Estimating Simultaneous Games with Incomplete Information under Median Restrictions

I estimate a simultaneous discrete game with incomplete information where players’ private information are only required to be median independent of observed states and can be correlated with observable states. This median restriction is weaker than other assumptions on players’ private information in the literature (e.g. perfect knowledge of its distribution or its independence of the observable states). I show index coefficients in players’ utility functions are point-identified under an exclusion restriction and fairly weak conditions on the support of states. This identification strategy is fundamentally different from that in a single-agent binary response models with median restrictions, and does not involve any parametric assumption on equilibrium selection in the presence of multiple Bayesian Nash equilibria. I then propose a two-step extreme estimator for the linear coefficients, and prove its consistency.Games with incomplete information, semiparametric identification, median restrictions, consistent estimation

Identification and Estimation of Stochastic Bargaining Models, Third Version

Stochastic sequential bargaining models (Merlo and Wilson (1995, 1998)) have found wide applications in different fields including political economy and macroeconomics due to their flexibility in explaining delays in reaching an agreement. This paper presents new results in nonparametric identification and estimation of such models under different data scenarios.Nonparametric identification, non-cooperative bargaining, stochastic sequential bargaining, rationalizable counterfactual outcomes

Identification of Stochastic Sequential Bargaining Models, Second Version

Stochastic sequential bargaining games (Merlo and Wilson (1995, 1998)) have found wide applications in various fields including political economy and macroeconomics due to their flexibility in explaining delays in reaching an agreement. In this paper, we present new results in nonparametric identification of such models under different scenarios of data availability. First, we give conditions for an observed distribution of players’ decisions and agreed allocations of the surplus, or the "cake", to be rationalized by a sequential bargaining model. We show the common discount rate is identified, provided the surplus is monotonic in unobservable states (USV) given observed ones (OSV). Then the mapping from states to surplus, or the "cake function", is also recovered under appropriate normalizations. Second, when the cake is only observed under agreements, the discount rate and the impact of observable states on the cake can be identified, if the distribution of USV satisfies some exclusion restrictions and the cake is additively separable in OSV and USV. Third, if data only report when an agreement is reached but never report the size of the cake, we propose a simple algorithm that exploits shape restrictions on the cake function and the independence of USV to recover all rationalizable probabilities for agreements under counterfactual state transitions. Numerical examples show the set of rationalizable counterfactual outcomes so recovered can be informative.Nonparametric identification, non-cooperative bargaining, stochastic sequential bargaining, rationalizable counterfactual outcomes

"Identification of Stochastic Sequential Bargaining Models"

Stochastic sequential bargaining games (Merlo and Wilson (1995, 1998)) have found wide applications in various fields including political economy and macroeconomics due to their flexibility in explaining delays in reaching agreement. In this paper, we present new results in nonparametric identification of such models under different scenarios of data availability. First, with complete data on players’ decisions, the sizes of the surplus to be shared (cakes) and the agreed allocations, both the mapping from states to the total surplus (i.e. the "cake function") and the players’ common discount rate are identified, if the unobservable state variable (USV) is independent of observable ones (OSV), and the total surplus is strictly increasing in the USV conditional on the OSV. Second, when the cake size is only observed under agreements and is additively separable in OSV and USV, the contribution by OSV is identified provided the USV distribution satisfies some distributional exclusion restrictions. Third, if data only report when an agreement is reached but never report the cake sizes, we propose a simple algorithm that exploits exogenously given shape restrictions on the cake function and the independence of USV from OSV to recover all rationalizable probabilities for reaching an agreement under counterfactual state transitions. Numerical examples show the set of rationalizable counterfactual outcomes so recovered can be informative.Nonparametric identification, non-cooperative bargaining, stochastic sequential bargaining, rationalizable counterfactual outcomes

Identification and Estimation of Stochastic Bargaining Models, Fourth Version

Stochastic sequential bargaining models (Merlo and Wilson (1995, 1998)) have found wide applications in different fields including political economy and macroeconomics due to their flexibility in explaining delays in reaching an agreement. This paper presents new results in nonparametric identification and estimation of such models under different data scenarios.Nonparametric identification and estimation, non-cooperative bargaining, stochastic sequential bargaining, rationalizable counterfactual outcomes

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version

This paper studies the inference of interaction effects (impacts of players' actions on each other's payoffs) in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in (but does not rely on) the presence of multiple equilibria in the data-generating process (DGP). As a by-product, we propose a formal test for multiple equilibria in the DGP. We also show how to extend our arguments to identify signs of interaction effects when private signals are correlated. We provide Monte Carlo evidence of the test's good performance in finite samples. We then implement the test using data on radio programming of commercial breaks in the U.S., and infer stations' incentives to synchronize their commercial breaks. Our results support the earlier finding by Sweeting (2009) that stations have stronger incentives.identification, inference, multiple equilibria, incomplete information games

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information

This paper studies the inference of interaction effects, i.e., the impacts of players' actions on each other's payoffs, in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in the presence of multiple equilibria, and, as a by-product of our approach, we propose a formal test for multiple equilibria in the data-generating process. We provide Monte Carlo evidence of the test's good performance in finite samples. We also implement the test to infer the direction of interaction effects in couples' joint retirement decisions using data from the Health and Retirement Study.identification, inference, multiple equilibria, incomplete information games

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version

This paper studies the inference of interaction effects, i.e., the impacts of players' actions on each other's payoffs, in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in the presence of multiple equilibria, and, as a by-product of our approach, we propose a formal test for multiple equilibria in the data-generating process. We provide Monte Carlo evidence of the test's good performance infinite samples. We also implement the test to infer the direction of interaction effects in couples' joint retirement decisions using data from the Health and Retirement Study.identification, inference, multiple equilibria, incomplete information games

Energy-Efficient Data Acquisition in Wireless Sensor Networks through Spatial Correlation

The application of Wireless Sensor Networks (WSNs) is restrained by their often-limited lifetime. A sensor node's lifetime is fundamentally linked to the volume of data that it senses, processes and reports. Spatial correlation between sensor nodes is an inherent phenomenon to WSNs, induced by redundant nodes which report duplicated information. In this paper, we report on the design of a distributed sampling scheme referred to as the 'Virtual Sampling Scheme' (VSS). This scheme is formed from two components: an algorithm for forming virtual clusters, and a distributed sampling method. VSS primarily utilizes redundancy of sensor nodes to get only a subset to sense the environment at any one time. Sensor nodes that are not sensing the environment are in a low-power sleep state, thus conserving energy. Furthermore, VSS balances the energy consumption amongst nodes by using a round robin method