Identification and Estimation of Discrete Games of Complete Information

Bajari, Patrick; Hong, Han; Ryan, Stephen P.

doi:10.3386/t0301

Cited by 72 publications

(102 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this setting, consumer search may be less relevant and, hence, the click volume in WebsiteX is less regular than described in the literature motivated from Yaoo!, Google and Microsoft; e.g., Varian (2006), Athey and Nekipelov (forthcoming). 24 Finally, the estimated coefficients of the Beta distribution parameters a and b are positive, with a >> b, for both the Model I and model II estimates (bottom of tables 3 and 5). This implies that the equilibrium selection density function is left-skewed, so that higher prices are much more likely to be chosen.…”

Section: Estimation Resultsmentioning

confidence: 91%

See 1 more Smart Citation

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

2015

View full text Add to dashboard Cite

We estimate a structural model of a sponsored search auction model. To accommodate the "position paradox", we relax the assumption of decreasing click volumes with position ranks, which is often assumed in the literature. Using data from "Website X", one of the largest online marketplaces in China, we find that merchants of different qualities adopt different bidding strategies: high quality merchants bid more aggressively for informative keywords, while low quality merchants are more likely to be sorted to the top positions for vague keywords. Counterfactual evaluations show that the price trend becomes steeper after moving to a score-weighted generalized second price auction, with much higher prices obtained for the top position but lower prices for the other positions. Overall there is only a very modest change in total revenue from introducing popularity scoring, despite the intent in bid scoring to reward popular merchants with price discounts. JEL classification numbers: D44; D47; C11; C15

show abstract

Section: Estimation Resultsmentioning

confidence: 91%

“…To proceed, we consider parametric equilibrium selection rules to complete the likelihood specification, following Bajari et al (2010). 17 Specifying such a distribution in our case is nontrivial, as the support P(V, α) depends on the latent variables.…”

Section: The Likelihood Of Auction Allocations and Pricesmentioning

confidence: 99%

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

2015

View full text Add to dashboard Cite

show abstract

“…31 The complexity of this task grows quickly with the number of players and the number of actions that each player can choose from. Notice, however, that this step has to be performed regardless of which features of normal form games are identi…ed: whether su¢ cient conditions are imposed for point identi…cation of the parameter vector of interest, as in Bajari, Hong, and Ryan (2009), or this vector is restricted to lie in an outer region, or its sharp identi…cation region is characterized through the methodology proposed in this paper. For example, Bajari, Hong, and Ryan (2009) work with an empirical application which has a very large number of players, but group the smaller ones together in order to reduce the number of players to 4.…”

Section: A4 Computational Aspects Of the Problemmentioning

confidence: 99%

Sharp identification regions in models with convex moment predictions

Beresteanu¹,

Molchanov²,

Molinari³

2010

View full text Add to dashboard Cite

We provide a tractable characterization of the sharp identi…cation region of the parameters in a broad class of incomplete econometric models. Models in this class have set valued predictions that yield a convex set of conditional or unconditional moments for the observable model variables. In short, we call these models with convex moment predictions. Examples include static, simultaneous move …nite games of complete and incomplete information in the presence of multiple equilibria; best linear predictors with interval outcome and covariate data; and random utility models of multinomial choice in the presence of interval regressors data. Given a candidate value for ; we establish that the convex set of moments yielded by the model predictions can be represented as the Aumann expectation of a properly de…ned random set. The sharp identi…cation region of ; denoted I ; can then be obtained as the set of minimizers of the distance from a properly speci…ed vector of moments of random variables to this Aumann expectation. Algorithms in convex programming can be exploited to e¢ ciently verify whether a candidate is in I : We use examples analyzed in the literature to illustrate the gains in identi…cation and computational tractability a¤orded by our method.

show abstract

“…Point identification of the class of models treated in this paper has been previously studied by Bjorn and Vuong (1985), Bresnahan and Reiss (1988, 1990, 1991, Berry (1992), Mazzeo (2002), Tamer (2003), and Bajari, Hong, and Ryan (2007) among others. These authors achieve point identification of the payoff parameters by adding assumptions to the model.…”

Section: Introductionmentioning

confidence: 99%

Sharp identification regions in games

Beresteanu¹,

Molchanov²,

Molinari³

2008

View full text Add to dashboard Cite

We study identification in static, simultaneous move finite games of complete information, where the presence of multiple Nash equilibria may lead to partial identification of the model parameters. The identification regions for these parameters proposed in the related literature are known not to be sharp. Using the theory of random sets, we show that the sharp identification region can be obtained as the set of minimizers of the distance from the conditional distribution of game's outcomes given covariates, to the conditional Aumann expectation given covariates of a properly defined random set. This is the random set of probability distributions over action profiles given profit shifters implied by mixed strategy Nash equilibria. The sharp identification region can be approximated arbitrarily accurately through a finite number of moment inequalities based on the support function of the conditional Aumann expectation. When only pure strategy Nash equilibria are played, the sharp identification region is exactly determined by a finite number of moment inequalities. We discuss how our results can be extended to other solution concepts, such as for example correlated equilibrium or rationality and rationalizability.We show that calculating the sharp identification region using our characterization is computationally feasible. We also provide a simple algorithm which finds the set of inequalities that need to be checked in order to insure sharpness. We use examples analyzed in the literature to illustrate the gains in identification afforded by our method.

show abstract

Identification and Estimation of Discrete Games of Complete Information

Cited by 72 publications

References 30 publications

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

To Score or Not to Score? Estimates of a Sponsored Search Auction Model

Sharp identification regions in models with convex moment predictions

Sharp identification regions in games

Contact Info

Product

Resources

About