Arbitrary Information Structure Research Articles

Robust Screens for Noncompetitive Bidding in Procurement Auctions

We document a novel bidding pattern observed in procurement auctions from Japan: winning bids tend to be isolated, and there is a missing mass of close losing bids. This pattern is suspicious in the following sense: its extreme forms are inconsistent with competitive behavior under arbitrary information structures. Building on this observation, we develop systematic tests of competitive behavior in procurement auctions that allow for general information structures as well as nonstationary unobserved heterogeneity. We provide an empirical exploration of our tests, and show they can help identify other suspicious patterns in the data.

Learning by matching

This paper studies a stability notion and matching processes in the job market with incomplete information on the workers' side. Each worker is associated with a type, and each firm cares about the type of her employee under a match. Moreover, firms' information structure is described by partitions over possible worker type profiles. With this firm‐specific information, we propose a stability notion which, in addition to requiring individual rationality and no blocking pairs, captures the idea that the absence of rematching conveys no further information. When an allocation is not stable under the status quo information structure, a new pair of an allocation and an information structure will be derived. We show that starting from an arbitrary allocation and an arbitrary information structure, the process of allowing randomly chosen blocking pairs to rematch, accompanied by information updating, will converge with probability one to an allocation that is stable under the updated information structure. Our results are robust with respect to various alternative learning patterns.

Unified Approach to Convex Robust Distributed Control Given Arbitrary Information Structures

We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this technical note, we focus on the requirement that the control policy is distributed, in the sense that it can only be based on partial information about the history of the outputs. It is well-known that when a condition denoted as Quadratic Invariance (QI) holds, the optimal distributed control policy can be computed in a tractable way. Our goal is to unify and generalize the class of information structures over which quadratic invariance is equivalent to a test over finitely many binary matrices. The test we propose certifies convexity of the output-feedback distributed control problem in finite-horizon given any arbitrarily defined information structure, including the case of time varying communication networks and forgetting mechanisms. Furthermore, the framework we consider allows for including polytopic constraints on the states and the inputs in a natural way, without affecting convexity.

Structurally constrained controller synthesis for general proper plants with application to vehicle platooning

ABSTRACTThis paper considers the problem of synthesising a static output feedback (SOF) subject to arbitrary information structure constraints; in particular, the plants can be non-strictly proper. In such a case, the existing methods are hardly applicable except few special cases. A general approach that significantly differs from the existing methods is proposed that is able to deal with the most general case with the feature that both finite-frequency and full-frequency H-infinity performance specifications can be addressed in a unified manner. Sufficient solvability conditions are derived in terms of a set of finite-frequency positive real and strictly positive real conditions of linear matrix inequalities (LMIs) form. Some frequency-dependent matrices are introduced into the design with the merit of making the conditions less restrictive. Several numerical examples are given that demonstrate the efficacy of the proposed approach, including applications to vehicle platooning.

On a Hankel-based Measure of Decentralized Controllability and Observability

This paper discusses the controllability of linear time-invariant (LTI) systems with decentralized controllers. Whether an LTI system is controllable (by LTI controllers) with respect to a given information structure can be determined by testing for fixed modes. Measures have been developed to further determine how far a system is from having a fixed mode, but these measures cannot actually be computed in most cases. We thus seek an easily computable, non-binary measure of controllability for LTI systems with decentralized controllers of arbitrary information structure. We develop a measure based on the Hankel operator, that combines the controllability gramian, the observability gramian, and a version of the cross-gramian which incorporates the information structure.

Higher Order Uncertainty and Information: Static and Dynamic Games

Weinstein and Yildiz (2007) have shown that in static games, only very weak predictions are robust to perturbations of higher order beliefs. These predictions are precisely those provided by interim correlated rationalizability (ICR). This negative result is obtained under the assumption that agents have no information on payoffs. This assumption is unnatural in many settings. It is therefore natural to ask whether Weinstein and Yildiz's results remain true under more general information structures. This paper characterizes the “robust predictions” in static and dynamic games, under arbitrary information structures. This characterization is provided by an extensive form solution concept: interim sequential rationalizability (ISR). In static games, ISR coincides with ICR and does not depend on the assumptions on agents' information. Hence the “no information” assumption entails no loss of generality in these settings. This is not the case in dynamic games, where ISR refines ICR and depends on the details of the information structure. In these settings, the robust predictions depend on the assumptions on agents' information. This reveals a hitherto neglected interaction between information and higher order uncertainty, raising novel questions of robustness.

Belief-free equilibria in games with incomplete information: Characterization and existence

Abstract We generalize the results of Horner and Lovo (2009) [15] to N-player games with arbitrary information structure. First, we characterize the set of belief-free equilibrium payoffs under low discounting as the set of feasible payoffs that are individually rational, jointly rational, and incentive compatible. Second, we provide necessary and sufficient conditions on the information structure for this set to be non-empty.

Control design for large-scale Lur’e systems with arbitrary information structure constraints

In this paper, an LMI-based approach is proposed for the design of static output feedback for multi-nonlinear Lur’e–Postnikov systems. The resulting control laws ensure absolute stability and, at the same time, maximize the size of the nonlinear sectors. The proposed method is computationally efficient, and can accommodate feedback laws with arbitrary information structure constraints. The effectiveness of this approach is demonstrated on a large-scale example with 100 state variables.

Belief-Free Equilibria in Games with Incomplete Information: Characterization and Existence

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs.

Control design with arbitrary information structure constraints

In this paper, a new method is proposed for designing robust control laws that are subject to arbitrary information structure constraints. The computation of the gain matrix is formulated in terms of a static output feedback problem, which can be efficiently solved using linear matrix inequalities. The resulting control laws ensure stability with respect to a broad class of additive nonlinear uncertainties in the system.

Optimal robust mean-variance hedging in incomplete financial markets

An optimal B-robust estimate is constructed for the multidimensional parameter in the drift coefficient of a diffusion-type process with a small noise. The optimal mean-variance robust (optimal V-robust) trading strategy is to hedge (in the mean-variance sense) the contingent claim in an incomplete financial market with an arbitrary information structure and a misspecified volatility of the asset price, which is modelled by a multidimensional continuous semimartingale. The obtained results are applied to the stochastic volatility model, where the model of the latent volatility process contains the unknown multidimensional parameter in the drift coefficient and a small parameter in the diffusion term.

Martingale densities for general asset prices

This paper discusses some properties of general asset prices in continuous time. We introduce the concept of a martingale density which is a generalization of an equivalent martingale measure, and we show that absence of arbitrage plus some technical conditions implies the existence of a martingale density. This is in turn already sufficient to derive a recent result of Back (1991) on local risk premia for asset returns. As an application, we obtain a simple condition, valid in arbitrary information structures, for the drift part of discounted security gains to be absolutely continuous with respect to the variance process of the martingale part.

Solvability of certain classes of multistage stochastic programming problems with arbitrary information structure

Solvability of certain classes of multistage stochastic programming problems with arbitrary information structure