Can boundedly rational sellers learn to play Nash?

How does Nash pricing compare to pricing with adaptive sellers using reinforcement learning (RL)? We consider a market game similar to Varian’s model (Am Econ Rev 70:651–659, 1980) with two types of consumers differing by the size of their fixed sample search rule and derive the Nash search equilibrium (NSE) strategy (the density, the mean and the variance of the posted price distribution). Our findings are twofold. First, we find that the RL price distribution does not converge in a statistical sense to the NSE one except when competition is à la Bertrand. Second, we show that the qualitative properties of the NSE with respect to a change in buyers‘ search behavior are still valid for the RL distribution. The average price and the variance of both price distributions exhibit similar variations to a change in buyers’ search.     

Selection in a field experiment with voluntary participation

The external validity of experiments in economics can be ensured only if participants reflect the relevant market population. We study data from a promotional campaign of NH‐Hoteles to study sample selection problems in a gift exchange field experiment. The promotion allowed guests to pay any non‐negative amount for a stay in one of 36 hotels in Belgium and the Netherlands. We distinguish between involuntary participants, who booked prior to the announcement of the promotional campaign, and voluntary participants, who booked after the campaign was announced. The involuntary participants pay, on average, substantially more. This different behavior cannot be explained by differences in satisfaction or observed compositional differences between both groups. During the promotion we varied the posted price of a room that was communicated to the guests. Only the involuntary participants respond to this exogenous variation in the posted price. We argue that the promotional campaign mainly attracted individuals with relatively few prosocial reputational concerns, because they benefit most from a name‐your‐own‐price scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Sales by multi‐product retailers

This paper examines the rationale underlying periodic price promotions, or sales, for perishable food products by supermarket retailers. Whereas previous studies explain sales in a single‐product context as arising from informational, storage cost, or demand heterogeneity, this study focuses on the central role of retailers as multi‐product sellers of complementary goods. By offering a larger number of discounted products within a particular category, retailers are able to attract a sufficient number of customers to offset the effect of lower margins on sale items by selling more high‐margin items. The implications that emerge from the resulting mixed‐strategy equilibrium are tested in a product‐level, retail‐scanner data set of fresh fruit sales. Hypotheses regarding the rationale and effectiveness of sales are tested by estimating econometric models that describe (1) the number of sales items per store, (2) the depth of a given sale, and (3) promotion effectiveness on store‐level demand. The results of this econometric analysis support the hypothesis that the breadth and depth of price promotions are complementary marketing tools, thus explaining how EDLP and HI‐LO store formats can exist in the same monopolistically competitive market equilibrium. Copyright © 2006 John Wiley & Sons, Ltd.     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

On the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions

In a classical result, Milgrom (1981a) established that the Monotone Likelihood Ratio Property (MLRP) is a sufficient condition for the existence of an increasing symmetric equilibrium in (k + 1)-st price common value auctions. We show: (1) If MLRP is violated, then for any number of bidders and objects there exists a distribution of the common value such that no increasing symmetric equilibrium exists; (2) If MLRP is violated, then for any distribution of the common value there exist infinitely many pairs of the number of bidders and the number of objects such that an increasing symmetric equilibrium does not exist; (3) There are examples where an increasing symmetric equilibrium exists even when the signal distribution violates MLRP.     

The Value of Online Seller Reputation: Evidence from a Price Comparison Site

This paper examines the value of seller reputation for e‐retailers trading via a price comparison site (PCS). E‐markets are widely held to accommodate sellers of differing service quality, including some who behave opportunistically. The paper uses a sample of offers on up to 295 digital cameras traded on a leading PCS, over a 134‐day period to estimate reputation's price impact. User‐generated reputation measures have a significant impact in the expected direction. However, their magnitude is small compared with variables capturing economy‐wide reputation. The strength of the reputation signal increased non‐monotonically with the number of reviews on which it was based. Copyright © 2015 John Wiley & Sons, Ltd.     

