scholarly journals Quantum absentminded driver problem revisited

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Piotr Fra̧ckiewicz ◽  
Katarzyna Rycerz ◽  
Marek Szopa
Keyword(s):  
Decision Maker ◽  
Decision Problem ◽  
Classical Problem ◽  
Classical Case ◽  
Behavioral Strategies ◽  
Quantum Domain ◽  
Quantum Objects ◽  
Quantum Approach ◽  
Strategic Position ◽  
Suitable Restriction

AbstractThe aim of the paper is to study the problem of absentminded driver in the quantum domain. In the classical case, it is a well-known example of a decision problem with imperfect recall that exhibits lack of equivalence between mixed and behavioral strategies. The optimal payoff outcome is significantly lower than the maximum payoff appearing in the game. This raises the question whether a quantum approach to the problem can increase the strategic position of the decision maker. The results that we present in the paper clearly reveal the benefits from playing the absentminded problem with the aid of quantum objects. Through appropriately chosen initial quantum state, the unitary strategies enable the decision maker to obtain the maximum possible payoff. At the same time, our scheme comes down to the classical problem with a suitable restriction of unitary strategies.

scholarly journals Two Remarks on Blackwell's Theorem

2008 ◽  
Vol 45 (02) ◽  
pp. 580-586 ◽  
Author(s):  
Ehud Lehrer ◽  
Eran Shmaya
Keyword(s):  
Decision Maker ◽  
Information Structure ◽  
Decision Problem ◽  
Partial Information ◽  
The Other ◽  
Actual State ◽  
Information Structures ◽  
Comparison Of Experiments ◽  
Classical Characterization ◽  
Blackwell's Theorem

In a decision problem with uncertainty a decision maker receives partial information about the actual state via an information structure. After receiving a signal, he is allowed to withdraw and gets zero profit. We say that one structure is better than another when a withdrawal option exists if it may never happen that one structure guarantees a positive profit while the other structure guarantees only zero profit. This order between information structures is characterized in terms that are different from those used by Blackwell's comparison of experiments. We also treat the case of a malevolent nature that chooses a state in an adverse manner. It turns out that Blackwell's classical characterization also holds in this case.

scholarly journals Resolving Time Inconsistency of Decision Problem with Non-expectation Operator: From Internal Conflict to Internal Harmony by Strategy of Self-Coordination

2020 ◽  
Author(s):  
Xiangyu Cui ◽  
Duan Li ◽  
Yun Shi
Keyword(s):  
Decision Maker ◽  
Decision Problem ◽  
Hyperbolic Discounting ◽  
Time Inconsistency ◽  
Internal Conflict ◽  
Equilibrium Strategy ◽  
Game Model ◽  
Long Run ◽  
Short Run ◽  
Time Inconsistent

When a stochastic decision problem is time inconsistent, the decision maker would be puzzled by his conflicting decisions optimally derived from his time-varying preferences at different time instants (with different time horizons). While the long-run self (LR) of the decision maker pursues the long-term optimality, the short-run selves (SRs) of the decision maker at different time instants bow to short-term temptations. While the literature began to recognize the importance to strike a balance between LR's and SRs' interests, the existing results are not applicable to situations where the decision maker's preferences involve non-expectation operators. We propose an operable unified two-tier dual-self game model with commitment by punishment, which can cope with general time inconsistent stochastic decision problems with both expectation and non-expectation operators in the objective function. By attaching punishment terms to both the preferences of LR and SRs which quantitatively evaluate the internal conflict among different selves, our game model aligns the interests of the LR and SRs to a certain degree. The equilibrium strategy, termed strategy of self-coordination, achieves some degree of internal harmony among various selves. We successfully apply the model to the investment and consumption problem with quasi-hyperbolic discounting and the dynamic mean-variance portfolio selection problem.

scholarly journals Fully discrete finite element data assimilation method for the heat equation

2018 ◽  
Vol 52 (5) ◽  
pp. 2065-2082 ◽  
Author(s):  
Erik Burman ◽  
Jonathan Ish-Horowicz ◽  
Lauri Oksanen
Keyword(s):  
Finite Element ◽  
Initial Data ◽  
Heat Equation ◽  
Time Derivative ◽  
Classical Problem ◽  
Classical Case ◽  
Space Time ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Element Discretization

We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we consider standard continuous affine finite element approximation, and the time derivative is discretized using a backward differentiation. We regularize the discrete system by adding a penalty on the H2-semi-norm of the initial data, scaled with the mesh-parameter. The analysis of the method uses techniques developed in E. Burman and L. Oksanen [Numer. Math. 139 (2018) 505–528], combining discrete stability of the numerical method with sharp Carleman estimates for the physical problem, to derive optimal error estimates for the approximate solution. For the natural space time energy norm, away from t = 0, the convergence is the same as for the classical problem with known initial data, but contrary to the classical case, we do not obtain faster convergence for the L2-norm at the final time.

