scholarly journals Near-Nash equilibrium strategies for LQ differential games with inaccurate state information

2006 ◽  
Vol 2006 ◽  
pp. 1-24 ◽  
Author(s):  
Manuel Jimenez-Lizarraga ◽  
Alex Poznyak
Keyword(s):  
Nash Equilibrium ◽  
Control Strategies ◽  
Perfect State ◽  
Linear Quadratic ◽  
State Information ◽  
Standard Solution ◽  
Nash Equilibrium Strategies ◽  
Zero Sum ◽  
Cost Game

ε-Nash equilibrium or “near equilibrium” for a linear quadratic cost game is considered. Due to inaccurate state information, the standard solution for feedback Nash equilibrium cannot be applied. Instead, an estimation of the players' states is substituted into the optimal control strategies equation obtained for perfect state information. The magnitude of theεin theε-Nash equilibrium will depend on the quality of the estimation process. To illustrate this approach, a Luenberger-type observer is used in the numerical example to generate the players' state estimates in a two-player non-zero-sum LQ differential game.

scholarly journals Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 132
Author(s):  
Valery Y. Glizer
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Cheap Control ◽  
Optimal Values ◽  
Definition Of ◽  
Zero Sum ◽  
Equilibrium Sequence

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

scholarly journals Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1669
Author(s):  
Jun Moon ◽  
Wonhee Kim
Keyword(s):  
Nash Equilibrium ◽  
Mean Field ◽  
Jump Diffusion ◽  
Linear Quadratic ◽  
Quadratic Mean ◽  
Field Type ◽  
The Mean ◽  
Zero Sum ◽  
Objective Functional

We consider the indefinite, linear-quadratic, mean-field-type stochastic zero-sum differential game for jump-diffusion models (I-LQ-MF-SZSDG-JD). Specifically, there are two players in the I-LQ-MF-SZSDG-JD, where Player 1 minimizes the objective functional, while Player 2 maximizes the same objective functional. In the I-LQ-MF-SZSDG-JD, the jump-diffusion-type state dynamics controlled by the two players and the objective functional include the mean-field variables, i.e., the expected values of state and control variables, and the parameters of the objective functional do not need to be (positive) definite matrices. These general settings of the I-LQ-MF-SZSDG-JD make the problem challenging, compared with the existing literature. By considering the interaction between two players and using the completion of the squares approach, we obtain the explicit feedback Nash equilibrium, which is linear in state and its expected value, and expressed as the coupled integro-Riccati differential equations (CIRDEs). Note that the interaction between the players is analyzed via a class of nonanticipative strategies and the “ordered interchangeability” property of multiple Nash equilibria in zero-sum games. We obtain explicit conditions to obtain the Nash equilibrium in terms of the CIRDEs. We also discuss the different solvability conditions of the CIRDEs, which lead to characterization of the Nash equilibrium for the I-LQ-MF-SZSDG-JD. Finally, our results are applied to the mean-field-type stochastic mean-variance differential game, for which the explicit Nash equilibrium is obtained and the simulation results are provided.

scholarly journals Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 47
Author(s):  
Sam Ganzfried
Keyword(s):  
Nash Equilibrium ◽  
Imperfect Information ◽  
Pure Strategy ◽  
Strategy Space ◽  
Equilibrium Strategies ◽  
Approximate Nash Equilibrium ◽  
Blotto Game ◽  
Nash Equilibrium Strategies ◽  
Zero Sum ◽  
Action Spaces

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games—in which the pure strategy space is (potentially uncountably) infinite—is far more challenging. Nonetheless, many real-world domains have continuous action spaces, e.g., where actions refer to an amount of time, money, or other resource that is naturally modeled as being real-valued as opposed to integral. We present a new algorithm for approximating Nash equilibrium strategies in continuous games. In addition to two-player zero-sum games, our algorithm also applies to multiplayer games and games with imperfect information. We experiment with our algorithm on a continuous imperfect-information Blotto game, in which two players distribute resources over multiple battlefields. Blotto games have frequently been used to model national security scenarios and have also been applied to electoral competition and auction theory. Experiments show that our algorithm is able to quickly compute close approximations of Nash equilibrium strategies for this game.

