Kostas Bimpikis

Abstract:

We develop a model of information exchange 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 decide which agents to form a communication link with incurring the associated cost and receive a private signal correlated with the underlying state. They then 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 is not always optimal, when the communication network induces asymptotic learning (in a large society), truthful communication is an ε-equilibrium.

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. Finally, we show how these results can be applied to several commonly studied random graph models, such as preferential attachment and Erdos-Renyi graphs.

Abstract:

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.

Abstract:

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 is 2(√ N -1)/(N-1) with N firms, and this bound is tight.

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.

Abstract:

We study the efficiency of oligopoly equilibria in a model where firms compete over prices. The motivating examples are the allocation of network flows in a communication network or of traffic in a transportation network. Contrary to most related papers, we study the case when the users are atomic, i.e., each user controls a non-negligible fraction of the total traffic. We show that competition among profit maximizing firms can reduce the overall efficiency of the system, measured as the difference between users' willingness to pay and delay costs. In particular, we characterize a tight bound of 1-N/6(N+1) on worst case efficiency in pure strategy equilibria, where N is the number of customers.