To answer database queries over incomplete data, the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their unions, even in the presence of constraints. With negation added, the problem becomes intractable however. We concentrate on the complexity of certain answers under constraints and on effficiently answering queries outside the usual classes of (unions) of conjunctive queries by means of rewriting as Datalog and first-order queries. We first notice that there are three different ways in which query answering can be cast as a decision problem. We complete the existing picture and provide precise complexity bounds on all versions of the decision problem, for certain and best answers. We then study a well-behaved class of queries that extends unions of conjunctive queries with a mild form of negation. We show that for them, certain answers can be expressed in Datalog with negation, even in the presence of functional dependencies, thus making them tractable in data complexity. We show that in general, Datalog cannot be replaced by first-order logic, but without constraints such a rewriting can be done in first order.

Nuclear and missile tests by North Korea, which directly threaten China's national interests, regional stability, and economic development, have consistently irritated China. Since the 1950s, China and North Korea have held high-level meetings aimed at discussing and improving their bilateral relationship. Using empirical analysis, this study attempts to examine the impact of these meetings on North Korea's missile and nuclear tests. The study argues that as the frequency of high-level meetings between China and North Korea increases, North Korea's provocative actions decrease. The high-level meetings serve to address the issue of incomplete information, create avenues for economic aid and cooperation, and reduce the likelihood of future nuclear and missile tests. The empirical findings indicate that while high-level meetings with or without the presence of top leaders can lead to a reduction in missile tests by North Korea, only summits between China and North Korea have a significant impact on the reduction of nuclear tests by North Korea.

We extend the classical setting of an optimal stopping problem under full information to include problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source learning problem. Assigning a prior distribution for the unknown state, standard filtering theory can be employed to embed the problem in a Markovian framework with one additional state variable representing the posterior of the unknown state. We provide a convenient formulation of this Markovian problem, based on a measure change technique that decouples the underlying process from the new state variable. Moreover, we show by means of several novel examples that this reduced formulation can be used to solve problems explicitly.

We study an optimal reinsurance problem for a diffusion model, in which the drift of the claim follows an Ornstein–Uhlenbeck process. The aim of the insurer is to maximize the expected exponential utility of its terminal wealth. We consider two cases: full information and partial information. Full information occurs when the insurer directly observes the drift; partial information occurs when the insurer observes only its claims. By applying stochastic control and by solving the corresponding Hamilton–Jacobi–Bellman equations, we find the value function and the optimal reinsurance strategy under both full and partial information. We determine a relationship between the value function and reinsurance strategy under full information with the value function and reinsurance strategy under partial information.

Most research on the compromise effect focuses on how consumers make their decisions in a complete information scenario; however, consumers generally lack sufficient information when they make purchase decisions. This research aims to explore the compromise effect with incomplete information. Three studies were conducted to examine the research hypotheses. The main findings was that consumers are more likely to choose the middle option when they have incomplete information than when they have complete information. Further, the compromise effect decreases when consumers can choose to defer their decision in an incomplete information scenario. Finally, the compromise effect decreases when consumers are asked to infer missing attribute values from the incomplete information.

In a highly uncertain world, individuals often have to make decisions in situations with incomplete information. We investigated in three experiments how partial cue information is treated in complex probabilistic inference tasks. Specifically, we test a mechanism to infer missing cue values that is based on the discrimination rate of cues (i.e., how often a cue makes distinct predictions for choice options). We show analytically that inferring missing cue values based on discrimination rate maximizes the probability for a correct inference in many decision environments and that it is therefore adaptive to use it. Results from three experiments show that individuals are sensitive to the discrimination rate and use it when it is a valid inference mechanism but rely on other inference mechanisms, such as the cues’ base-rate of positive information, when it is not. We find adaptive inferences for incomplete information in environments in which participants are explicitly provided with information concerning the base-rate and discrimination rate of cues (Exp. 1) as well as in environments in which they learn these properties by experience (Exp. 2). Results also hold in environments of further increased complexity (Exp. 3). In all studies, participants show a high ability to adaptively infer incomplete information and to integrate this inferred information with other available cues to approximate the naïve Bayesian solution.

In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $\sqrt {NT}$, where $N$ denotes the number of products and $T$ denotes the time horizon. This result is shown under the assumption that the product revenues are constant, and thus leaves the question open whether a lower regret rate can be achieved for nonconstant revenue parameters. In this note, we show that this is not the case: we show that, for any vector of product revenues there is a positive constant such that the regret of any policy is bounded from below by this constant times $\sqrt {N T}$. Our result implies that policies that achieve ${{\mathcal {O}}}(\sqrt {NT})$ regret are asymptotically optimal for all product revenue parameters.

A counterexample to the notion that money is memory is provided—one that relies on incomplete information. There exists an implementable allocation for it with money that is not implementable with memory. The result arises because money conveys only a limited amount of information about past actions, which can be beneficial in settings with incomplete information.

International cooperation often requires costly policy adjustments. States may worry, however, that such adjustments weaken their outside options, and thus reduce their bargaining power. How does uncertainty about the effects of policy adjustments on outside options influence the depth of cooperation that states can achieve? My game-theoretic analysis shows that uncertainty about outside options is an obstacle to deep cooperation. If states agree on deep cooperation, they have to compensate vulnerable states with weak outside options for their losses. Under uncertainty, states that are not vulnerable have an incentive to falsely claim that they are vulnerable (i) to avoid a side payment or (ii) to obtain compensation for being vulnerable. The result holds even if the added value of deep cooperation would be large enough to fully compensate the losers. In equilibrium, the more vulnerable state sometimes offers a side payment to the less vulnerable one. More broadly, the analysis reveals a new international cooperation problem and provides a new rationale for costly signaling mechanisms and delegation to international organizations.

We extend the 0-approximation of sensing actions and incomplete information in Son and Baral (2001) to action theories with static causal laws and prove its soundness with respect to the possible world semantics. We also show that the conditional planning problem with respect to this approximation is NP-complete. We then present an answer set programming based conditional planner, called ASCP, that is capable of generating both conformant plans and conditional plans in the presence of sensing actions, incomplete information about the initial state, and static causal laws. We prove the correctness of our implementation and argue that our planner is sound and complete with respect to the proposed approximation. Finally, we present experimental results comparing ASCP to other planners.