When to haggle,when to hold firm? Lessons from the used‐car retail market

Though haggling has been the conventional way for auto retailers to sell cars, the last two decades have witnessed the systematic adoption of no‐haggle prices by many large dealerships, including the largest new‐ and used‐car dealership chains. This paper develops a structural empirical model to estimate sellers' profits under posted price and haggling, and investigates how market conditions affect sellers' optimal pricing formats. The model incorporates a simple class of bargaining mechanisms into a standard random‐coefficient discrete‐choice model. With the extension, the product‐level demand system is estimated using data with only list prices, and the unobserved price discounts are also recovered in the estimation. The counterfactual experiments yield a few interesting findings. First, dealers' adopted pricing formats seem superior to the alternative ones. Second, dealers enjoying larger market power through vertical differentiation and carrying a large number of models are more likely to have posted price as their optimal pricing format.     

On the lowest-winning-bid and the highest-losing-bid auctions

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for sale and n bidders with unit demand, and prove that it converges to the bidding function of the highest-losing-bid auction if and only if the number of losers n−k gets large. When the number of losers grows large, the bidding functions converge at a linear rate and the prices in the two auctions converge in probability to the expected value of an object to the marginal winner.     

Equilibrium price and advertisement distributions

We consider an economy where many sellers sell identical goods to many buyers. Each seller has a unit supply and each buyer has a unit demand. The only possible information flow about prices is through costly advertising. We show that in equilibrium the sellers use mixed strategies in pricing which leads to price and advertisement distributions. With convex advertising costs each seller sends only one advertisement in the market. We also delineate a class of advertising costs which ensures that sellers may send multiple advertisements in equilibrium. Higher prices are advertised more than lower prices.     

Coupon Advertising Under Imperfect Price Information*

This paper studies sales promotions through coupons in an oligopoly under imperfect price information. Sellers can distribute either ordinary coupons, or coupon (price) advertising, or both types of coupons, at distant locations to attract consumers from their rivals' markets. A unique symmetric pure-strategy equilibrium exists where rebates and couponing intensity are always positive. In the ordinary-coupon equilibrium, prices, promotional efforts, and sellers' profits are higher than in the coupon-advertising equilibrium. However, if sellers are allowed to distribute both types of coupons, only coupon advertising is sent out in equilibrium.     

A Computational Dynamic Model of Strategic Behavior in the US Retail Banking Market

This paper examines the dynamics of bank strategies and performance in retail deposit markets. I develop an infinite‐horizon computational dynamic equilibrium duopoly model of value‐maximizing banks. It is used to analyze several critical aspects of behavior in local banking markets such as price and non‐price competition, strategic interactions between small and large banks, de novo bank growth, and consumer switching. The results suggest that growing banks offer higher deposit interest rates than established banks. Established banks are more likely to engage in non‐price competition, which can impede the effectiveness of de novo bank strategies and growth. Copyright © 2015 John Wiley & Sons, Ltd.     

Competition among mechanism designers in a common value environment

A competitive economy is studied in which sellers offer alternative direct mechanisms to buyers who have private information about their own private use value for the commodity being traded. In addition the commodity has a common value to all buyers, perhaps represented by the future resale value of the commodity. A competitive equilibrium in mechanisms is described. In every such equilibrium it is shown that sellers must offer mechanisms that are allocationally equivalent to English ascending price auctions. The reservation prices that sellers set are shown to be below their ex post cost of trading the commodity. Received: 24 April 1998 / Accepted: 8 March 1999     

Technology Adoption with Multiple Alternative Designs and the Option to Wait

Technology adoption is one the most important elements of a firm's strategy. In this paper, we address an essential, yet largely overlooked, question: What should a firm do when faced with several alternative proprietary designs of a new technology? In our base case we assume there are two technology designs, each described by an independent stochastic process of technology evolution. We show that, in equilibrium, a buyer chooses the leading technology design as soon as the discounted payoff from doing so is positive. When the option value of waiting is very high, it is jointly optimal to delay adoption. But because sellers cannot commit not to extract all of the buyer's future rents, inefficiently early adoption takes place. Strategies that improve commitment to low future license fees, such as increasing the number of competitors or cross‐licensing, may alleviate the hold up problem. Although previous research stressed the benefit of such commitments in terms of increasing the rate of technology adoption, we present a class of cases when the benefit from commitment is efficiently to delay adoption.     

