Recursos de colección
Caltech Authors (144.724 recursos)
Repository of works by Caltech published authors.
Group = Social Science Working Papers
Repository of works by Caltech published authors.
Group = Social Science Working Papers
Chiong, Khai X.; Galichon, Alfred; Shum, Matthew
Using results from convex analysis, we investigate a novel approach to identification and estimation of discrete choice models which we call the "Mass Transport Approach" (MTA). We show that the conditional choice probabilities and the choice-specific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem. Based on this, we propose a new two-step estimator for these models; interestingly, the first step of our estimator involves solving a linear program which is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971). The application of...
McKelvey, Richard D.; Palfrey, Thomas R.
This paper describes a statistical model of equiliobrium behaviour in games, which we call Quantal Response Equilibrium (QRE). The key feature of the equilibrium is that individuals do not always play responses to the strategies of their opponents, but play better strategies with higher probability than worse strategies. we illustrate several different applications of this approach, and establish a number of theoretical properties of this equilibrium concept. We also demonstrate an equililance between this equilibrium notion and Bayesian games derived from games of complete information with perturbed payoffs
Banks, Jeffrey S.; Duggan, John
We present a general model of legislative bargaining in which the status quo is an arbitrary point in a multidimensional policy space. In contrast to other bargaining models, the status quo is not assumed to be “bad,” and delay may be Pareto efficient. We prove existence of stationary equilibria. The possibility of equilibrium delay depends on four factors: risk aversion of the legislators, the dimensionality of the policy space, the voting rule, and the possibility of transfers across districts. If legislators are risk averse, if there is more than one policy dimension, and if voting is by majority rule, for example, then delay will almost never occur....
Cramton, Peter C.; Palfrey, Thomas R.
What cartel agreements are possible when firms have private information about productions costs? For private cost uncertainty we characterize the set of cartel agreements that can be supported, recognizing incentive and participation constraints. If defection results in either Cournot or Bertrand competition, the incentive problem in large cartels is severe enough to prevent the cartel from achieving the monopoly outcome. However if the cartel agreement requires less than unanimous ratification by the member firms, then the incentive problem can be overcome in large cartels. With common cost uncertainty, perfect collusion is possible in large cartels, regardless of the ratification rule.
Forsythe, Robert; Isaac, R. Mark; Palfrey, Thomas R.
In this article we report the results from a series of laboratory markets in which sellers have better information about the quality of an item than any of the potential buyers. Sellers may voluntarily choose to reveal this information or they may instead decide to "blind bid" the item. We find that a sequential equilibrium model where buyers "assume the worst" is a good predictor of behavior in these simple markets. This equilibrium is not instantaneously attained, however, but there is an unraveling process which describes how this equilibrium is approached. At the conclusion of the market, allocations tend to...
Ordeshook, Peter C.; Palfrey, Thomas R.
The literature on agendas with sincere and strategic voting represents an important contribution to our understanding of committees, of institutions, and of the opportunities to manipulate outcomes by the manipulation of institutions. That literature, though, imposes an assumption that may be unrealistic in many situations; namely, that everyone knows the preferences of everyone else. In this essay we apply Bayesian equilibrium analysis to show that the properties of agendas that others derive by assuming complete information do not hold necessarily under incomplete information. First, a Condorcet winner need not be selected, even if nearly everyone on the committee most prefers...
McKelvey, Richard D.; Palfrey, Thomas R.
We report on a series of experiments in which individuals play a version of the centipede game. In this game, two players alternately get a chance to take the larger portion of a continually escalating pile of money. As soon a.s one person takes, the game ends with that player getting the larger portion of the pile, and the other player getting the smaller portion. If one views the experiment as a complete information game, all standard game theoretic equilibrium concepts predict the first mover should take the large pile on the first round. The experimental results show that this...
El-Gamal, Mahmoud; McKelvey, Richard D.; Palfrey, Thomas R.
We apply a sequential Bayesian sampling procedure to study two models of learning in repeated games. In the first model individuals learn only about an opponent when they play her or him repeatedly but do not update from their experience with that opponent when they move on to play the same game with other opponents. We label this the nonsequential model. In the second model individuals use Bayesian updating to learn about population parameters from each of their opponents, as well as learning about the idiosyncrasies of that particular opponent. We call this the sequential model. We sequentially sample observations...
Palfrey, Thomas R.; Pevnitskaya, Svetlana
This paper presents the results of an experimental study of endogenous entry in first-price independent private value auctions. N potential bidders simultaneously decide whether to participate in an auction or receive a known outside option. In the second stage, entrants submit bids after learning their own private values and the number of entrants. An equilibrium model of heterogeneous risk averse bidders implies a self-selection effect, where bidding in the auction is lower with endogenous entry because only less risk averse bidders enter. This effect is confirmed by the experiment. We also observe excessive entry relative to the theoretical model.
Srivastava, Sanjay; Palfrey, Thomas R.