NASH EQUILIBRIUM IN TWO-SIDED MATE CHOICE PROBLEM

2008 ◽  
Vol 10 (04) ◽  
pp. 421-435 ◽  
Author(s):  
VLADIMIR MAZALOV ◽  
ANNA FALKO
Keyword(s):  
Nash Equilibrium ◽  
Search Model ◽  
Individual Choice ◽  
Choice Problem ◽  
Expected Payoff ◽  
Last Stage ◽  
Nash Equilibrium Strategies ◽  
The Individual

We consider a two-sided search model in which individuals from two distinct populations would like to form a long-term relationship with a member of the other population. The individual choice is determined by the quality of the partner. Initially the quality of individuals in the population is uniform. At every stage the individuals randomly matched from their populations recognize the quality of the partner. If they accept each other they create a couple and leave the game. The partner's quality is the payoff. Unmatched players go to the next stage. At the last stage the individuals accept any partner. Each player aims to maximize her/his expected payoff. In this paper explicit formulas for Nash equilibrium strategies are derived. Also, the model with incoming individuals is analyzed.

scholarly journals New Orthophoto Generation Strategies from UAV and Ground Remote Sensing Platforms for High-Throughput Phenotyping

2021 ◽  
Vol 13 (5) ◽  
pp. 860
Author(s):  
Yi-Chun Lin ◽  
Tian Zhou ◽  
Taojun Wang ◽  
Melba Crawford ◽  
Ayman Habib
Keyword(s):  
Remote Sensing ◽  
Control Strategies ◽  
Target Function ◽  
Canopy Cover ◽  
Surface Model ◽  
Flowering Date ◽  
Sensing Platforms ◽  
Geolocation Accuracy ◽  
New Strategies

Remote sensing platforms have become an effective data acquisition tool for digital agriculture. Imaging sensors onboard unmanned aerial vehicles (UAVs) and tractors are providing unprecedented high-geometric-resolution data for several crop phenotyping activities (e.g., canopy cover estimation, plant localization, and flowering date identification). Among potential products, orthophotos play an important role in agricultural management. Traditional orthophoto generation strategies suffer from several artifacts (e.g., double mapping, excessive pixilation, and seamline distortions). The above problems are more pronounced when dealing with mid- to late-season imagery, which is often used for establishing flowering date (e.g., tassel and panicle detection for maize and sorghum crops, respectively). In response to these challenges, this paper introduces new strategies for generating orthophotos that are conducive to the straightforward detection of tassels and panicles. The orthophoto generation strategies are valid for both frame and push-broom imaging systems. The target function of these strategies is striking a balance between the improved visual appearance of tassels/panicles and their geolocation accuracy. The new strategies are based on generating a smooth digital surface model (DSM) that maintains the geolocation quality along the plant rows while reducing double mapping and pixilation artifacts. Moreover, seamline control strategies are applied to avoid having seamline distortions at locations where the tassels and panicles are expected. The quality of generated orthophotos is evaluated through visual inspection as well as quantitative assessment of the degree of similarity between the generated orthophotos and original images. Several experimental results from both UAV and ground platforms show that the proposed strategies do improve the visual quality of derived orthophotos while maintaining the geolocation accuracy at tassel/panicle locations.

scholarly journals An Analytic and Numerical Investigation of a Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 66
Author(s):  
Aviv Gibali ◽  
Oleg Kelis
Keyword(s):  
Differential Game ◽  
Equation Approach ◽  
Linear Quadratic ◽  
Control Cost ◽  
Dual Representation ◽  
Cost Functional ◽  
Variational Derivatives ◽  
Zero Sum ◽  
The Cost ◽  
Derivatives Of

