Price and Capacity Competition

We study the efficiency of oligopoly equilibria in a model where firms compete over capacities and prices. The motivating example is a communication network where service providers invest in capacities and then compete in prices. Our model economy corresponds to a two-stage game. First, firms (service providers) independently choose their capacity levels. Second, after the capacity levels are observed, they set prices. Given the capacities and prices, users (consumers) allocate their demands across the firms. We first establish the existence of pure strategy subgame perfect equilibria (oligopoly equilibria) and characterize the set of equilibria. These equilibria feature pure strategies along the equilibrium path, but off-the-equilibrium path they are supported by mixed strategies. We then investigate the efficiency properties of these equilibria, where "efficiency" is defined as the ratio of surplus in equilibrium relative to the first best. We show that efficiency in the worst oligopoly equilibria of this game can be arbitrarily low. However, if the best oligopoly equilibrium is selected (among multiple equilibria), the worst-case efficiency loss has a tight bound, approximately equal to 5/6 with 2 firms. This bound monotonically decreases towards zero when the number of firms increases. We also suggest a simple way of implementing the best oligopoly equilibrium. With two firms, this involves the lower-cost firm acting as a Stackelberg leader and choosing its capacity first. We show that in this Stackelberg game form, there exists a unique equilibrium corresponding to the best oligopoly equilibrium. We also show that an alternative game form where capacities and prices are chosen simultaneously always fails to have a pure strategy equilibrium. These results suggest that the timing of capacity and price choices in oligopolistic environments is important both for the existence of equilibrium and for the extent of efficiency losses in equilibrium.

Strategic delay and information exchange in endogenous social networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 160-165).This thesis studies optimal stopping problems for strategic agents in the context of two economic applications: experimentation in a competitive market and information exchange in social networks. The economic agents (firms in the first application, individuals in the second) take actions, whose payoffs depend on an unknown underlying state. Our framework is characterized by the following key feature: agents time their actions to take advantage of either the outcome of the actions of others (experimentation model) or information obtained over time by their peers (information exchange model). Equilibria in both environments are typically inefficient, since information is imperfect and, thus, there is a benefit in being a late mover, but delaying is costly. More specifically, in the first part of the thesis, we develop a model of experimentation and innovation in a competitive multi-firm environment. Each firm receives a private signal on the success probability of a research project and decides when and which project to implement. A successful innovation can be copied by other firms. We start the analysis by considering the symmetric environment, where the signal quality is the same for all firms. Symmetric equilibria (where actions do not depend on the identity of the firm) always involve delayed and staggered experimentation, whereas the optimal allocation never involves delays and may involve simultaneous rather than staggered experimentation. The social cost of insufficient experimentation can be arbitrarily large. Then, we study the role of simple instruments in improving over equilibrium outcomes. We show that appropriately-designed patents can implement the socially optimal allocation (in all equilibria) by encouraging rapid experimentation and efficient ex post transfer of knowledge across firms. In contrast to patents, subsidies to experimentation, research, or innovation cannot typically achieve this objective. We also discuss the case when signal quality is private information and differs across firms. We show that in this more general environment patents again encourage experimentation and reduce delays. In the second part, we study a model of information exchange among rational individuals through communication and investigate its implications for information aggregation in large societies. An underlying state (of the world) determines which action has higher payoff. Agents receive a private signal correlated with the underlying state. They then exchange information over their social network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking an action that is close to optimal converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the social network most agents are a short distance away from "information hubs", which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication is not always optimal, when the communication network induces asymptotic learning (in a large society), truthful communication is an equilibrium. Then, we discuss the welfare implications of equilibrium behavior. In particular, we compare the aggregate welfare at equilibrium with that of the optimal allocation, which is defined as the strategy profile a social planner would choose, so as to maximize the expected aggregate welfare. We show that when asymptotic learning occurs all equilibria are efficient. A partial converse is also true: if asymptotic learning does not occur at the optimal allocation and an additional mild condition holds at an equilibrium, then the equilibrium is inefficient. Furthermore, we discuss how our learning results can be applied to several commonly studied random graph models, such as preferential attachment and Erdos-Renyi graphs. In the final part, we study strategic network formation in the context of information exchange. In particular, we relax the assumption that the social network over which agents communicate is fixed, and we let agents decide which agents to form a communication link with incurring an associated cost. We provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Our result shows that societies with too many and sufficiently large social cliques do not induce asymptotic learning, because each social clique would have sufficient information by itself, making communication with others relatively unattractive. Asymptotic learning results if social cliques are neither too numerous nor too large, in which case communication across cliques is encouraged.by Kostas Bimpikis.Ph.D

