Volume 10, Issue 1

I analyze investment and pricing incentives in a differentiated products framework with uncertain demand. Firms choose production capacities before observing demand and choose prices after demand is realized. Unlike previous models, when firms are identical, symmetric pure-strategy equilibria exist, even in the presence of very low capacity costs. The equilibrium outcomes are significantly different from the equivalent Cournot model. Firms choose to underutilize their capacity at times of low demand, and hold more capacity than predicted by Cournot. I show with a simple policy example that even the sign of the comparative statics may differ between the two models.

We study information revelation in markets with pairwise meetings. We focus on the one-sided case and perform a dynamic analysis of a constant entry flow model. The same question has been studied in an identical framework in Serrano and Yosha (1993) but they limit their analysis to the stationary steady states. Blouin and Serrano (2001) study information revelation in a one-time entry model and obtain different results from the ones of Serrano and Yosha (1993). We establish that the main difference is not due to the steady state analysis but to the differences concerning the entry assumption.

This paper studies the effects of principal's risk aversion on principal-agent relationship under hidden information. It finds that the agent's equilibrium effort increases and approaches the efficient level as the principal's risk aversion increases and tends to infinity. Allowing for random participation by the agent, his effort can be efficient even when the principal's risk aversion is finite. For the case of common agency with random participation, it is optimal for the principals to make the agent the residual claimant on profits and the principals' net profits monotonically decrease to zero when their risk aversion tends to infinity.

A firm's innovation process requires employees to develop novel ideas and to coordinate with each other to turn the tacit knowledge embodying these ideas into better products and services. Such work outcomes provide signals about employees' abilities to the labor market, and therefore career concerns arise. The effects of career concerns can both be ‘good' (enhancing incentives for effort in developing ideas) and ‘bad' (preventing voluntary coordination). Our model shows how a firm can take these conflicting forces into account through the design of its explicit incentive system and the way it organizes work processes.

We interpret the discriminatory power, r, in the Power Contest Success Function (Tullock, 1980) as the contest designer's accuracy level. We look at the cases where two contestants are heterogeneous in ability and construct an equilibrium set for r > 0. We find that if the contestants are sufficiently different in ability, there always exists an optimal accuracy level for the contest designer. Additionally, as the difference in their abilities increases, the optimal accuracy level decreases.

This paper investigates the use of reputation in an economy where principals hire agents for two different kinds of tasks, in which the agents have differing aptitudes. Principal-agent matches are remade every period, but a principal can acquire some information on the past behavior of her current agent. I consider two different reputation mechanisms—one in which an agent's past record of defections makes no reference to the kind of task (Integrated Reputation), and another in which information about past defections is available separately for each task (Fragmented Reputation). The two kinds of reputation can be interpreted as "personal honor" and performance record (e.g. credit history) respectively.I first characterize the equilibria under the two mechanisms and make some welfare comparisons, showing that IR strictly welfare dominates FR over a significant range of parameter values. I then show that, when both mechanisms are available, integrated reputation will not be used in equilibrium by principals. Thus if the economy is in equilibrium using only the IR mechanism, and the FR mechanism becomes subsequently available, then IR will become obsolete. In the appropriate ranges of parameter values, this change reduces welfare.

I study efficient risk-sharing in an endowments economy when enforcement is achieved by the threat of reversion to punishments that may be less severe than autarkic consumption. I characterize (up to a technical condition) the set of allocations that may be interpreted as efficient with respect to some punishment convention. The conditions rationalizing such efficiency are very weak; they are (i) resource exhaustion, (ii) satisfaction of individual rationality constraints at each continuation, and (iii) finiteness of the value of the allocation under the implicit decentralizing price system. I show how efficient allocations may be decentralized, and I state versions of the Welfare Theorems for these economies.

In this paper, I analyze an example in which two perfectly informed experts advise a decision maker. Each expert has private information about her own bias. I show that consulting two experts is better than consulting just one. I compare the efficiency of information transmission between simultaneous, sequential, and hierarchical forms of communication. I show that simultaneous communication achieves the highest efficiency, followed by sequential and hierarchical communication. However, hierarchical communication, in which a second expert chooses whether to block the first expert's message, achieves a moderate level of efficiency, even though the decision maker receives only one message. Finally, there are preference settings in which both sequential and hierarchical communication are superior to simultaneous communication.

