We consider a general mechanism design setting where each agent can acquire (covert) information before participating in the mechanism. The central question is whether a mechanism exists which provides the efficient incentives for information acquisition ex-ante and implements the efficient allocation conditional on the private information ex-post.
It is shown that in every private value environment the Vickrey-Groves-Clark mechanism guarantees both ex-ante as well as ex-post efficiency. In contract, with common values, ex-ante and ex-post efficiency cannot be reconciled in general. Sufficient conditions in terms of sub- and supermodularity are provided when (all) ex-post efficient mechanisms lead to private under- or over-acquisition of information.
This note shows that the optimal choice of k simultaneous experiments in a stationary multi-armed bandit problem can be characterized in terms of the Gittins index of each arm. The index characterization remains equally valid after the introduction of switching costs.
A model of repeated price competition with large buyers is analyzed. The sellers are allowed to offer different prices to different buyers and the buyers act strategically. The set of subgame perfect Equilibria is investigated under public and private monitoring.
With public monitoring the equilibrium set with large buyers expands relative to the standard model where each buyer is small and behaves myopically.
With private monitoring, where prices are not observable to the competing sellers, the set of equilibrium payoffs shrinks. In the finitely repeated game with private monitoring, all sales are made by the efficient seller. In the infinitely repeated game this result is preserved as long as the sellers condition their prices on the public history. In contrast to the finite horizon game, the set of pure strategy equilibria expands if the sellers are allowed to condition their own past prices. Comparisons are drawn to Markovian equilibria of similar dynamic games.
This note shows that the optimal choice of k simultaneous experiments in a stationary multi-armed bandit problem can be characterized in terms of the Gittins index of each arm. The index characterization remains equally valid after the introduction of switching costs.
A model of repeated price competition with large buyers is analyzed. The sellers are allowed to offer different prices to different buyers and the buyers act strategically. The set of subgame perfect Equilibria is investigated under public and private monitoring.
With public monitoring the equilibrium set with large buyers expands relative to the standard model where each buyer is small and behaves myopically.
With private monitoring, where prices are not observable to the competing sellers, the set of equilibrium payoffs shrinks. In the finitely repeated game with private monitoring, all sales are made by the efficient seller. In the infinitely repeated game this result is preserved as long as the sellers condition their prices on the public history. In contrast to the finite horizon game, the set of pure strategy equilibria expands if the sellers are allowed to condition their own past prices. Comparisons are drawn to Markovian equilibria of similar dynamic games.
This paper analyzes the optimal entry into experience goods markets with vertically differentiated buyers. We consider the case where the value of the new product is imperfectly known, but common to all buyers (common values) as well as the case where the quality is different across buyers (private values).
We distinguish between new products that are improvements to existing products and new products that are substitutes. Different types of products have qualitatively distinct diffusion paths. Improvements are introduced slowly relative to the full information case, while substitutes are introduced more aggressively. The slow entry strategy is associated with increasing supply and decreasing prices over time. The reverse pattern holds for an aggressive entry strategy
The incentives to innovate display a similar distinction. A firm with a currently inferior product opts for a large but risky innovation, whereas a currently superior producer chooses a smaller but certain innovation.
We present a model of entry and exit with Bayesian learning and price competition. A new product of initially unknown quality is introduced in the market, and purchases of the product yield information on its true quality. We assume that the performance of the new product is publicly observable. As agents learn from the experiments of others, informational externalities arise.
We determine the Markov Perfect Equilibrium prices and allocations. In a single market, the combination of the informational externalities among the buyers and the strategic pricing by the sellers results in excessive experimentation. If the new product is launched in many distinct markets, the path of sales converges to the efficient path in the limit as the number of markets grows.
We present a model of entry and exit with Bayesian learning and price competition. A new product of initially unknown quality is introduced in the market, and purchases of the product yield information on its true quality. We assume that the performance of the new product is publicly observable. As agents learn from the experiments of others, informational externalities arise.
We determine the Markov Perfect Equilibrium prices and allocations. In a single market, the combination of the informational externalities among the buyers and the strategic pricing by the sellers results in excessive experimentation. If the new product is launched in many distinct markets, the path of sales converges to the efficient path in the limit as the number of markets grows.
We consider a general model of dynamic common agency with symmetric information. We focus on Markov perfect equilibria and characterize the equilibrium set for a refinement of the Markov perfect equilibria.
