Incomplete Information Case Research Articles

Implementation with Extensive Form Games: One Round of Signaling Is Not Enough

In situations of complete information, when a social choice function can be implemented using an extensive form game it is always the case that there is an equilibrium which does not go beyond the first stage (that is, an equilibrium with “one round of signaling”). We show that this is not true in the incomplete information case. We provide an example in which a social choice function cannot be implemented with an extensive form game if the mechanism has an equilibrium with one round of signaling and we put some restrictions on the way in which out-of-equilibrium beliefs are formed. The social choice function can, however, be implemented using an extensive form mechanism, but the equilibrium has to reach the second stage. Journal of Economic Literature Classification numbers: C72, D70.

Fringe Visibility and Which-Way Information in an Atom Interferometer

We experimentally investigate the reduction of the fringe visibility in an atom interferometer due to the storage of which-way information. We focus on the case of incomplete which-way information and use the distinguishability $D$ to quantify how much information is stored. For a given value of $D$, the fringe visibility $V$ is limited by the duality relation ${D}^{2}{+V}^{2}\ensuremath{\le}1$. We have measured $D$ and $V$ independently. Combining the results, we find good agreement with the duality relation.

The design of supply contracts as a problem of delegation

We consider the design of a supply contract as a problem of delegation in a buying firm. In general the agent (who acts on behalf of a principal in the firm) cannot be assumed to transform her information in probability estimates like the principal would do possessing the same information. In the investigated case of incomplete information the design of contracts is affected by the beliefs about characteristics of the supplier. Therefore it is important to analyze in which way the expected profit depends on these probabilities in order to find the principal's optimal instruction. The best instruction is determined by a trade-off between the costs due to the time the principal spends on dealing with the problem and formulating the instructions and the costs due to a suboptimal menu of contracts offered by the agent.

Control of linear systems with rational expectations. The case of incomplete information

The problem of optimal control of linear economic systems with rational expectations and quadratic objective function is solved for the case of incomplete information. The case of complete information has been previously studied. In both problems the hypothesis of causality is not satisfied and, therefore, the standard techniques of control theory cannot be directly applied, though the method used is based on these techniques.

Sliding mode control and a variable structure system observer as a dual problem for systems with non-linear uncertainties

Sliding mode control is described for continuous-time systems with uncertain nonlinear elements, in which the euclidean norm of the unknown element is bounded by a known value. For a case of complete state information, we first consider a sliding mode controller consisting of three parts: a linear state feedback control, an equivalent input and a min-max control. It is then shown that the present attractiveness condition is simpler than that for a case without using the concept of equivalent input. We next derive a variable structure system (VSS) observer as a completely dual form to the sliding mode controller. The attractiveness condition is also simpler than that for a case an equivalent term is not used, but a more severe assumption is required to solve such a VSS observer. Finally, we discuss a case of incomplete state information by applying the VSS observer.

A new method for discovering rules from examples in expert systems

The experts often cannot explain why they choose this or that decision in terms of formalized “if-then” rules; in these cases we have a set of examples of their real decisions, and it is necessary to reveal the rules from these examples. The existing methods of discovering rules from examples either demand that the set of examples be in some sense complete (and it is often not complete) or they are too complicated. We present a new algorithm which is always applicable. This algorithm is based on the formalization of rough set theory, a formalization which describes the case of incomplete information.

Stochastic pursuit-evasion differential games in the plane

Four stochastic pursuit-evasion differential games involving two players, P and E, moving in the plane are considered. The difference between the games lies in their information structures. In each of the games, sufficient conditions on optimal feedback strategies, in the cases of complete information, and on weak optimal feedback strategies, in the cases of incomplete information, are derived. Optimal strategies are computed for the cases of complete information and weak suboptimal strategies for the cases of incomplete information. The results indicate that the correct measurement of the direction of the segment PE is more important than the measurement of the distance (P, E).

Demands Identification Problems in Inventory Control Systems

The demands estimation problem for semi-products inventory control in industrial plant is formulated as the problem of identification of the operator mapping the need in semi-products into output products volumes. The semi-products production schedule is subject to several point-wise and integral constraints. For linear case the desired estimate is determined by the Wiener-Hopf - type equations solution. The procedure of sequential updating of desired demands schedule is designed using the set of inverse operator estimates. The adaptive algorithms of optimal inventory control policies parameters updating for single-product inventory systems with random demand and replenishment are proposed when a priori information about probability density functions of demand and replenishment is incomplete. Problem modifications with one and two possible replenishment sources are considered. The proposed adaptive algorithms converge to the parameter values of optimal (in terms of the expected cost criterion) control law respecting the case of incomplete information.

Optimal Control of Discrete Processes with Complete or Incomplete Information

N stage decision processes described by state vectors, control vectors and parameter vectors are considered. The objective function is given by an additive function of real-valued or vector-valued functions. In the oase of complete information, we formulate Bellmanean functional equations with parameters as sufficient optimality conditions. The case of incomplete information (also for multi-criterion optimization) is formulated by an operator in such away that in our theory stochastic control, adaptive control, and games (minimax control) are special cases. Extended Bellmanean functional equations are given as sufficient optimality conditions, if the operator has the properties multiplicativity and mo no tonicity. As an example of a class of applied problems for our theory, we formulate a transport control problem in the building industry.An approximative algorithm for the solution of optimal control problems with incomplete information together with error estimations is given as an example of suitable computational methods. The error bound functions are determined as solutions of new functional inequalities.