This paper studies the problem of designing efficient trading mechanisms that are immune to pre-play communication. It is well known that equilibrium behavior can be affected, sometimes drastically, if players have the opportunity to exchange messages prior to playing some particular game. We investigate the relationship between efficiency, pre-play communication, and unique implementation in Bayesian environments with independent types and private values. We identify a class of simple mechanisms which are immune to pre-play communication and show that any incentive efficient allocation can be uniquely implemented by such a mechanism.
Iarycowzer, Matias; Shum, Matthew
We estimate an equilibrium model of decision-making in the US Supreme Court which takes into account both private information and ideological differences between justices. We present a measure of the value of information in the court: the probability that a justice votes differently than what she would have voted for in the absence of case-specific information. Our results suggest a sizable value of information: in roughly 44% of cases, justices' initial leanings are changed by their personal assessments of the case. Our results also confirm the increased politicization of the Supreme Court in the last quarter century. We perform counterfactual simulations to draw implications for institutional design.
Palfrey, Thomas R.; Srivastava, Sanjay
We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any correspondence which satisfies the usual no veto power condition is implementable unless some agents are completely indifferent over all possible outcomes. Many common welfare criteria, such as the Pareto correspondence, and several familiar voting rules, such...
Shi, Xiaoxia; Shum, Matthew
This note proposes a new two-stage estimation and inference procedure for a class of partially identified models. The procedure can be considered an extension of classical minimum distance estimation procedures to accommodate inequality constraints and partial identification. It involves no tuning parameter, is nonconservative and is conceptually and computationally simple. The class of models includes models of interest to applied researchers, including the static entry game, a voting game with communication and a discrete mixture model.
Hu, Yingyao; Shum, Matthew; Tan, Wei
We present a method for estimating Markov dynamic models with unobserved state variables which can be serially correlated over time. We focus on the case where all the model variables have discrete support. Our estimator is simple to compute because it is noniterative, and involves only elementary matrix manipulations. Our estimation method is nonparametric, in that no parametric assumptions on the distributions of the unobserved state variables or the laws of motions of the state variables are required. Monte Carlo simulations show that the estimator performs well in practice, and we illustrate its use with a dataset of doctors’ prescription of pharmaceutical drugs.
Chiong, Khai X.; Shum, Matthew
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, the high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclic monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semi-parametric and does not require explicit distributional assumptions to be made regarding the random utility errors. The random projection procedure is justified via the Johnson-Lindenstrauss Lemma: - the pairwise distances between data points are preserved during data compression, which we exploit to show convergence of our...
Melo, Emerson; Pogorelskiy, Kirill; Shum, Matthew
This paper develops a formal test for consistency of players' behavior in a series of games with the quantal response equilibrium (QRE). The test exploits a characterization of the equilibrium choice probabilities in a QRE as the gradient of a convex function, which thus satisfies the cyclic monotonicity inequalities. Our testing procedure utilizes recent econometric results for moment inequality models. We assess the performance of the test using both Monte Carlo simulation and lab experimental data from a series of generalized matching pennies games. Our experimental findings are consistent with the literature: the joint hypothesis of QRE, risk neutrality and player...
Shi, Xiaoxia; Shum, Matthew; Song, Wei
This paper proposes a new identification and estimation approach to semi-parametric multinomial choice models that easily applies to not only cross-sectional settings but also panel data settings with unobservable fixed effects. Our approach is based on cyclic monotonicity, which is a defining feature of the random utility framework underlying multinomial choice models. From the cyclic monotonicity property, we derive identifying inequalities without requiring any shape restriction for the distribution of the random utility shocks. These inequalities point identify model parameters under straightforward assumptions on the covariates. We propose a consistent estimator based on these inequalities, and apply it to a panel...
Hsieh, Yu-Wei; Shum, Matthew; Yang, Sha
We estimate a structural model of a sponsored search auction model. To accomodate 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 market places 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 value keywords. Counterfactual evaluations show that the price trend becomes steeper after moving to a score-weighted generalized...
Ledyard, John O.; Palfrey, Thomas R.
This paper characterizes interim efficient mechanisms for public good production and cost allocation in a two-type environment with risk neutral, quasi-linear preferences and fixed size projects, where the distribution of the private good, as well as the public goods decision, affects social welfare. An efficient public good decision can always be accomplished by a majority voting scheme, where the number of "YES" votes required depends on the welfare weights in a simple way. The results are shown to have a natural geometry and an intuitive interpretation. We also extend these results to allow for restrictions on feasible transfer rules, ranging from the traditional unlimited transfers to the extreme...
Cull, Robert; Hoffman, Philip T.; Hughson, Eric
We bring new evidence to bear on McCloskey's argument that farmers in the open fields reduced risk by scattering their land holdings. The new evidence is the grain output from a number of plots of land in two French villages, Onnaing and Quarouble, during the years 1701-1790. When combined with prices and wages, the output figures provide financial returns for each plot of land, and financial theory then allows us to construct land portfolios that minimize portfolio variance for a given mean return. The virtue of using returns (rather than simple output correlations) is that the returns take into account...