In a model with internal and external risks together with incentive problems, this paper investigates the role of a risky environment on contractual incompleteness. We consider a typical employment contract with an extra control option. This option is contractable ex ante, exercisable ex post, and good for incentives. But, the employer may choose not to have it in a contract. We identify some interesting circumstances under which the option is not in the optimal contract. Our main findings are that (1) external risks determine contractual incompleteness, and (2) a complete contract can better handle incentives, while an incomplete contract can better handle external risks. Hence, our analysis of incomplete contracts is somewhat consistent with Williamson's (1985) idea of low-powered incentives inside the firm and high-powered incentives outside the firm.

In two-player contests, optimal delegation involves giving the agent incentives to maximize the principal's payoff while in contests with more than two players incentives will be different from the principal's payoff maximization. These results are related to the evolutionary stability of payoff-maximizing preferences in the model of indirect evolution in general symmetric games, which depends on the slope of the reaction function being zero at equilibrium. Further examples of the relationship are also discussed.

This paper shows that the quality scores in sponsored search auctions can be optimally chosen to extract all the advertisers' surplus. The reason for the full extraction result is that the quality scores may effectively set all the bidders' valuations equal to the highest valuation, which induces intense bidding competition.

The ability to commit to a contract may increase a player's payoff. In a repeated relationship, the lack of a complete contingency contract is usually explained by the presence of contracting costs. We study optimal contracts in a specific class of credibility models: relationships in which the surplus comes solely from screening. We show that the optimal contract is to reproduce the Perfect Bayesian Equilibrium of the game without commitment. In this sense, sequential rationality constraints do not bind. Therefore, we provide an alternative explanation for why a specific class of long-term relationships may often not be contracted upon.

When communicating with an uninformed decision maker, the motives behind an expert's message are often unclear. To explore this and investigate its impact on organizational design, we extend the cheap-talk model of Crawford and Sobel (1982) to allow for uncertainty over the expert's bias. We find that, in contrast to Dessein (2002), it is possible that the decision maker prefers communication to delegation; that is, it can be optimal for a decision maker to retain control and to solicit advice from the expert.

This paper analyzes a model of social learning in a social network. Agents decide whether or not to adopt a new technology with unknown payoffs based on their prior beliefs and the experiences of their neighbors in the network. Using a mean-field approximation, we prove that the diffusion process always has at least one stable equilibrium, and we examine the dependence of the set of equilibria on the model parameters and the structure of the network. In particular, we show how first and second order stochastic dominance shifts in the degree distribution of the network impact diffusion. We find that the relationship between equilibrium diffusion levels and network structure depends on the distribution of payoffs to adoption and the distribution of agents' prior beliefs regarding those payoffs, and we derive the precise conditions characterizing those relationships. For example, in contrast to contagion models of diffusion, we find that a first order stochastic dominance shift in the degree distribution can either increase or decrease equilibrium diffusion levels depending on the relationship between agents' prior beliefs and the payoffs to adoption. Surprisingly, adding more links can decrease diffusion even when payoffs from the new technology exceed those of the status quo in expectation.

This note analyzes a model of a monopolist selling multiple goods to a continuum of heterogeneous consumers. The implementation of Direct Revelation Mechanisms is analyzed in that setting, finding that it is possible for the monopolist to implement all Stochastic Incentive Compatible Mechanisms by committing to post a decreasing sequence of prices. The posted prices depend on time and have the desirable property of being step functions. When the optimal mechanisms are stochastic, it is optimal for the monopolist to price discriminate over time, contrary to the conventional wisdom that a single-good monopolist committed to an ex-ante price strategy will not price discriminate.

Rationalizability is a widely accepted solution concept in the study of strategic-form games with complete information and is fully characterized in terms of assumptions on the rationality of the players and common certainty of rationality.Battigalli and Siniscalchi extend rationalizability taking as given some exogenous restrictions on players' beliefs and derive the solution concept called ?-rationalizability. This new solution concept has been applied to games with incomplete information as well as dynamic games.On this note, I focus on games with incomplete information and characterize ?-rationalizability with a new notion of iterative dominance that is able to capture the additional hypothesis on players' beliefs.