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

scholarly journals A game strategy model in the digital curling system based on NFSP

2021 ◽  
Author(s):  
Yuntao Han ◽  
Qibin Zhou ◽  
Fuqing Duan
Keyword(s):  
Reinforcement Learning ◽  
Nash Equilibrium ◽  
Action Space ◽  
Learning Networks ◽  
Game Tree ◽  
Continuous Action ◽  
Extensive Game ◽  
Strategy Model ◽  
Zero Sum ◽  
Tree Searching

AbstractThe digital curling game is a two-player zero-sum extensive game in a continuous action space. There are some challenging problems that are still not solved well, such as the uncertainty of strategy, the large game tree searching, and the use of large amounts of supervised data, etc. In this work, we combine NFSP and KR-UCT for digital curling games, where NFSP uses two adversary learning networks and can automatically produce supervised data, and KR-UCT can be used for large game tree searching in continuous action space. We propose two reward mechanisms to make reinforcement learning converge quickly. Experimental results validate the proposed method, and show the strategy model can reach the Nash equilibrium.

Manufacturing service order allocation in the context of social manufacturing based on Stackelberg game

2018 ◽  
Vol 233 (8) ◽  
pp. 1890-1901
Author(s):  
Wei Guo ◽  
Pingyu Jiang
Keyword(s):  
Quality Of Service ◽  
Nash Equilibrium ◽  
Manufacturing Industry ◽  
Stackelberg Game ◽  
Game Model ◽  
Service Cost ◽  
Order Allocation ◽  
Multi Objective ◽  
Bird Swarm Algorithm

For adapting the socialization, individuation and servitization in manufacturing industry, a new manufacturing paradigm called social manufacturing has received a lot of attention. Social manufacturing can be seen as a network that enterprises with socialized resources self-organized into communities that provide personalized machining and service capabilities to customers. Since a community of social manufacturing has multiple enterprises and emphasizes on the importance of service, manufacturing service order allocation must be studied from the new perspective considering objectives on service cost and quality of service. The manufacturing service order allocation can be seen as a one-to-many game model with multi-objective. In this article, a Stackelberg game model is proposed to tackle the manufacturing service order allocation problem with considering the payoffs on cost and quality of service. Since this Stackelberg game can be mapped to a multi-objective bi-level programming, a modified multi-objective hierarchical Bird Swarm Algorithm is used to find the Nash equilibrium of the game. Finally, a case from a professional printing firm is analyzed to validate the proposed methodology and model. The objective of this research is to find the Nash equilibrium on the manufacturing service order allocation and provide strategies guidance for customer and small- and medium-sized enterprises with optimal service cost and lead time. According to the game process and Nash equilibrium, some rules are revealed, and they are useful for guiding practical production.

Evaluation of Uncertainty for the Determination of Magnesium Oxide Content in Limestone by the Atomic Absorption Spectrometry

2014 ◽  
Vol 707 ◽  
pp. 283-288
Author(s):  
Xiang Dong Wen ◽  
Zheng Zhou ◽  
Wen Yang Pan ◽  
Mei Shao
Keyword(s):  
Atomic Absorption Spectrometry ◽  
Atomic Absorption ◽  
Magnesium Oxide ◽  
Influence Factors ◽  
Absorption Spectrometry ◽  
Oxide Content ◽  
Standard Solution ◽  
The Mathematical Model

According to GB/T3286.1-2012(The determination of calcium oxide and magnesium oxide content in limestone and dolomite), the mathematical model of magnesium oxide content determination in limestone by atomic absorption spectrometry was established. The various uncertainty factors of different elements for a sample were discussed and compared in the testing process. The confidence interval for the measurement result was (0.74±0.03)%,k=2 in uncertainty evaluation .The results showed that the variability of working curve and accuracy of standard solution volume for working curve were main influence factors of uncertainty. It could effectively reduce the uncertainty from the perspective of the main factors,and improve the quality of analysis.

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