Price Discrimination under Customer Recognition and Mergers

This paper studies the interaction between horizontal mergers and price discrimination by endogenizing the merger formation process in the context of a repeated purchase model with two periods and three firms wherein firms may engage in behavior‐based price discrimination (BBPD). From a merger policy perspective, this paper's main contribution is twofold. First, it shows that when firms are allowed to price discriminate, the (unique) equilibrium merger gives rise to significant increases in profits for the merging firms (the ones with information to price discriminate), but has no ex‐post effect on the outsider firm's profitability, thereby eliminating the so‐called (static) “free‐riding problem.” Second, this equilibrium merger is shown to increase industry profits at the expense of consumers' surplus, leaving total welfare unaffected. This then suggests that competition authorities should scrutinize with greater zeal mergers in industries where firms are expected to engage in BBPD.     

Adverse Selection with Competitive Inspection

We develop a model with heterogeneous buyers and sellers in which the sellers have private information about their goods' qualities. We show that efficient trading cannot occur without middlemen. Middlemen can provide two services: one is inspection, and the other is the sorting of buyers and sellers through the rationing of sellers and the provision of two different price schedules. The latter service permits the possibility of achieving the first best. When the first best is not attainable, there is a second best characterized by two intervals, one consisting of low-quality noninspected goods, and the other of high-quality inspected goods. We determine whether first and second best outcomes can be implemented in a market equilibrium with both zero and infinite buyer-seller search costs. First and second best outcomes are attainable under a larger set of parameter values when search costs are infinite; also, typically too much inspection occurs in a market equilibrium. Welfare may be either raised or lowered by the introduction of middlemen.     

Pricing used books on Amazon.com: a spatial approach to price dispersion

This paper estimates a spatial autoregressive (SAR) model of price dispersion using publicly available internet bookselling data. It uses a semiparametric adaptive estimator that does not require the usual Gaussian assumption of maximum likelihood (ML) estimators. The results suggest that both price competition and seller heterogeneity are key drivers of the observed price dispersion. The paper finds that sellers with large sales volume, newly established sellers and US mainland states-based sellers tend to price lower. The identified significant spatial interaction is evidence of spatial price competition. Controlling for everything else, a seller asks a lower price when large sellers charge relatively high prices, which is also evidence of price-based selling and undercutting.     

Incentives of low‐quality sellers to disclose negative information

The paper studies incentives of low‐quality sellers to disclose negative information about their products. We develop a model in which one's quality can be communicated via cheap‐talk messages only. This setting limits the ability of high‐quality sellers to separate, as any communication strategy they pursue can be costlessly imitated by low‐quality sellers. We study two factors that can incentivize low‐quality sellers to communicate their quality: buyers' loss aversion and competition. Quality disclosure reduces buyers' risk, thereby increasing their willingness to pay for the product. It also introduces product differentiation, softening the competition.     

The holdout problem and urban sprawl: Experimental evidence

Conventional wisdom as well as economic theory suggests it is more costly to reassemble fragmented land due to transactions costs and strategic bargaining costs. Both costs are expected to increase with the number of sellers. Inefficient allocation of land resources may result including property entropy (Parisi, 2002), urban sprawl (Miceli and Sirmans, 2007) and deteriorating inner cities. Given the difficulty of observing actual values attached by buyers and sellers to land, little empirical evidence exists to support the conventional wisdom and theoretical work. We use experimental methods to examine transactions costs and strategic bargaining costs in a land-assembly market game with one buyer, 1-4 sellers, and complementary exchanges. The buyer’s final earnings vary inversely with the number of sellers, ceteris paribus, indicating an incentive to purchase consolidated land. Delay costs reduce holdout, but result in lower payoffs for both buyers and sellers. Competition between sellers reduces holdout and the buyer’s total purchase price.     

On second-price auctions and imperfect competition

Consider two sellers each of whom has one unit of an indivisible good and two buyers each of whom is interested in buying one unit. The sellers simultaneously set reserve prices and use second-price auctions as rationing device. An equilibrium in pure strategies where each seller has a regular customer is characterized. The result is applied in order to demonstrate that not allowing sellers to use second-price auctions may enhance total surplus.