We examine an environment with n voters, each with a private value over two alternatives. We compare the social surplus of two mechanisms for deciding between them: majority voting and shouting. In majority voting, the choice with the most votes wins. With shouting, the voter who shouts the loudest (sends the costliest wasteful signal) chooses the outcome. We find that it is optimal to use voting in the case where n is large and the value for each particular alternative of the voters is bounded. For other cases, the superior mechanism is depends upon the order statistics of the distribution of values.

Sequential procurement of multiple contracts/lots is widespread and often regularly repeated. We analyze how sequentiality and its interaction with asymmetries across bidders and lots affect the sustainability of supplier/bidder collusion. Sequential procurement stabilizes supplier collusion (compared to simultaneous procurement) by allowing not only to identify or punish deviations within the sequence, but also to allocate the “last lot” to the bidder with the highest incentive to defect. We then analyze how to counteract these effects by exploiting (or creating) asymmetries in the value of lots, finding that the most effective policy procures the most valuable lot at the end of each sequence.

This paper develops an intertemporal model in which individuals care about consumption not only for its own sake, but also for the status it implies. By putting an additive status term into the utility function, I show that the level of inequality in the initial wealth distribution affects individuals’ saving and consumption behavior. The direction of the distortion in intertemporal choice relative to the standard model without a concern for status depends on the elasticity of intertemporal substitution in the utility from absolute consumption. In particular, I prove that, for conventional parameter values of the elasticity (e.g. CES parameter larger than one), people save less than what they do without the status concern but the magnitude of this decrease is reduced by the concern for future status. It is also possible that people save more than what they do without the status concern. I also analyze how changes in the initial wealth distribution affect saving. For example, when wealth is Pareto distributed, for a reasonable parameterization, the rich save more and the poor save less when society gets more unequal, which implies that inequality is self-enforcing in this economy. Finally, the resulting allocation is Pareto inefficient due to the externalities generated by the concern for status.

We model a hierarchy consisting of a fixed number of heterogeneous agents, each of which reports (possibly distorted) information to its direct superior who can detect and correct the misreport with some probability. Two problems are simultaneously considered: designing the efficient hierarchy structure and configuring the agents who are heterogeneous in their trustworthiness. We develop the Unimprovability Principle, which is an analogy of Bellman Principle. By applying the principle, we show that efficiency requires only the least reliable agent in any rank to have subordinates.

We show in a simple duopoly model of vertical differentiation that when a welfare maximizing regulator wishes to ensure entry while avoiding strategic quality underprovision, regulating the incumbent's capacity is preferable to imposing a “Minimum Quality Standard” on products. In order to establish this result, we make an original contribution to the study of Bertrand-Edgeworth competition in a market with differentiated products.

In this paper, we analyze successive oligopolies where downstream firms share the same decreasing returns technology of the Cobb-Douglas type. We stress the differences between the conclusions obtained under this assumption and those resulting from the traditional literature in which output firms use a constant returns technology. It is shown that when firms use a decreasing returns technology, (i) the profit of a downstream firm can decrease when the upstream market is more competitive; (ii) the input price does not tend to the corresponding marginal cost when the number of firms in both markets tends to infinite; and (iii) double marginalization is lower. Finally, the effects of mergers are revisited to highlight the role played by the technology of output firms.

The paper investigates the credibility of an intermediary's advice in a bilateral trade model. A seller and a buyer with private and independent valuations exchange a unit of good. Trade is mediated by an intermediary, who observes a coarse signal about the buyer's valuation and may reveal it to the seller before bargaining. We show that if the broker gets a fixed per-transaction fee, he can fully transmit information via cheap talk. This information transmission increases ex ante welfare of the seller and the broker but has an ambiguous impact on the buyer. We show that limits to informative communication may arise if the intermediary observes signals about valuations of both participants or because of competition between intermediaries. Finally, using mechanism design approach, we show that choosing an appropriate system of two-part tariffs allows the intermediary to secure the same expected profit as in the optimal direct mechanism.

