**Behavior-Based Price Discrimination by a Patient Seller.**S. Bikhchandani, K. McCardle. July 2011.

We investigate a model in which one seller and one buyer trade in each of two periods. The buyer has demand for one unit of a non-durable object per period. The buyer's reservation value for the good is private information and is the same in both periods. The seller commits to prices in each of two periods. Prices in the second period may depend on the buyer's first-period behavior. Unlike the equal discount factor case studied in earlier papers, we show that when the seller is more patient than the buyer, second-period prices increase after a purchase. In particular, the optimal dynamic pricing scheme is not a repetition of the optimal static pricing scheme.

**Mechanism Design with Information Acquisition: Efficiency and Full Surplus Extraction.**S. Bikhchandani, I. Obara. April 2011.

Consider a mechanism design setting in which agents acquire costly information about an unknown, payoff-relevant state of nature. Information gathering is covert and the agents' information is correlated. We investigate conditions under which (i) efficiency and (ii) full surplus extraction are Bayesian incentive compatible and interim individually rational.

**Transitive Regret.**S. Bikhchandani, U. Segal.

*Theoretical Economics*. 6: 95-108. 2011.

Preferences may arise from regret, i.e., from comparisons with alternatives forgone by the decision maker. We ask whether regret-based behavior is consistent with nonexpected utility theories of transitive choice and show that the answer is no. If choices are governed by ex ante regret and rejoicing, then nonexpected utility preferences must be intransitive.

**Information Acquisition and Full Surplus Extraction.**S. Bikhchandani.

*Journal of Economic Theory*. 145(6): 2282-2308. 2010.

It is well known that when agents' types are correlated, the mechanism designer can extract the entire surplus. This creates an incentive for agents to acquire information about other agents' types. Robust lotteries (are payment schemes that) support full extraction and partially robust lotteries support efficient implementation in the presence of information acquisition opportunities. Necessary and sufficient conditions for existence of robust and partially robust lotteries are derived. If an agent's information signal spans other agents' types then robust lotteries do not exist. However, if all agents report their signal realizations then robust lotteries exist in an extended type space.

**Information Cascades.**S. Bikhchandani, D. Hirshleifer, I. Welch.

*The New Palgrave Dictionary of Economics*. 2008.

An information cascade occurs when individuals, having observed the actions and possibly payoffs of those ahead of them, take the same action regardless of their own information signals. Informational cascades may realize only a fraction of the potential gains from aggregating the diverse information of many individuals, which helps explain some otherwise puzzling aspects of human and animal behaviour. For example, why do individuals tend to converge on similar behaviour? Why is mass behaviour prone to error and fads? The theory of observational learning, and particularly of information cascades, has much to offer economics and other social sciences.

**Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation.**S. Bikhchandani, S. Chatterji, R. Lavi, A. Mualem, N. Nisan, A. Sen.

*Econometrica*. 74(4): 1109-1132. 2006.

We characterize dominant-strategy incentive compatibility with multidimensional types. A deterministic social choice function is dominant-strategy incentive compatible if and only if it is weakly monotone (W-Mon). The W-Mon requirement is the following: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social choice function, then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be no less than this difference in utilities evaluated at the original type of this agent.

**Ex Post Implementation in Environments with Private Goods.**S. Bikhchandani.

*Theoretical Economics*. 1: 369-393. 2006.

We prove by construction that ex post incentive compatible mechanisms exist in a private goods setting with multi-dimensional signals and interdependent values. The mechanism shares features with the generalized Vickrey auction of one dimensional signal models. The construction implies that for environments with private goods, informational externalities (i.e., interdependent values) are compatible with ex post equilibrium in the presence of multi-dimensional signals.

**From the Assignment Model to Combinatorial Auctions.**S. Bikhchandani, J. Ostroy.

*Combinatorial Auctions*. Eds.: P. Cramton, Y. Shoham, R. Steinberg. MIT Press. 2006.

The goal of this chapter is to describe efficient auctions for multiple, indivisible objects in terms of the duality theory of linear programming. Because of its well-known incentive properties, we shall focus on Vickrey auctions. These are efficient auctions in which buyers pay the social opportunity cost of their purchases and consequently are rewarded with their (social) marginal product. We use the assignment model to frame our analysis.

