilibrium. In the present paper, we explicitly solve for the additional equilibria and use computational experiments to examine the structure and stability of the set of equilibria of the Groves Ledyard Mechanism. We find that all of the equilibria found by Berstrom, Simon, and Titus are unstable and that for a high level of the punishment parameter these equilibria do not exist. Further, we find that there exists an additional boundary equilibrium for each of the equilibria found by Bergstrom, Simon, and Titus. The boundary equilibria are all stable.     

International Trade with Increasing Returns in the Transportation Sector

In this general equilibrium framework, the transportation sector is modeled as a distinct sector with increasing returns. A more advanced technology has a higher fixed cost but a lower marginal cost of production. Even with both manufacturing finns and transportation firms engaged in oligopolistic competition and optimally choosing their technologies, the model is tractable and results are derived analytically. Technology adoptions in the manufacturing sector and transportation sector are reinforcing, and multiple equilibria may exist. Firms choose more advanced technologies and the prices decrease when the size of the population is larger.     

Bidding for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

Elections,Information, and State‐Dependent Candidate Quality

The quality of political candidates often depends on the current state of the world, for example because their personal characteristics are more valuable in some situations than in others. We explore the implications of state‐dependent candidate quality in a model of electoral competition where voters are uncertain about the state. Candidates are fully informed and completely office‐motivated. With a reasonable restriction on voters' beliefs, an equilibrium where candidates' positions reveal the true state does not exist. Nonrevealing equilibria always exist. Some main findings are that candidates' positions can diverge more in equilibrium when they differ more in state‐dependent quality and when the electorate is less well informed.     

The determination of public tuition fees in a mixed education system: A majority voting model

We study the determination of public tuition fees through majority voting in a vertical differentiation model where agents' returns on educational investment differ and public and private universities coexist and compete in tuition fees. The private university offers higher educational quality than its competitor, incurring higher unit cost per trained student. The tuition fee for the state university is fixed by majority voting while that for the private follows from profit maximization. Then agents choose to train at the public university or the private one or to remain uneducated. The tax per head adjusts in order to balance the state budget. Because there is a private alternative, preferences for education are not single‐peaked and no single‐crossing condition holds. An equilibrium is shown to exist, which is one of three types: high tuition fee (the “ends” are a majority), low tuition fee (the “middle” is a majority), or mixed (votes tie). The cost structure determines which equilibrium obtains. The equilibrium tuition is either greater (majority at the ends) or smaller (majority at the middle) than the optimal one.     

Nonconvergent Electoral Equilibria under Scoring Rules: Beyond Plurality

We use Hotelling's spatial model of competition to investigate the position‐taking behavior of political candidates under a class of electoral systems known as scoring rules, though the model also has a natural interpretation in the firm location context. Candidates choose ideological positions so as to maximize their support in society. Convergent Nash equilibria in which all candidates adopt the same policy were characterized by Cox (1987). Here, we investigate nonconvergent equilibria, where candidates adopt divergent policies. We identify a number of classes of scoring rules exhibiting a range of different equilibrium properties. For some of these, nonconvergent equilibria do not exist. For others, nonconvergent equilibria in which candidates cluster at positions spread across the issue space are observed. In particular, we prove that the class of convex rules does not have Nash equilibria (convergent or nonconvergent) with the exception of some derivatives of Borda rule. We also look at “two‐party” equilibria. Implications for the firm location model are discussed.     

Broadcasting Opinions with an Overconfident Sender*

We analyze a model where an altruistic, but possibly overconfident sender broadcasts one of a finite set of messages to rational receivers. If broadcasting is costless and the sender is rational, there is an informationally efficient equilibrium, but multiple equilibria may arise, and asymmetric equilibria might be more informative than the symmetric equilibrium even if the prior is symmetric. Although overconfidence on the part of the sender reduces informativeness in some cases, it may also eliminate less informative equilibria and lead to better information transmission. Overconfidence can also improve the informativeness of the message when broadcasting is costly.     