A series of experiments suggest that, compared to the Bayesian benchmark, people may either underreact or overreact to new information. We consider a setting where agents repeatedly process new data. Our main result shows a basic distinction between the long-run beliefs of agents who underreact to information and agents who overreact to information. Like Bayesian learners, non-Bayesian updaters who underreact to observations eventually forecast accurately. Hence, underreaction may be a transient phenomenon. Non-Bayesian updaters who overreact to observations eventually forecast accurately with positive probability but may also, with positive probability, converge to incorrect forecasts. Hence, overreaction may have long-run consequences.

The paper considers the consequences of competition between two widely used exchange mechanisms, a “decentralized bargaining'' market, and a “centralized'' market. In every period, members of a large heterogenous group of privately-informed traders who each wish to buy or sell one unit of some homogenous good may opt for trading through one exchange mechanism. Traders may also postpone their trade to a future period. It is shown that trade outside the centralized market completely unravels. In every strong Nash equilibrium, all trade takes place in the centralized market. No trade ever occurs through direct negotiations.

We consider the effect of giving incentives to ordinary citizens to report potential criminal activity. Additionally we look at the effect of 'profiling' and biased reporting. If police single out or profile a group for more investigation, then crime in the profiled group decreases. If a certain group is reported on more frequently through biased reporting by citizens, crime in the group reported on actually increases. In the second model, we consider a neighbourhood structure where individuals get information on possible criminal activity by neighbours on one side and decide whether to report or not based on the signal. When costs of reporting are low relative to the cost of being investigated, the costs of investigation increase in the number of reports and there is at least one biased individual. We show there is a "contagion equilibrium" where everyone reports his or her neighbour.

We consider homogeneous two-sided markets, in which connected buyer-seller pairs bargain and trade repeatedly. In this infinite market game with exogenous matching probabilities and a common discount factor, we prove the existence of equilibria in stationary strategies. The equilibrium payoffs are given implicitly as a solution to a system of linear equations. Then, we endogenize the matching mechanism in a link formation stage that precedes the market game. When agents are sufficiently patient and link costs are low, we provide an algorithm to construct minimally connected networks that are pairwise stable with respect to the expected payoffs in the trading stage. The constructed networks are essentially efficient and consist of components with a constant buyer-seller ratio. The latter ratio increases (decreases) for a buyer (seller) that deletes one of her links in a pairwise stable component.

We design a Generalized Position Auction for players with private values and private budget constraints. Our mechanism is a careful modification of the Generalized English Auction of Edelman, Ostrovsky and Schwarz (2007). By enabling multiple price trajectories that ascent concurrently we are able to retrieve all the desired properties of the Generalized English Auction, that was not originally designed for players with budgets. In particular, the ex-post equilibrium outcome of our auction is Pareto-efficient and envy-free. Moreover, we show that any other position auction that satisfies these properties and does not make positive transfers must obtain in ex-post equilibrium the same outcome of our mechanism, for every tuple of distinct types. This uniqueness result holds even if the players' values are fixed and known to the seller, and only the budgets are private.

This paper examines a reputation-based mechanism that sustains the provision of high quality in the presence of competition among providers, where the incentive for high-quality production comes from a reputation premium: firms with higher reputations charge higher prices. The way we model the market highlights the fact that prices are not solely determined from consumers' willingness to pay as in the monopolistic setting studied in the previous literature. In effect, equilibrium prices are determined endogenously, from the interaction of the distribution of consumers' valuations for high quality and the distribution of firms' reputations—the demand and the supply sides of the market, respectively. This paper shows that: (i) there is a steady-state distribution of reputations, a result that allows the study of a stationary equilibrium; (ii) there are parameter configurations for which the existence of a high-quality equilibrium is guaranteed, and where the incentives for high quality production in the repeated game depend on the shape of the price function; and (iii) the Walrasian-equilibrium price function depends on the shape of the steady-state distribution of reputations, and the assignment of consumers to firms with different reputation levels in such an equilibrium is positively assortative if quality is a normal good.