A MODEL BASED ON INFLUENCE DIAGRAMS FOR MULTI-CRITERIA DECISION-MAKING

2012 ◽  
Vol 21 (04) ◽  
pp. 1250018 ◽  
Author(s):  
KARIMA SEDKI ◽  
VÉRONIQUE DELCROIX
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Decision Problem ◽  
Expert Knowledge ◽  
External Factors ◽  
Influence Diagrams ◽  
Multi Criteria Decision Making ◽  
Model Based ◽  
Decision Variables ◽  
Other Information

In this paper, we focus on multi-criteria decision-making problems. We propose a model based on influence diagrams; this model is able to handle uncertainty, represent interdependencies among the different decision variables and facilitate communication between the decision-maker and the analyst. The particular structure of the proposed model makes it possible to take into account the alternatives described by an attribute set, the decision-maker's characteristics and preferences, and other information (e.g., internal or external factors) that influence the decision. Modeling the decision problem in terms of influence diagrams requires a lot of work to gather expert knowledge. However, once the model is built, it can be easily and efficiently used for different instances of the decision problem. In fact, using our model simply requires entering some basic information, such as the values of internal or external factors and the decision-maker's characteristics. Our model also defines the importance of each criterion in terms of what is known about the decision maker, the quality index and the utility of each alternative.

scholarly journals A Mathematical Model of Communication with Reputational Concerns

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Ce Huang ◽  
Yuanyuan Zhang ◽  
Chong Lai
Keyword(s):  
Mathematical Model ◽  
Decision Maker ◽  
Decision Problem ◽  
The One ◽  
Reputational Concerns

We investigate a mathematical model where an expert advises a decision maker for two periods. The decision maker is initially unsure about whether the expert is biased or not. After consulting the expert on the decision problem of period one, the decision maker updates belief about the expert’s bias and consults the expert on the problem of period two. We find that more information is delivered in the model’s first period than in the one-period situation of communication.

scholarly journals Computing Euclidean Steiner trees over segments

2020 ◽  
Vol 8 (3-4) ◽  
pp. 309-325 ◽  
Author(s):  
Ernst Althaus ◽  
Felix Rauterberg ◽  
Sarah Ziegler
Keyword(s):  
Euclidean Plane ◽  
Classical Problem ◽  
Classical Case ◽  
Minimum Length ◽  
Second Phase ◽  
Two Phase ◽  
Math Program ◽  
Steiner Minimum Tree ◽  
Set Of Points ◽  
Selection Of

Abstract In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superset of so-called full components of an SMT in the first phase. We prove a structural theorem for these full components, which allows us to use almost the same GeoSteiner algorithm as in the classical SMT problem. The second phase, the selection of a minimal cost subset of constructed full components, is exactly the same as in GeoSteiner approach. Finally, we report some experimental results that show that our approach is more efficient than the approximate solution that is obtained by sampling the segments.

scholarly journals Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment

2019 ◽  
Vol 10 (2) ◽  
pp. 478-492
Author(s):  
P. Jean-Jacques Herings ◽  
Andrey Meshalkin ◽  
Arkadi Predtetchinski
Keyword(s):  
Decision Maker ◽  
Decision Problem ◽  
Decision Problems ◽  
Multiple Selves ◽  
Important Special Case ◽  
Optimal Policies ◽  
Markov Decision ◽  
History Of ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

Abstract The paper considers a class of decision problems with an infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. Our results are twofold: Firstly, we demonstrate that the set of subgame optimal policies coincides with the set of subgame perfect equilibria of the decision problem. Furthermore, the set of subgame optimal policies is contained in the set of optimal policies and the set of optimal policies is contained in the set of Nash equilibria. Secondly, we show that the set of pure subgame optimal policies is the unique minimal curb set of the decision problem. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.

The quantum monty hall problem

2002 ◽  
Vol 2 (5) ◽  
pp. 355-366
Author(s):  
G.M. D'Ariano ◽  
R.D. Gill ◽  
M. Keyl ◽  
B. Kummerer ◽  
H. Maassen ◽  
...  
Keyword(s):  
Optimal Strategy ◽  
Decision Problem ◽  
Prior Information ◽  
Classical Case ◽  
Statistical Decision ◽  
Statistical Decision Problem ◽  
Finite Set ◽  
Quantum Version ◽  
Person Game ◽  
Classical Game

We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal strategy is to use a completely entangled quantum notepad, on which to encode his prior information.

Post-decision consolidation, as a function of the instructions to the decision maker and of the decision problem

1994 ◽  
Vol 87 (2-3) ◽  
pp. 181-197 ◽  
Author(s):  
Ola Svenson ◽  
Amparo Ortega Rayo ◽  
Mikael Andersen ◽  
Annika Sandberg ◽  
Ingrid Svahlin
Keyword(s):  
Decision Maker ◽  
Decision Problem

Addressing Limitations of Pareto Front in Design Under Uncertainty

2011 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Zissimos P. Mourelatos ◽  
Efstratios Nikolaidis
Keyword(s):  
Decision Maker ◽  
Decision Problem ◽  
Utility Theory ◽  
Pareto Front ◽  
Optimization Problem ◽  
Reduction Gear ◽  
Design Under Uncertainty ◽  
Design Constraints ◽  
Multi Attribute Utility Theory ◽  
Single Attribute

Engineering design reconciles design constraints with decision maker preferences. The task of eliciting and encoding decision maker preferences is, however, extremely difficult. A Pareto front representing the locus of the non-dominated designs is therefore, often generated to help a decision maker select the best design. In this paper, we show that this method has a shortcoming. We show that when there is uncertainty in both the decision problem variables and in the decision maker’s preferences, this methodology is inconsistent with multi-attribute utility theory, unless the decision maker trades off attributes or some functions of them linearly. This is a strong restriction. To account for this, we propose a methodology that enables a decision maker to select the best design on a modified Pareto front which is acquired using envelopes of a set of certainty equivalent surfaces. This methodology does not require separability of the multi-attribute utility function into single attribute utilities, nor does it require the decision maker to trade the attributes (or any function of them) linearly. We demonstrate this methodology on a simple optimization problem and in design of a reduction gear.

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