A Note on Kuhn's Theorem with Ambiguity Averse Players

Kuhn's Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrate the limits of Kuhn's Theorem in an environment with ambiguity averse players who use maxmin decision rule and full Bayesian updating.Comment: 7 figure

A Point Decision For Partially Identified Auction Models

This paper proposes a decision theoretic method to choose a single reserve price for partially identified auction models, such as Haile and Tamer, 2003, using data on transaction prices from English auctions. The paper employs Gilboa and Schmeidler, 1989 for inference that is robust with respect to the prior over unidentified parameters. It is optimal to interpret the transaction price as the highest value, and maximize the posterior mean of the seller’s revenue. The Monte Carlo study shows substantial gains relative to the average revenues of the Haile and Tamer interval.

Testing for Collusion in Asymmetric First-Price Auctions

This paper proposes fully nonparametric tests to detect possible collusion in first-price procurement (auctions). The aim of the tests is to detect possible collusion before knowing whether or not bidders are colluding. Thus we do not rely on data on anti-competitive hearing, and in that sense is ’ex-ante’. We propose a two steps (model selection) procedure: First, we use a reduced form test of independence and symmetry to shortlist bidders whose bidding behavior is at-odds with competitive bidding, and Second, the recovered (latent) cost for these bidders must be higher under collusion than under competition, because collusion dwarfs competition, hence detecting collusion boils down to testing if the estimated cost distribution under collusion first order stochastically dominates that under competition. We propose rank based and Kolmogorov-Smirnov (K-S) tests. We implement the tests for Highway Procurement data in California and conclude that there is no evidence of collusion even though the reduced form test supports collusion.

Semiparametric Estimation of First-Price Auction Models

We propose a semiparametric method to estimate the density of private values in first-price auctions. Specifically, we model private values through a set of conditional moment restrictions and use a two-step procedure. In the first step we recover a sample of pseudo private values using Local Polynomial Estimator. In the second step we use a GMM procedure to estimate the parameter(s) of interest. We show that the proposed semiparametric estimator is consistent, has an asymptotic normal distribution, and attains the parametric ("root-n") rate of convergence.Comment: 66 pages, 2 figure

Identification of Insurance Models with Multidimensional Screening

We study the identification of an insurance model with multidimensional screening, where insurees are characterized by risk and risk aversion. The model is solved using the concept of certainty equivalence under constant absolute risk aversion and an unspecified joint distribution of risk and risk aversion. The paper then analyzes how data availability constraints identification under four data scenarios from the ideal situation to a more realistic one. The observed number of accidents for each insuree plays a key role to identify the model. In a first part, we consider the case of a continuum of coverages offered to each insuree whether the damage distribution is fully observed or truncated. Truncation arises from that an insuree files a claim only when the accident involves a damage above the deductible. Despite bunching due to multidimensional screening, we show that the joint distribution of risk and risk aversion is identified. In a second part, we consider the case of a finite number of coverages offered to each insuree. When the full damage distribution is observed, we show that despite additional pooling due to the finite number of contracts, the joint distribution of risk and risk aversion is identified under a full support assumption and a conditional independence assumption involving the car characteristics. When the damage distribution is truncated, the joint distribution is identified up to the probability that the damage is above the deductible. In a third part, we derive the restrictions imposed by the model on observables for the fourth scenario. We also propose several identification strategies for the damage probability at the deductible. These identification results are further exploited in a companion paper developing an estimation method with an application to insurance data

Empirical Framework for Cournot Oligopoly with Private Information

We propose an empirical framework for asymmetric Cournot oligopoly with private information about variable costs. First, considering a linear demand for a homogenous product with a random intercept, we characterize the Bayesian Cournot-Nash equilibrium. Then we establish the identification of the joint distribution of demand and firm-specific cost distributions. Following the identification steps, we propose a likelihood-based estimation method and apply it to the global market for crude-oil and quantify the welfare effect of private information. We also consider extensions of the model to include either product differentiation, conduct parameters, nonlinear demand, or selective entry.Comment: forthcoming, The RAND Journal of Economic

Nonidentification of Insurance Models with Probability of Accidents

In contrast to Aryal, Perrigne and Vuong (2009), this note shows that in an insurance model with multidimensional screening when only information on whether the insuree has been involved in some accident is available, the joint distribution of risk and risk aversion is not identified.