In this paper we provide a taxonomy of price cap regulation in oligopoly under demand uncertainty. We show that independently of the nature of uncertainty high price caps always increase production and welfare as compared to setting no price cap. We also derive conditions on the demand distribution under which a price cap close to marginal cost can be optimal and when it is not. For demand distributions with an increasing hazard rate we show that price regulation under demand uncertainty can be viewed as a well behaved extension of the analysis for deterministic demand. For this class of distributions we characterize the optimal price cap, which is unique and may or may not be close to marginal cost. Our general framework nests the limit case of deterministic demand as well as results by Earle et al. (2007), who have shown that standard arguments supporting the imposition of price caps may break down in the presence of demand uncertainty.

We show that with more than two options, a discrete choice model cannot generate linear demand. In doing so, we demonstrate a prediction of such discrete choice models that is falsifiable based on local second-order properties of demand.

In all the existing literature on survival in heterogeneous economies, the rate at which an agent vanishes in the long run relative to another agent can be characterized by the difference of the so-called survival indices, where each survival index only depends on the preferences of the corresponding agent and the properties of the aggregate endowment. In particular, one agent experiences extinction relative to another (that is, the wealth ratio of the two agents goes to zero) if and only if she has a smaller survival index. We consider a simple complete market model and show that the survival index is more complex if there are more than two agents in the economy. In fact, the following phenomenon may take place: even if agent one experiences extinction relative to agent two, adding a third agent to the economy may reverse the situation and force the agent two to experience extinction relative to agent one. We also calculate the rates of convergence.

We analyze a symmetric Bayesian game in which two players individually contribute to fund a discrete public good; contributions are refunded if they do not reach a threshold set by the seller of the good. We characterize the distributions of players' private values that can support a symmetric equilibrium in continuous piecewise-linear strategies, and we calculate these strategies. Allowing the seller to charge an entry fee before players make their private contributions, we show these piecewise-linear equilibrium strategies maximize the seller's expected profit over all incentive compatible selling mechanisms.

The Hotelling model with finite consumer reservation price is, in its various forms, perhaps the canonical model of horizontal product differentiation. Yet the following key aspects of this model are little understood: (i) the existence of asymmetric price equilibria when consumers have unit demands and (ii) for a very broad set of model specifications, the non-monotonicity of price as a function of consumers' transportation cost, i.e., the degree of product differentiation in the market. We provide a complete characterization of the asymmetric equilibria, show that they exist for a comparatively "wide" range of markets, and argue that their existence is robust to various extensions of the prototype model. Introducing elasticity into consumer demands suppresses the kink in the firms' demand functions and ensures the uniqueness (and symmetry) of the price equilibrium. However, the key perverse comparative static of the symmetric kinked equilibrium, decreasing price as a function of transport cost, survives relaxation of the unit-demand assumption. Indeed the symmetric kinked equilibrium of the unit-demand case is a special case of a general but largely unexplored set of equilibria in the Hotelling model we call weak duopoly. Weak-duopoly equilibria exist for intermediate values of transportation cost for a very broad class of consumer demands. They occupy a comparatively wide range of the model parameter space, and firm behavior in weak duopoly differs fundamentally from that which occurs for lower values of the transportation cost, or when consumers have no reservation price.

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the previous analysis of the problem is the so-called uniform rule. Thomson (1995b) proved that the uniform rule is the only rule satisfying Pareto optimality, no-envy, one-sided population-monotonicity, and replication-invariance. Replacing one-sided population-monotonicity by one-sided replacement-domination yields another characterization of the uniform rule (Thomson, 1997a). Until now, the independence of replication-invariance from the other properties in these characterizations was an open problem. In this note we prove this independence by means of a single example.

In practice, collusive bidders' rings in English auctions with a single object frequently distribute collusive gains among ring members via sequences of re-auctions called knockouts. The present paper introduces a model of sequences of knockouts under the situation in which each bidder has information on his evaluation and the order of the evaluations of all bidders for the object. The present paper examines the distributive function of sequences of knockouts from the viewpoint of cooperative game theory. Each sequence of knockouts yields an element of the core, two particular sequences yielding the Shapley value and the nucleolus respectively. The present paper highlights the sequence of knockouts yielding the nucleolus.

