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Register a new userA Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria
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This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two levels of game-theoretic reasoning intertwined. First, each player looks for an intra-personal equilibrium among her current and future selves, so as to resolve time inconsistency triggered by non-exponential discounting. Next, given the other players chosen stopping policy, each player selects a best response among her intra-personal equilibria. A resulting inter-personal equilibrium is then a Nash equilibrium between the two players, each of whom employs her best intra-personal equilibrium with respect to the other players stopping policy. Under appropriate conditions, we show that an inter-personal equilibrium exists, based on concrete iterative procedures along with Zorns lemma. To illustrate our theoretic results, we investigate a two-player real options valuation problem: two firms negotiate a deal of cooperation to initiate a project jointly. By deriving inter-personal equilibria explicitly, we find that coercive power in negotiation depends crucially on the impatience levels of the two firms.
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A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms strong equilibria and weak equilibria are coined for controls under the new and the standard definitions, respectively. When the state process is a time-homogeneous continuous-time Markov chain, a careful asymptotic analysis gives complete characterizations of weak and strong equilibria. Thanks to Kakutani-Fans fixed-point theorem, general existence of weak and strong equilibria is also established, under additional compactness assumption. Our theoretic results are applied to a two-state model under non-exponential discounting. In particular, we demonstrate explicitly that there can be incentive to deviate from a weak equilibrium, which justifies the need for strong equilibria. Our analysis also provides new results for the existence and characterization of discrete-time equilibria under infinite horizon.
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the time-inconsistent stopping control problems under general multi-dimensional controlled diffusion model and propose a formal definition of their equilibriums. We show that an admissible pair $(hat{u},C)$ of control-stopping policy is equilibrium if and only if the axillary function associated to it solves the extended HJB system. We provide almost equivalent conditions to the boundary term of this extended HJB system, which is related to the celebrated smooth fitting principles. As applications of our theoretical results, we develop an investment-withdrawal decision model for time-inconsistent decision makers in infinite time horizon. We provide two concrete examples, one of which includes constant proportion investment with one side threshold withdrawal strategy as equilibrium; in another example, all strategies with constant proportion investment are proved to be irrational, no matter what the withdrawal strategy is.
In this paper we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic to tackle the theoretical aspects of the considered stochastic control problem. Consequently, as an important application of the theoretical results, by applying a machine learning algorithm we solve numerically the mean-variance portfolio selection problem under the model uncertainty.
One of the most important aspects of security organization is to establish a framework to identify security significant points where policies and procedures are declared. The (information) security infrastructure comprises entities, processes, and technology. All are participants in handling information, which is the item that needs to be protected. Privacy and security information technology is a critical and unmet need in the management of personal information. This paper proposes concepts and technologies for management of personal information. Two different types of information can be distinguished: personal information and nonpersonal information. Personal information can be either personal identifiable information (PII), or nonidentifiable information (NII). Security, policy, and technical requirements can be based on this distinction. At the conceptual level, PII is defined and formalized by propositions over infons (discrete pieces of information) that specify transformations in PII and NII. PII is categorized into simple infons that reflect the proprietor s aspects, relationships with objects, and relationships with other proprietors. The proprietor is the identified person about whom the information is communicated. The paper proposes a database organization that focuses on the PII spheres of proprietors. At the design level, the paper describes databases of personal identifiable information built exclusively for this type of information, with their own conceptual scheme, system management, and physical structure.
Personal Information Management (PIM) refers to the practice and the study of the activities a person performs in order to acquire or create, store, organize, maintain, retrieve, use, and distribute information in each of its many forms (paper and digital, in e-mails, files, Web pages, text messages, tweets, posts, etc.) as needed to meet lifes many goals (everyday and long-term, work-related and not) and to fulfill lifes many roles and responsibilities (as parent, spouse, friend, employee, member of community, etc.). PIM activities are an effort to establish, use, and maintain a mapping between information and need. Activities of finding (and re-finding) move from a current need toward information while activities of keeping move from encountered information toward anticipated need. Meta-level activities such as maintaining, organizing, and managing the flow of information focus on the mapping itself. Tools and techniques of PIM can promote information integration with benefits for each kind of PIM activity and across the life cycle of personal information. Understanding how best to accomplish this integration without inadvertently creating problems along the way is a key challenge of PIM.
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