**Incentive Compatibility in Multi-Unit Auctions.**S. Bikhchandani, S. Chatterjee, A. Sen. June 2003.

We characterize incentive compatibility in multi-unit auctions with multi-dimensional types. An allocation mechanism is incentive compatible if and only if it is nondecreasing in marginal utilities (NDMU). The notion of incentive compatibility we adopt is dominant strategy in private value models and ex post incentive compatibility in models with interdependent values. NDMU is the following requirement: if changing one buyer’s type, while keeping everyone else’s types the same, changes this buyer’s allocation then the new allocation must be relatively more attractive (or relatively less unattractive) to this buyer. We also establish a price characterization of incentive compatible mechanisms.

**On the Right of First Refusal.**S. Bikhchandani, S. Lippman, R. Ryan.

*Advances in Theoretical Economics*. 5(1:4). 2005.

When the seller of an asset grants a right-of-first-refusal to a buyer, this special buyer has the opportunity to purchase the asset at the best price the seller can obtain from the other potential buyers. We show that the right-of-first-refusal is inefficient, and it benefits the special buyer at the expense of the seller and other buyers. In a private values model, the benefit the special buyer obtains via the right-of-first-refusal equals the cost to the seller. When buyers' valuations are correlated, the presence of a special buyer exacerbates the winner's curse on regular buyers. Consequently, the special buyer's expected gain from the right-of-first-refusal is often less than the expected loss to the seller. Thus, our analysis suggests that the seller should exercise considerable caution prior to deciding whether to grant this right to a buyer.

**An Ascending Vickrey Auction for Selling Bases of a Matroid.**S. Bikhchandani, S. de Vries, J. Schummer, R. Vohra.

*Operations Research*. 59(2): 400-413. 2011.

Consider selling bundles of indivisible goods to buyers with concave utilities that are additively separable in money and goods. We propose an ascending auction for the case when the seller is constrained to sell bundles whose elements form a basis of a matroid. It extends easily to polymatroids. Applications include scheduling, allocation of homogeneous goods, and spatially distributed markets, among others. Our ascending auction induces buyers to bid truthfully and returns the economically efficient basis. Unlike other ascending auctions for this environment, ours runs in pseudopolynomial or polynomial time. Furthermore, we prove the impossibility of an ascending auction for nonmatroidal independence set-systems.

**Ascending Price Vickrey Auctions.**S. Bikhchandani, J. Ostroy.

*Games and Economic Behavior*. 55(2): 215-241. 2006.

We show that an ascending price auction for multiple units of a homogeneous object proposed by Ausubel (i) raises prices for packages until they reach those nonlinear and non-anonymous market clearing prices at which bidders get their marginal products and (ii) the auction is a primal–dual algorithm applied to an appropriate linear programming formulation in which the dual solution yields those same market clearing prices. We emphasize the similarities with efficient incentive compatible ascending price auctions to implement Vickrey payments when there is a single object or when objects are heterogeneous but each buyer does not desire more than one unit. A potential benefit of these common threads is that it helps to establish the principles upon which Vickrey payments may be implemented through decentralized, incentive compatible procedures.

**The Treasury Bill Auction and the When-Issued Market: Some Evidence.**S. Bikhchandani, P. Edsparr, C.Huang. Revised August 2000.

We empirically examine the link between the when-issued market and the auction for Treasury bills. We find that on average it is cheaper to buy Treasury bills in the auction than in the when-issued market just before the auction closes. Surprisingly, primary dealers often submit bids in the auction that are higher in price than the concurrent when-issued ask price. We present evidence to show that this is due to the cost of revealing positive information too early by trading in when-issued markets before the auction. In addition, we examine what determines the dispersion of bids in the auction as well as test for collusive behavior in the bidding process.

**Linear Programming and Vickrey Auctions.**S. Bikhchandani, S. de Vries, J. Schummer, R. Vohrapp.

*Mathematics of the Internet: E-Auction and Markets*. B. Dietrich, R. Vohra (eds.). 75-115. The Institute of Mathematics and its Applications. New York: Springer Verlag. 2002.

The Vickrey sealed bid auction occupies a central place in auction theory because of its efficiency and incentive properties. Implementing the auction requires the auctioneer to solve n + 1 optimization problems, where n is the number of bidders. In this paper we survey various environments (some old and some new) where the payments bidders make under the Vickrey auction correspond to dual variables in certain linear programs. Thus, in these environments, at most two optimization problems must be solved to determine the Vickrey outcome. Furthermore, primal-dual algorithms for some of these linear programs suggest ascending auctions that implement the Vickrey outcome.