Particular attention is given to the existence of a marginal contribution equilibrium where each principal receives her contribution to the coalition of agent and remaining principals. The structure of the intertemporal payoffs is analyzed in terms of the flow marginal contribution. As a byproduct, new results for the static common agency game are obtained.
The general characterization results are then applied to two dynamic bidding games for a common agent: (i) multi-task allocation and (ii) job matching under uncertainty.
We consider a general model of dynamic common agency with symmetric information. We focus on Markov perfect equilibria and characterize the equilibrium set for a refinement of the Markov perfect equilibria.
Particular attention is given to the existence of a marginal contribution equilibrium where each principal receives her contribution to the coalition of agent and remaining principals. The structure of the intertemporal payoffs is analyzed in terms of the flow marginal contribution. As a byproduct, new results for the static common agency game are obtained.
The general characterization results are then applied to two dynamic bidding games for a common agent: (i) multi-task allocation and (ii) job matching under uncertainty.
The diffusion of a new product of uncertain value is analyzed in a duopolistic market in continuous time. The two sides of the market, buyers and sellers, learn the true value of the new product over time as a result of experimentation. Buyers have heterogeneous preferences over the products and sellers compete in prices.
The pricing policies and market shares of the sellers in the unique Markov perfect equilibrium are obtained explicitly. The dynamics of the equilibrium market shares display excessive sales of the new product relative to the social optimum in early stages and too low sales later on. The dynamic resolution of uncertainty implies ex post differentiation and hence both sellers value information positively. As information is generated only by experiments with the new product, this relaxes the price competition in the dynamic setting. Finally, the diffusion path of a successful product is shown to be S-shaped
We present a continuous-time model of Bayesian learning in a duopolistic market. Initially the value of one product offered is unknown to the market. The market participants learn more about the true value of the product as experimentation occurs over time. Firms set prices to induce experimentation with their product. The aggregate outcomes are public information.
As agents learn from the experiments of others, informational externalities arise. Surprisingly, the informational externality leads to too much learning. Buyers do not consider the impact of their experimentation on other buyers while the sellers internalize the gains from experiments conducted by the buyers. The firms free ride on the market as the social costs of experiments are not appropriately reflected in the equilibrium prices. The value functions of the sellers display preference for information in contrast to the buyers who are information averse.
We determine Markov Perfect Equilibrium prices and allocations in this two-sided learning model. The analysis is presented for a finite number of buyers as well as for a continuum of buyers. The severity of the inefficiency is shown to be monotonically increasing in the number of buyers.
We present a continuous-time model of Bayesian learning in a duopolistic market. Initially the value of one product offered is unknown to the market. The market participants learn more about the true value of the product as experimentation occurs over time. Firms set prices to induce experimentation with their product. The aggregate outcomes are public information.
As agents learn from the experiments of others, informational externalities arise. Surprisingly, the informational externality leads to too much learning. Buyers do not consider the impact of their experimentation on other buyers while the sellers internalize the gains from experiments conducted by the buyers. The firms free ride on the market as the social costs of experiments are not appropriately reflected in the equilibrium prices. The value functions of the sellers display preference for information in contrast to the buyers who are information averse.
We determine Markov Perfect Equilibrium prices and allocations in this two-sided learning model. The analysis is presented for a finite number of buyers as well as for a continuum of buyers. The severity of the inefficiency is shown to be monotonically increasing in the number of buyers.
We consider the situation where a single consumer buys a stream of goods from different sellers over time. The true value of each seller’s product to the buyer is initially unknown. Additional information can be gained only by experimentation. For exogenously given prices the buyer’s problem is a multi-armed bandit problem. The innovation in this paper is to endogenize the cost of experimentation to the consumer by allowing for price competition between the sellers. The role of prices is then to allocate intertemporally the costs and benefits of learning between buyer and sellers. We examine how strategic aspects of the oligopoly model interact with the learning process.
All Markov Perfect Equilibria (MPE) are efficient. We identify an equilibrium which besides its unique robustness properties has a strikingly simple, seemingly myopic pricing rule. Prices below marginal cost emerge naturally to sustain experimentation. Intertemporal exchange of the gains of learning is necessary to support efficient experimentation. We analyze the asymptotic behavior of the equilibria.