Dynamics of information exchange in endogenous social networks

We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An \textit{underlying state} determines payoffs from different actions. Agents decide which others to form a costly \textit{communication link} with, incurring the associated cost. After receiving a \textit{private signal} correlated with the underlying state, they exchange information over the induced \textit{communication network} until taking an (irreversible) action. We define \textit{asymptotic learning} as the fraction of agents taking the correct action converging to one as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from ``information hubs'', which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication may not always be a best response, it is an equilibrium when the communication network induces asymptotic learning. Moreover, we contrast equilibrium behavior with a socially optimal strategy profile, i.e., a profile that maximizes aggregate welfare. We show that when the network induces asymptotic learning, equilibrium behavior leads to maximum aggregate welfare, but this may not be the case when asymptotic learning does not occur. We then provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Our result shows that societies with too many and sufficiently large social cliques do not induce asymptotic learning, because each social clique would have sufficient information by itself, making communication with others relatively unattractive. Asymptotic learning results either if social cliques are not too large, in which case communication across cliques is encouraged, or if there exist very large cliques that act as information hubs

Dynamics of Information Exchange in Endogenou Social Networks

We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state determines payoffs from different actions. Agents decide which others to form a costly communication link with incurring the associated cost. After receiving a private signal correlated with the underlying state, they exchange information over the induced communication network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking the correct action converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from “information hubs,” which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication may not always be a best response, it is an equilibrium when the communication network induces asymptotic learning. Moreover, we contrast equilibrium behavior with a socially optimal strategy profile, i.e., a profile that maximizes aggregate welfare. We show that when the network induces asymptotic learning, equilibrium behavior leads to maximum aggregate welfare, but this may not be the case when asymptotic learning does not occur. We then provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals inked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Our result shows that societies with 599 many and sufficiently large social cliques do not induce asymptotic learning, because each social clique would have sufficient information by itself, making communication with others relatively unattractive. Asymptotic learning results if social cliques are neither too numerous nor too large, in which communication across cliques is encouraged

Experimentation, patents, and innovation

October 8, 200

Experimentation, Patents, and Innovation

This paper studies a simple model of experimentation and innovation. Our analysis suggests that patents may improve the allocation of resources by encouraging rapid experimentation and efficient ex post transfer of knowledge across firms. Each firm receives a private signal on the success probability of one of many potential research projects and decides when and which project to implement. A successful innovation can be copied by other firms. Symmetric equilibria (where actions do not depend on the identity of the firm) always involve delayed and staggered experimentation, whereas the optimal allocation never involves delays and may involve simultaneous rather than staggered experimentation. The social cost of insufficient experimentation can be arbitrarily large. Appropriately-designed patents can implement the socially optimal allocation (in all equilibria). In contrast to patents, subsidies to experimentation, research, or innovation cannot typically achieve this objective. We also show that when signal quality differs across firms, the equilibrium may involve a nonmonotonicity, whereby players with stronger signals may experiment after those with weaker signals. We show that in this more general environment patents again encourage experimentation and reduce delays.

Dynamics of Information Exchange in Endogenous Social Networks

We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state determines payoffs from different actions. Agents decide which others to form a costly communication link with incurring the associated cost. After receiving a private signal correlated with the underlying state, they exchange information over the induced communication network until taking an (irreversible) action. We define asymptotic learning as the fraction of agents taking the correct action converging to one in probability as a society grows large. Under truthful communication, we show that asymptotic learning occurs if (and under some additional conditions, also only if) in the induced communication network most agents are a short distance away from "information hubs", which receive and distribute a large amount of information. Asymptotic learning therefore requires information to be aggregated in the hands of a few agents. We also show that while truthful communication may not always be a best response, it is an equilibrium when the communication network induces asymptotic learning. Moreover, we contrast equilibrium behavior with a socially optimal strategy profile, i.e., a profile that maximizes aggregate welfare. We show that when the network induces asymptotic learning, equilibrium behavior leads to maximum aggregate welfare, but this may not be the case when asymptotic learning does not occur. We then provide a systematic investigation of what types of cost structures and associated social cliques (consisting of groups of individuals linked to each other at zero cost, such as friendship networks) ensure the emergence of communication networks that lead to asymptotic learning. Our result shows that societies with too many and sufficiently large social cliques do not induce asymptotic learning, because each social clique would have sufficient information by itself, making communication with others relatively unattractive. Asymptotic learning results if social cliques are neither too numerous nor too large, in which case communication across cliques is encouraged.

Optimal Pricing in Networks with Externalities

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers who are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumer's usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolist's optimal pricing strategy may involve offering discounts to certain agents who have a central position in the underlying network. Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive a characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that consists of three components: (i) a nominal term that is independent of the network structure, (ii) a discount term proportional to the influence that this agent exerts over the rest of the social network (quantified by the agent's Bonacich centrality), and (iii) a markup term proportional to the influence that the network exerts on the agent. In the second part of the paper, we discuss the optimal strategy of a monopolist who can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price. Third, we assume that the monopolist can offer the good in two prices, full and discounted, and we study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard; however, we provide an explicit characterization of the set of agents who should be offered the discounted price. Next, we describe an approximation algorithm for finding the optimal set of agents. We show that if the profit is nonnegative under any feasible price allocation, the algorithm guarantees at least 88% of the optimal profit. Finally, we highlight the value of network information by comparing the profits of a monopolist who does not take into account the network effects when choosing her pricing policy to those of a monopolist who uses this information optimally