**The Package Assignment Model.**S. Bikhchandani, J. Ostroy.

*Journal of Economic Theory*. 107: 377-406. 2002.

We study assignment problems where buyers and sellers trade packages consisting of several objects, a generalization of the standard assignment problem in which individuals buy or sell (at most) one object. Although buyers' reservations values are non-additive, the problem of achieving an efficient allocation can be formulated as a linear programming problem in which the pricing functions expressing duality may be non-linear in the objects constituting the packages. The interconnections among the linear programming formulation of the package model, Walrasian equilibrium, and the core are established. In the single seller (auction) version of the model, equilibria with non-linear, non-anonymous prices exist and fill out the core. A necessary and sufficient condition is given for the Vickrey payoff point to be implementable by a price equilibrium. Implications of our results for efficient auctions of multiple objects are examined.

**Symmetric Separating Equilibria in English Auctions.**S. Bikhchandani, P. Haile, J. Riley.

*Games and Economic Behavior*. 2002.

We characterize the set of perfect Bayesian equilibria in symmetric separating strategies in the model of English auctions given by P. R. Milgrom and R. J. Weber (1982, Econometrica, 50, 1089-1122). There is a continuum of such equilibria. The equilibrium derived by Milgrom and Weber is that in which bids are maximal. Only in the case of pure private values does a restriction to weakly undominated strategies select a unique equilibrium. This has important implications for empirical studies of English auctions, particularly outside the pure private values paradigm.

**Herd Behavior in Financial Markets: A Review.**S. Bikhchandani, S, Sharma.

*IMF Staff Papers*. 2001.

This paper provides an overview of the recent theoretical and empirical research on herd behavior in financial markets. It looks at what precisely is meant by herding, the causes of herd behavior, the success of existing studies in identifying the phenomenon, and the effect that herding has on financial markets.

**Auctions of Heterogeneous Objects.**S. Bikhchandani.

*Games and Economic Behavior*. 26: 193-220. 1999.

Simultaneous sealed bid auctions of heterogeneous objects are analyzed. Each bidder's reservation value for an object depends upon the other objects he obtains. Bidders' reservation values are common knowledge. In simultaneous first-price auctions, the set of Walrasian equilibrium allocations contains the set of pure strategy Nash equilibrium allocations which in turn contains the set of strict Walrasian equilibrium allocations. Hence, pure strategy Nash equilibria (when they exist) are efficient. Mixed strategy Nash equilibria may be inefficient. In simultaneous second-price auctions, any efficient allocation can be implemented as a pure strategy Nash equilibrium outcome if a Walrasian equilibrium exists. Journal of Economic Literature Classification Numbers: D44, D51. Copyright 1999 Academic Press.

**Learning from the Behavior of Others: Conformity, Fads, and Informational Cascades.**S. Bikhchandani, D. Hirshleifer, I. Welch.

*Journal of Economic Perspectives*. 12: 151-170. 1998.

We will argue in this essay that learning by observing the past decisions of others can help explain some otherwise puzzling phenomena about human behavior. For example, why do people tend to converge on similar behavior, in what is know as "herding"? Why is mass behavior prone to error and fads? We will further argue that the theory of observational learning has much to offer economics and business strategy.

**Competitive Equilibrium in a Exchange Economy with Indivisibilites.**S. Bikhchandani, J. Mamer.

*Journal of Economic Theory*. 74: 385-413. 1997.

We analyze an exchange economy in which (i) all commodities except money are indivisible, (ii) agents' preferences can be described by a reservation value for each bundle of indivisible objects, and (iii) all agents are price-takers. We obtain a necessary and sufficient condition under which market clearing prices exist. Implications for market mechanisms are discussed. Journal of Economic Literature Classification Numbers: D51, C78.

**Optimal Search with Learning.**S. Bikhchandani, S. Sharma.

*Journal of Economic Dynamics and Control*. 20: 333-359. 1996.

The sequential search problem, without the assumption that the searcher knows the underlying distribution, is investigated. Both search with recall and without recall are examined. Sufficient conditions for the existence of optimal stopping rules with the reservation property are provided. Comparative static results with respect to stochastic dominance (appropriately defined) are obtained.