Information Structures in Optimal Auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers.Optimal Auction, Private Values, Information Structures, Partitions

Testing for Equilibrium Multiplicity in Dynamic Markov Games

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that the data are generated from a single equilibrium. We formulate tests of (i) the conditional choice probabilities, (ii) the steady-state distribution of states and (iii) the conditional distribution of states conditional on an initial state. In a Monte Carlo study we find that the chi-squared test of the steady-state distribution performs well and has high power even with a small number of markets and time periods. We apply the chi-squared test to the empirical application of Ryan (2012) that analyzes dynamics of the U.S. Portland Cement industry and test if his assumption of single equilibrium is supported by the data

Identification and Estimation of Dynamic Games

This paper studies the identification problem in infinite horizon Markovian games and proposes a generally applicable estimation method. Every period firms simultaneously select an action from a finite set. We characterize the set of Markov equilibria. Period profits are a linear function of equilibrium choice probabilities. The question of identification of these values is then reduced to the existence of a solution to this linear equation system. We characterize the identification conditions. We propose a simple estimation procedure which follows the steps in the identification argument. The estimator is consistent, asymptotic normally distributed, and efficient. We have collected quarterly time series data on pubs, restaurants, coffeehouses, bakeries and carpenters for two Austrian towns between 1982 and 2002. A dynamic entry game is estimated in which firms simultaneously decide whether to enter, remain active, or exit the industry. The period profit estimates are used to simulate the equilibrium behavior under a policy experiment in which a unit tax is imposed on firms deciding to enter the industry.

Estimation of a Dynamic Auction Game

This paper proposes an estimation method for a repeated auction game under the presence of capacity contraints. The estimation strategy is computationally simple as it does not require solving for the equilibrium of the game. It uses a two stage approach. In the first stage the distribution of bids conditional on state variables is estimated using data on bids, bidder characteristics and contract characteristics. In the second stage, an expression of the expected sum of future profits based on the distribution of bids is obtained, and costs are inferred based on the first order condition of optimal bids. We apply the estimation method to repeated highway construction procurement auctions in the state of California between May 1996 and May 1999. In this market, previously won uncompleted contracts reduce the probability of winning further contracts. We quantify the effect of intertemporal constraints on bidders' costs and on bids. Due to the intertemporal effect and also to bidder asymmetry, the auction can be inefficient. Based on the estimates of costs, we quantify efficiency losses.

Information Structures in Optimal Auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers

Equilibrium Bids in Sponsored Search Auctions: Theory and Evidence

This paper presents a game theoretic analysis of the generalized second price auc- tion that the company Overture operated in 2004 to sell sponsored search listings on its search engine. We present results that indicate that this auction has a multi- plicity of Nash equilibria. We also show that weak dominance arguments do not in general select a unique Nash equilibrium. We then analyze bid data assuming that advertisers choose Nash equilibrium bids. We offer some preliminary conclu- sions about advertisers’ true willingness to bid for sponsored search listings. We find that advertisers’ true willingness to bid is multi-dimensional and decreasing in listing position.auctions, sponsored search.

Pooling data across markets in dynamic Markov games

This paper proposes several statistical tests for finite state Markov games to examine whether data from distinct markets can be pooled. We formulate homogeneity tests of (i) the conditional choice and state transition probabilities, (ii) the steady-state distribution, and (iii) the conditional state distribution given an initial state. The null hypotheses of these homogeneity tests are necessary conditions (or maintained assumptions) for poolability of the data. Thus rejections of these null imply that the data cannot be pooled across markets. Acceptances of these null are considered as supporting evidences for the maintained assumptions of estimation using pooled data. In a Monte Carlo study we find that the test based on the steady-state distribution performs well and has high powereven with small numbers of markets and time periods. We apply the tests to the empirical study of Ryan (2012) that analyzes dynamics of the U.S. Portland Cement industry and assess if the data across markets can be pooled

Horizontal Mergers in the Paper Industry

This paper examines mergers and acquisitions in the US paper and paperboard industry. This industry experienced a wave of horizontal mergers during the mid 1980s. We study implications of mergers on consumers, rival firms, and welfare. The analysis is based on a model of investment decisions. We compare the equilibrium investment decisions prior to and after the merger wave. The evidence indicates that the efficiency of the majority of acquiring firms increases following an acquisition. Based on the parameter estimates, we calculate merger welfare effects. We find that total welfare increased by $583.5 million as a result of the mergers.

Old Money, the Nouveaux Riches and Brunhilde's Marriage Strategy

A woman assessing the wealth of a potential husband may observe some, but not all, of his wealth. She may screen, leading to status consumption and wasteful gift giving. The screening activity is costly not only for the potential husband, but also for the woman, as it reduces the wealth of the man she may marry. A sound observable financial background ('old money') benefits the candidate but also the woman, and reduces wasteful status consumption spending. Also, aging and attractiveness of the woman affect the equilibrium conspicuous spending pattern

Combination bidding in multi-unit auctions

This paper considers the problem of identification and estimation in the firstprice multi-unit auction. It is motivated by the auctions of bus routes held in London where bidders submit bids on combinations of routes as well as on individual routes. We show that submitting a combination bid lower than the sum of the bids on the constituent routes does not require cost synergies and can instead serve as a tool to leverage market power across the different routes. As a result, the welfare consequences of allowing combination bidding in the first price auction are ambiguous, and depend on the importance of the cost synergies. We provide conditions for non-parametric identification of the multidimensional private information in the multi-unit first price auction and derive partial identification results when they are not satisfied. We propose an estimation method consisting of two stages: In the first stage, the distribution of bids is estimated parametrically. In the second stage, the (set of) costs and distribution(s) of costs consistent with the observed behavior are inferred based on the first order conditions for optimally chosen bids. We apply the estimation method to data from the London bus routes market. We quantify the magnitude of cost synergies and assess possible efficiency losses arising in this market