We develop a model of a contest between two political candidates who may care about their reputations separately from how they affect the election outcome. In the game's first stage, each candidate chooses to maintain his maximum reputation or to shirk to lower it. In the second stage, candidates undertake positive or negative campaigns. We allow the magnitudes of reputational effects of positive and negative campaigns, and the relative importance candidates place on reputation and winning, to vary. Under many parameter values, candidates shirk in order to either decrease negative campaigning in the second stage or to increase their probability of winning the election. This result persists even when some of the main assumptions of the model are relaxed.

We analyze a game in strategic form, where each player's payoff depends on his action and his social status, which is given by his rank in the actions distribution. Our focus is on the relation between the degree of heterogeneity among status-seeking players and the distribution of their Nash equilibrium actions. We find that if among players intrinsic concerns are sufficiently important relative to status concerns, individual equilibrium actions diverge, but if status concerns are relatively important, individual equilibrium actions are the same. Another key result of the analysis is that, in contrast to what is usually claimed, status seeking need not always be socially inefficient. If players are sufficiently heterogeneous, there exists a Nash equilibrium that is unique, separating, and Pareto efficient.

This paper provides necessary and sufficient conditions for the existence of a pure strategy Bertrand equilibrium in a model of price competition with fixed costs. It unveils an interesting and unexplored relationship between Bertrand competition and natural monopoly. That relationship points out that the non-subadditivity of the cost function at the output level corresponding to the oligopoly break-even price, denoted by D(pL(n)), is sufficient to guarantee that the market sustains a (not necessarily symmetric) Bertrand equilibrium in pure strategies with two or more firms supplying at least D(pL(n)). Conversely, the existence of a pure strategy equilibrium ensures that the cost function is not subadditive at every output greater than or equal to D(pL(n)).

The main contribution of this paper is to place smooth infinite economies in the setting of the equilibrium manifold and the natural projection map à la Balasko. We show that smooth infinite economies have an equilibrium set that has the structure of a Banach manifold and that the natural projection map is smooth. We define regular and critical economies, and regular and critical prices, and we show that the set of regular economies coincides with the set of economies whose excess demand function has only regular prices. Generic determinacy of equilibria follows as a by-product.

In this note, we extend the result of Sato (2010) to economies with unbounded-from-below choice sets: we prove the existence of a competitive equilibrium (to be exact, a quasi-equilibrium) by assuming “boundary satiation” introduced in Sato (2010) and the “strong compactness of the individually rational utility set” introduced in Martins-da-Rocha and Monteiro (2009). As a result, we obtain a new equilibrium existence theorem that can be applied to the case in which choice sets are unbounded from below and satiation occurs only inside the set of individually rational feasible choices. We also investigate the relationships between boundary satiation and some other conditions concerning satiation provided in the literature.

Fixing a risky intertemporal, interagent consumption profile, its total cost is the total willingness to pay for smoothing everyone's consumption. It decomposes into a micro cost that captures the inefficiency in the cross-sectional distribution of total consumption, risky as it is, and a macro cost that captures the additional benefit of eliminating the risk in total consumption, once efficiently redistributed.We consider the risk that a household experiences income mobility and the consequent consumption mobility. U.S. panel data estimates a consumption profile for which we compute the costs. The total cost is 9-18% of total initial consumption for CRRA parameters 1.25-3.5. Of this, 80-90% is the micro cost and only 10-20% is the macro cost. The magnitude of these results, and in particular the relative importance of the micro cost, is in line with previous empirical evidence.Motivated by this evidence we develop the theory of micro cost. Moreover, because the micro cost does not admit a closed form, for general preferences, we lay out an approximation method.

In this article, I analyze a class of contest success functions (CSFs) that satisfy Luce's Choice Axiom. I show that the functional forms of these CSFs can be fully identified if they are characterized by a partial differential equation (PDE), which has several intuitive economic interpretations. This PDE approach provides foundations for popular CSFs and their generalizations.

