Private monitoring with infinite histories

This paper develops new recursive methods for studying stationary sequential equilibria in games with private monitoring. We first consider games where play has occurred forever into the past and develop methods for analyzing a large class of stationary strategies, where the main restriction is that the strategy can be represented as a finite automaton. For a subset of this class, strategies which depend only on the players’ signals in the last k periods, these methods allow the construction of all pure strategy equilibria. We then show that each sequential equilibrium in a game with infinite histories defines a correlated equilibrium for a game with a start date and derive simple necessary and sufficient conditions for determining if an arbitrary correlation device yields a correlated equilibrium. This allows, for games with a start date, the construction of all pure strategy sequential equilibria in this subclass.

Standards Coalitions Formation and Market Structure in Network Industries

We discuss the formation of technical standards platforms in industries with network externalities where firms are free to choose their degree of technical compatibility with competitors. In our model, firms choose affiliation to a technical standards coalition in the first stage of a game, and play an oligopoly game in the second stage. In adding itself to a technical standards coalition, a firm benefits from the network effects of the whole coalition, but also faces increased competition in the output market from other firms in the coalition. Also, the increase of the size of the coalition changes the competitive position of members of that coalition relative to other firms. We find that the extent and size of coalitions at equilibrium depends crucially on the degree of the intensity of network effects. When network effects are very strong, full compatibility prevails. When externalities are slightly weaker, two standards coalitions are formed, a singleton, and one with all remaining firms. On the other extreme, for very weak network effects, the equilibrium is total incompatibility, and for slightly more intense network effects, coalitions are of small size. We characterize a number of other equilibria for intermediate strengths of network externalities.standards, coalition formation, network effects

Selling Information

We study a dynamic buyer-seller problem in which the good is information and there are no property rights. The potential buyer is reluctant to pay for information whose value to him is uncertain, but the seller cannot credibly convey its value to the buyer without disclosing the information itself. Information comes as divisible hard evidence. We show how and why the seller can appropriate a substantial fraction of the value through gradual revelation, and how the entire value can be extracted with the help of a mediator.Value of information, Dynamic game

Selling Information

We characterize optimal selling protocols/equilibria of a game in which an Agent first puts hidden effort to acquire information and then transacts with a Firm that uses this information to take a decision. We determine the equilibrium payoffs that maximize incentives to acquire information. Our analysis is similar to finding ex ante optimal self-enforcing contracts since information sharing, outcomes and transfers cannot be contracted upon. We show when and how selling and transmitting information gradually helps. We also show how mixing/side bets increases the Agent’s payoff. In fact, she can get the entire surplus with rich enough tests.Value of information, Dynamic game

The role of information in repeated games with frequent actions

We show that the ways incentives can be provided during dynamic interaction depend very crucially on the manner in which players learn information. This conclusion is established in a general stationary environment with noisy public monitoring and frequent actions. The monitoring process can be represented by a sum of a multi-dimensional Brownian component and a jump process. We show that jumps can be used to provide incentives both with transfers and value burning while continuous information can be used to provide incentives only with transfers. Also, it is asymptotically optimal to use the cumulative realization of the Brownian component linearly. Additionally, we approximate the equilibrium payoff set for fixed small discount rates as the periods become short by a series of linear programming problems. These problems highlight how the two types of information can be used to provide incentives.repeated games, dynamic incentives, frequent moves

Inflation and Price Setting in a Natural Experiment

We analyze the behaviour of prices using a large disaggregated data set for Poland during transition from a planned to a market economy. The size of price changes and the frequency of adjustment both fall as the inflation rate declines. Price setters follow a mixture of state- and time-contingent policies. We find that price setters are forward-looking. Intermarket price variability increases with inflation and the effect of expected inflation is much stronger than the effect of unexpected inflation. So the bottom line is this: it takes sellers of sausage, eggs, toothpaste, vacuum cleaners, car-wash operators etc. just a few years to figure out how to adjust prices in a market environment. Our results support both the menu cost, and the rational expectations, hypotheses.

Collusion under Monitoring of Sales

Collusion under imperfect monitoring is explored when firms?prices are private information and their quantities are public information; an information structure consistent with several recent price-fixing cartels such as those in lysine and vitamins. For a class of symmetric duopoly games, it is shown that symmetric equilibrium punishments cannot sustain any collusion. An asymmetric punishment is characterized which does sustain collusion and it has the firm with sales exceeding its quota compensating the firm with sales below its quota. In practice, cartels have performed such transfers through sales among the cartel members.

Revenues in the 700 MHz Spectrum Auction

There have been several comments that criticize auction rules that prevent the two major low-frequency incumbents from winning all of the newly available spectrum and incorporating it into their proprietary networks. Such rules include new-entrant set-asides, new-entrant bidding credits, and the open access plan. We disagree with these criticisms and argue that given the current market structure, such rules are likely to improve welfare and auction revenues. We are submitting this report to provide sound economic analysis of these claims.Auctions, spectrum auctions, market design

Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices

Motivated by recent cartel practices, a stable collusive agreement is characterized when firms' prices and quantities are private information. Conditions are derived whereby an equilibrium exists in which firms truthfully report their sales and then make transfers within the cartel based on these reports. The properties of this equilibrium fit well with the cartel agreements used in a number of markets including citric acid, lysine, and vitamins.

Economic Comments on the Design of the 700 MHz Spectrum Auction

We comment on the service and auction rules discussed in the Report and Order and Further Notice of Proposed Rule Making, FCC 07-72, 27 April 2007. We recommend that the FCC designate one license for a wholesale operation that provides open access nationwide on nondiscriminatory terms. This is necessary to enable entry of new businesses offering wireless services in retail markets. It also enables local operators to offer roaming at competitive prices. The new license accords with the Commission’s policy to encourage competition, and recognizes the benefits to consumers from low prices and expanded services.Auctions, spectrum auctions, market design