A Political Economy Model of Earnings Mobility and Redistribution Policy

This paper presents a politico‐economic model that includes a mutual link between life cycle earnings mobility and redistributive politics. The model demonstrates that when an economy features a high opportunity of upward mobility and high risk of downward mobility, it attains a unique equilibrium where unskilled, low‐income agents support a low redistribution because of the hope of upward mobility in future. In contrast, the economy attains multiple equilibria when mobility opportunity and risk are low: one is an unskilled‐majority equilibrium defined by low mobility and the other is a skilled‐majority equilibrium defined by high mobility. The paper gives a comparison between the political equilibrium and the social planner's allocation in terms of mobility, and shows that the skilled‐majority equilibrium realizes mobility close to the optimal one.     

A second chance at success: A political economy perspective

This paper characterizes a stationary Markov-perfect political equilibrium where agents vote over income taxation that distorts educational investment. Agents become rich or poor through educational investment, and the poor have a second chance at success. The results show the following concerning the cost of a second chance. First, when the cost is low, the economy is characterized by high levels of upward mobility and inequality, and a low tax burden supported by the poor with prospects for upward mobility. Second, when the cost is high, there are multiple equilibria with various patterns of upward mobility, inequality and redistribution. Numerical examples show that the shift from a high-cost economy to a low-cost economy may reduce social welfare.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Hotelling–Downs Competition with Free Entry When Voters Have an Option to Contest

Osborne shows that for almost all distributions of voters’ preferences, a pure strategy Nash equilibrium does not exist in the classical Hotelling–Downs model of electoral competition with free entry. We show that equilibrium is generically possible if in addition one allows voters an option to announce their candidacy to compete side‐by‐side with office‐seeking players. The model studied in this paper renders Osborne and the celebrated citizen‐candidate model à la Osborne and Slivinski as two extreme cases. We characterize the equilibrium set with two central questions: (i) can there be equilibria where only voters contest? and (ii) are equilibria with contesting office‐seeking players possible? We also show that in our general setting, extremists are typically voter‐candidates so that in every two‐party contest, office‐seeking politicians stay out of competition.     

QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

Public input competition

Public investment in infrastructure may help create agglomeration economies, by attracting mobile factors such as skilled labour. Competition among regions in public investment can then be destructive. This paper analyzes the Nash equilibria to a simple model of public input competition. Even though the regions are assumed identical, the equilibrium may not be symmetric. The problem with non-cooperative behaviour is not (only) that regions invest too much, but that too many regions may choose to invest. Depending on the parameter values, the Nash equilibrium may be efficient, may be inefficient or may not exist (at least not in pure strategies). Better mobility among regions leads to more aggressive competition. The analysis suggests that rents from public investment may be dissipated by governments' competition to attract mobile factors.     

An Asymptotic Solution for Sealed Bid Common-Value Auctions with Bidders Having Asymmetric Information

We investigate a first-price common-value auction where bidders have asymmetric information about an item of unknown value. We compute the unique Nash equilibrium when the bidders are constrained to translation-invariant bid functions. Further, this profile of bid functions is also an asymptotic Nash equilibrium (without the constraint on the bidders' strategies) as the a priori distribution of the true value becomes increasingly diffuse. All bidders have positive expected profits at equilibrium. In the second-price analogue with two bidders there is a continuum of Nash equilibria in which both bidders have positive expected profits. Journal of Economic Literature Classification Number: C7.     

Implementing efficient graphs in connection networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash implementation (PNI), requires that the efficient outcome always be implemented in a Nash equilibrium and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism and other asymmetric variations are the only mechanisms that meet PNI. These mechanisms are also characterized under strong Nash implementation. The second property, weakly Pareto Nash implementation (WPNI), requires that the least inefficient equilibrium Pareto dominates any other equilibrium. The egalitarian mechanism (EG) and other asymmetric variations are the only mechanisms that meet WPNI and individual rationality. EG minimizes the price of stability across all individually rational mechanisms.     

How urbanization affect employment and social interactions

We develop a model where the unemployed workers in the city can find a job either directly or through weak or strong ties. We show that, in denser areas, individuals choose to interact with more people and meet more random encounters (weak ties) than in sparsely populated areas. We also demonstrate that, for a low urbanization level, there is a unique steady-state equilibrium where workers do not interact with weak ties, while, for a high level of urbanization, there is a unique steady-state equilibrium with full social interactions. We show that these equilibria are usually not socially efficient when the urban population has an intermediate size because there are too few social interactions compared to the social optimum. Finally, even when social interactions are optimal, we show that there is over-urbanization in equilibrium.