No Arabic abstract
We study testable implications of multiple equilibria in discrete games with incomplete information. Unlike de Paula and Tang (2012), we allow the players private signals to be correlated. In static games, we leverage independence of private types across games whose equilibrium selection is correlated. In dynamic games with serially correlated discrete unobserved heterogeneity, our testable implication builds on the fact that the distribution of a sequence of choices and states are mixtures over equilibria and unobserved heterogeneity. The number of mixture components is a known function of the length of the sequence as well as the cardinality of equilibria and unobserved heterogeneity support. In both static and dynamic cases, these testable implications are implementable using existing statistical tools.
We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and efficient and easily implementable combinatorial methods are described to check them. In all normal form games, the identified set is characterized in terms of the value of a submodular or convex optimization program. Efficient algorithms are then given and compared to check inclusion of a parameter in this identified set. The latter are illustrated with family bargaining games and oligopoly entry games.
This paper studies the econometric aspects of the generalized local IV framework defined using the unordered monotonicity condition, which accommodates multiple levels of treatment and instrument in program evaluations. The framework is explicitly developed to allow for conditioning covariates. Nonparametric identification results are obtained for a wide range of policy-relevant parameters. Semiparametric efficiency bounds are computed for these identified structural parameters, including the local average structural function and local average structural function on the treated. Two semiparametric estimators are introduced that achieve efficiency. One is the conditional expectation projection estimator defined through the nonparametric identification equation. The other is the double/debiased machine learning estimator defined through the efficient influence function, which is suitable for high-dimensional settings. More generally, for parameters implicitly defined by possibly non-smooth and overidentifying moment conditions, this study provides the calculation for the corresponding semiparametric efficiency bounds and proposes efficient semiparametric GMM estimators again using the efficient influence functions. Then an optimal set of testable implications of the model assumption is proposed. Previous results developed for the binary local IV model and the multivalued treatment model under unconfoundedness are encompassed as special cases in this more general framework. The theoretical results are illustrated by an empirical application investigating the return to schooling across different fields of study, and a Monte Carlo experiment.
In this paper, we consider the problem of wireless power control in an interference channel where transmitters aim to maximize their own benefit. When the individual payoff or utility function is derived from the transmission efficiency and the spent power, previous works typically study the Nash equilibrium of the resulting power control game. We propose to introduce concepts of correlated and communication equilibria from game theory to find efficient solutions (compared to the Nash equilibrium) for this problem. Communication and correlated equilibria are analyzed for the power control game, and we provide algorithms that can achieve these equilibria. Simulation results demonstrate that the correlation is beneficial under some settings, and the players achieve better payoffs.
The literature on dynamic discrete games often assumes that the conditional choice probabilities and the state transition probabilities are homogeneous across markets and over time. We refer to this as the homogeneity assumption in dynamic discrete games. This homogeneity assumption enables empirical studies to estimate the games structural parameters by pooling data from multiple markets and from many time periods. In this paper, we propose a hypothesis test to evaluate whether the homogeneity assumption holds in the data. Our hypothesis is the result of an approximate randomization test, implemented via a Markov chain Monte Carlo (MCMC) algorithm. We show that our hypothesis test becomes valid as the (user-defined) number of MCMC draws diverges, for any fixed number of markets, time-periods, and players. We apply our test to the empirical study of the U.S. Portland cement industry in Ryan (2012).
We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the hardness results on the computation of normal-form correlated equilibria, we introduce the notion of normal-form coarse correlated equilibrium, extending the definition of coarse correlated equilibrium to sequential games. We show that, in two-player games without chance moves, an optimal (e.g., social welfare maximizing) normal-form coarse correlated equilibrium can be computed in polynomial time, and that in general multi-player games (including two-player games with Chance), the problem is NP-hard. For the former case, we provide a polynomial-time algorithm based on the ellipsoid method and also propose a more practical one, which can be efficiently applied to problems of considerable size. Then, we discuss how our algorithm can be extended to games with Chance and games with more than two players.