A Dynamic Mechanism and Surplus Extraction Under Ambiguity

In the standard independent private values (IPV)model, each bidder’s beliefs about the values of any other bidder is represented by a unique prior. In this paper we relax this assumption and study the question of auction design in an IPV setting characterized by ambiguity: bidders have an imprecise knowledge of the distribution of values of others, and are faced with a set of priors. We also assume that their preferences exhibit ambiguity aversion; in particular, they are represented by the epsilon-contamination model. We show that a simple variation of a discrete Dutch auction can extract almost all surplus. This contrasts with optimal auctions under IPV without ambiguity as well as with optimal static auctions with ambiguity - in all of these, types other than the lowest participating type obtain a positive surplus. An important point of departure is that the modified Dutch mechanism we consider is dynamic rather than static, establishing that under ambiguity aversion – even when the setting is IPV in all other respects – a dynamic mechanism can have additional bite over its static counterparts.Ambiguity Aversion; Epsilon Contamination; Modified Dutch Auction; Dynamic Mechanism; Surplus Extraction

Optimal auctions with ambiguity

A crucial assumption in the optimal auction literature is that each bidder's valuation is known to be drawn from a unique distribution. In this paper we study the optimal auction problem allowing for ambiguity about the distribution of valuations. Agents may be ambiguity averse (modeled using the maxmin expected utility model of Gilboa and Schmeidler 1989.) When the bidders face more ambiguity than the seller we show that (i) given any auction, the seller can always (weakly) increase revenue by switching to an auction providing full insurance to all types of bidders, (ii) if the seller is ambiguity neutral and any prior that is close enough to the seller's prior is included in the bidders' set of priors then the optimal auction is a full insurance auction, and (iii) in general neither the first nor the second price auction is optimal (even with suitably chosen reserve prices). When the seller is ambiguity averse and the bidders are ambiguity neutral an auction that fully insures the seller is in the set of optimal mechanisms.Auctions, mechanism design, ambiguity, uncertainty

Optimal auctions with ambiguity

A crucial assumption in the optimal auction literature has been that each bidder's valuation is known to be drawn from a single unique distribution. In this paper we relax this assumption and study the optimal auction problem when there is ambiguity about the distribution from which these valuations are drawn and where the seller or the bidder may display ambiguity aversion. We model ambiguity aversion using the maxmin expected utility model where an agent evaluates an action on the basis of the minimum expected utility over the set of priors, and then chooses the best action amongst them. We first consider the case where the bidders are ambiguity averse (and the seller is ambiguity neutral). Our first result shows that the optimal incentive compatible and individually rational mechanism must be such that for each type of bidder the minimum expected utility is attained by using the seller's prior. Using this result we show that an auction that provides full insurance to all types of bidders is always in the set of optimal auctions. In particular, when the bidders' set of priors is the ε- contamination of the seller's prior the unique optimal auction provides full insurance to bidders of all types. We also show that in general, many classical auctions, including first and second price are not the optimal mechanism (even with suitably chosen reserve prices). We next consider the case when the seller is ambiguity averse (and the bidders are ambiguity neutral). Now, the optimal auction involves the seller being perfectly insured. Hence, as long as bidders are risk and ambiguity neutral, ambiguity aversion on the part of the seller seems to play a similar role to that of risk aversion.Optimal auction, mechanism design, ambiguity, uncertainty

Optimal Pricing and Endogenous Herding

We consider a monopolist who sells indetical objects of common but unknown value in a herding-prone environment. Buyers make their purchasing decisions sequentially, and rely on a private signal as well as previous buyers´actions to infer the common value of the object. The model applies to a variety of cases, such as the introduction of a new product or the sale of licenses to use a patent. We characterize the monopolist´s optimal pricing strategy and its implications for the temporal pattern of prices and for herding.The analysis is performed under alternative assumptions about observability of prices. We find that when previous prices are observable, herding may but need not arise. In contrast, herding arises immediately when previous prices are unobservable and the seller´s equilibrium strategy is a pure Markov strategy. While the possibility of social learning is present in the first case, it is absent in the second. Finally, we examine the seller´s to manipulate the buyers´evaluation of the object when buyers are naive. Using secret discounts the seller succsessfully interferes with social learning, and herding occurs in finite time.