We extend the revealed preference theory of consumer’s behavior originating in Samuelson’s Weak Axiom of Revealed Preference to simultaneously permit both non-singleton choice sets and random choice. We provide a consistency postulate for demand behavior when such behavior is represented in terms of a stochastic demand correspondence. When the consumer spends his or her entire wealth, our rationality postulate is equivalent to a condition we term “stochastic substitutability.” This equivalence generates as special cases in most of the basic results regarding consumers’ demand behavior in the existing revealed preference literature.

This paper explores implementation of efficiency in an alternating-move game. Incentives are provided with contracts that specify a scheme of monetary obligations. The analysis focuses on time-invariant payment schedules that satisfy budget balance. We derive contracting forms that generate efficient investments in Markov-perfect equilibria. Some notable solutions are highlighted: repeated transfer of ownership, partnership and Markovian expectation damages.

We examine a two-stage duopoly game in which firms advertise their existence to consumers in stage 1 and compete in prices in stage 2. Whenever the advertising technology generates positive overlap in customer bases, the equilibrium for the stage-1 game is asymmetric in that one firm chooses to remain small in comparison to its competitor. For a specific random advertising technology, we show that one firm will always be half as large as the other. No pure-strategy price equilibrium exists in the stage-2 game, and as long as there is some overlap in customer bases, the mixed-strategy price equilibrium does not converge to the Bertrand equilibrium.

This paper studies global social interactions in a stylized model of marriage and divorce with complementarities across agents. The key point of departure from traditional models of social interactions is that actions are interrelated and sequential. We establish existence and uniqueness results akin to those in traditional models. In contrast to these models, however, we show that the presence of strategic complementarities is no longer sufficient to generate a social multiplier that exceeds one in this environment. Self-fulfilling conformity, whereby a greater desire to conform at the individual level leads to greater homogeneity of choices in the aggregate, is not retained either. Some empirical implications are also discussed.

We present a dynamic duopoly model of technical innovation in which R&D costs decrease exogenously with time and inter-firm knowledge spillover lowers the second comer's R&D cost. The spillover effect only becomes available after a disclosure lag. These features allow us to identify a new type of equilibrium: the leader delays investment until the R&D cost is low enough that the follower finds it optimal to invest as soon as he can benefit from the spillover. This equilibrium is subgame perfect over a wide range of parameters and raises several interesting implications. First, in our new equilibrium, the time delay between the two R&D investments is realistically short. Second, while the presence of a spillover favors the second-mover, this benefit is not enough to rule out a first-mover advantage. Indeed, the first-mover advantage survives whenever technical progress is sufficiently fast and the disclosure lag is relatively long. Third, in case of a major innovation, our equilibrium implies under-investment, which requires a substantial public intervention in favor of the investment activity.

This paper extends the concept of weak renegotiation-proof equilibrium (WRP) to allow for costly renegotiation and shows that even small renegotiation costs can have dramatic effects on the set of equilibria. More specifically, the paper analyzes the infinitely repeated Bertrand game. It is shown that for every level of renegotiation cost, there exists a discount factor such that any collusive profit can be supported as an equilibrium outcome. Hence, any arbitrary small renegotiation cost will suffice to facilitate collusive outcomes for sufficiently patient firms. This result stands in stark contrast to the unique pure strategy WRP equilibrium without renegotiation costs, which implies marginal-cost pricing in every period. Moreover, in comparison to the findings of McCutcheon (1997), who states that renegotiation costs have to be substantial to facilitate collusion, this result points to a quite different conclusion.

We describe a simple initial indicator of whether a proposed merger between rivals in a differentiated product industry is likely to raise prices through unilateral effects. Our diagnostic calibrates upward pricing pressure (UPP) resulting from the merger, based on the price/cost margins of the merging firms' products and the extent of direct substitution between them. As a screen for likely unilateral effects, this approach is practical, more transparent, and better grounded in economics than are concentration-based methods.

Joseph Farrell and Carl Shapiro have proposed a measure of Upward Pricing Pressure (UPP) as offering a presumption of anticompetitive unilateral effects in a merger. We explain that the underlying framework (which relies on Bertrand competition) is in fact a special case of a more general merger simulation methodology. We discuss the strengths and weaknesses of the framework as a policy tool.

We reply here to a comment by Epstein and Rubinfeld to our paper on the antitrust evaluation of horizontal mergers.