Optimal Pricing and Endogenous Herding

We consider a monopolist who sells identical objects of common but unknown value in a herding-prone environment. Buyers make their purchasing decisions sequentially, and rely on a private signal as well as We consider a monopolist who sells identical objects of common but previous buyers’ actions to infer the common value of the object. The model applies to a variety of cases, such as the introduction of a new product or the sale of licenses to use a patent. We characterize the monopolist’s optimal pricing strategy and its implications for the temporal pattern of prices and for herding. The analysis is performed under alternative assumptions about observability of prices. We find that when previous prices are observable, herding may but need not arise. In contrast, herding arises immediately when previous prices are unobservable and the seller’s equilibrium strategy is a pure Markov strategy. While the possibility of social learning is present in the first case, it is absent in the second. Finally, we examine the seller’s incentive to manipulate the buyers’ evaluation of the object when buyers are naive. Using secret discounts the seller successfully interferes with social learning, and herding occurs in finite time.herding, informational cascades, optimal pricing

Dynamics Of 2-Level Systems In Glasses

We investigate the relaxation of a two-level system (TLS) in the golden-rule approximation by taking into account phonon-mediated interactions between TLS’s

Unitary Transformation And The Dynamics Of A 3-Level Atom Interacting With 2 Quantized Field Modes

Starting from a three-level atom coupled to two modes of radiation field, we derive a Raman-coupled Hamiltonian by a unitary transformation, evaluated perturbatively in coupling constants. The Rabi oscillation frequency and the collapse and revival times of the atomic coherence are found to have strikingly different photon-intensity dependence than those found previously

Two-photon resonance fluorescence

We present a theory of two-photon resonance fluorescence of an atom or molecule in which the excitation by an external electromagnetic field as well as fluorescence emission is mediated by two-photon processes. The treatment is based on first dressing the atom or molecule by the external field and then evaluating perturbatively the effect of the interaction with the vacuum or fluorescent field and so resonance fluorescence can be considered as spontaneous emission from the dressed atom. The introduction of the combined system of atom and external field via dressed states leads to simpler calculations and more transparent physics. The fluorescence spectrum derived by us has similarities as well as differences with that of one-photon resonance fluorescence and earlier theoretical predictions for the two-photon case

Macroscopic\u27\u27 quantum superpositions: Atom-field entangled and steady states by two-photon processes

The dynamics of an exact two-photon Hamiltonian is used to study the time evolution of an initially disentangled pure state of the atom-field system as it goes through cycles of entanglement separated by instances of disentanglement. For specific initial states of the electromagnetic field, the output state is a pure quantum superposition of a squeezed vacuum state and an orthogonal, odd-photon-number state. The odd-photon-number state, which is not a squeezed state, exhibits both nonclassical sub-Poissonian and classical super-Poissonian photon statistics. In the latter case the quantum superposition resembles a macroscopic superposition state. Conditions are obtained on the atom-cavity interaction time for such states to represent the steady states in the injection in a high-Q cavity of a monoenergetic, low-density beam of three-level atoms in a coherent state

The Harmonic Lattice, Recoilless Transitions, And The Coherent State

The probability for recoilless transitions, relevant for the understanding of x-ray scattering from atoms bound in a crystal (applicable also to elastic scattering of neutrons from solids and to the Mossbauer effect), given by the Debye-Waller factor, is derived in a novel manner using the coherent state basis for the normal mode oscillators describing the harmonic lattice, a method which, while being simple and elegant, also reveals the relationship to a heuristic classical discussion of the problem