Optimal Strategy for Multiple Evaders Against an Agile Pursuer

2019 ◽  
Author(s):  
Chunsheng Liu ◽  
Mark V. Trevorrow
Keyword(s):  
Nash Equilibrium ◽  
Optimal Strategy ◽  
Optimal Solution ◽  
Hierarchical Approach ◽  
Detection Capability ◽  
Traditional Methods ◽  
Close Point ◽  
Perfect Knowledge ◽  
Player Game ◽  
Slow Moving

Abstract This paper focuses on the problem of multiple slow moving and less maneuverable evaders against an agile pursuer, addressing the optimal strategy for multiple evaders. This is the so-called wolf-sheep game. Two scenarios are examined: 1) both pursuer and evaders have perfect knowledge about opponents, and 2) the pursuer has limited detection capability. Since the wolf-sheep game involves the Boolean value state, the game is hard to solve using traditional methods. This paper adopts a hierarchical approach. The two player game is solved first. Then the solution of the multiplayer game is based on the two-player game and the pursuer chasing order. The optimal strategy is calculated based on Nash equilibrium. The game with limited detection capability is solved by maximizing the Close Point of Approach (CPA). The optimal solution will be found theoretically and numerically.

scholarly journals Variable and sub-optimal responses to a choice problem are a persistent default mode

2019 ◽  
Author(s):  
Amelia R. Hunt ◽  
Warren James ◽  
Josephine Reuther ◽  
Melissa Spilioti ◽  
Eleanor Mackay ◽  
...  
Keyword(s):  
Optimal Strategy ◽  
Decision Rules ◽  
Optimal Solution ◽  
The Other ◽  
Rational Decision ◽  
Choice Problem ◽  
Default Mode ◽  
Potential Benefits ◽  
Simple Logic ◽  
Simple Decision Rule

Here we report persistent choice variability in the presence of a simple decision rule. Two analogous choice problems are presented, both of which involve making decisions about how to prioritize goals. In one version, participants choose a place to stand to throw a beanbag into one of two hoops. In the other, they must choose a place to fixate to detect a target that could appear in one of two boxes. In both cases, participants do not know which of the locations will be the target when they make their choice. The optimal solution to both problems follows the same, simple logic: when targets are close together, standing at/fixating the midpoint is the best choice. When the targets are far apart, accuracy from the midpoint falls, and standing/fixating close to one potential target achieves better accuracy. People do not follow, or even approach, this optimal strategy, despite substantial potential benefits for performance. Two interventions were introduced to try and shift participants from sub-optimal, variable responses to following a fixed, rational rule. First, we put participants into circumstances in which the solution was obvious. After participants correctly solved the problem there, we immediately presented the slightly-less-obvious context. Second, we guided participants to make choices that followed an optimal strategy, and then removed the guidance and let them freely choose. Following both of these interventions, participants immediately returned to a variable, sub-optimal pattern of responding. The results show that while constructing and implementing rational decision rules is possible, making variable responses to choice problems is a strong and persistent default mode. Borrowing concepts from classic animal learning studies, we suggest this default may persist because choice variability can provide opportunities for reinforcement learning.

THE PRICE OF NASH EQUILIBRIA IN MULTICAST TRANSMISSION GAMES

2010 ◽  
Vol 11 (03n04) ◽  
pp. 97-120 ◽  
Author(s):  
VITTORIO BILÒ
Keyword(s):  
Nash Equilibrium ◽  
Cost Sharing ◽  
Price Of Anarchy ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Price Of Stability ◽  
Common Source ◽  
Cost Share ◽  
Worst Case ◽  
The Cost

We consider the problem of sharing the cost of multicast transmissions in non-cooperative undirected networks where a set of receivers R wants to be connected to a common source s. The set of choices available to each receiver r ∈ R is represented by the set of all (s, r)-paths in the network. Given the choices performed by all the receivers, a public known cost sharing method determines the cost share to be charged to each of them. Receivers are selfish agents aiming to obtain the transmission at the minimum cost share and their interactions create a non-cooperative game. Devising cost sharing methods yielding games whose price of anarchy (price of stability), defined as the worst-case (best-case) ratio between the cost of a Nash equilibrium and that of an optimal solution, is not too high is thus of fundamental importance in non-cooperative network design. Moreover, since cost sharing games naturally arise in socio-economical contests, it is convenient for a cost sharing method to meet some constraining properties. In this paper, we first define several such properties and analyze their impact on the prices of anarchy and stability. We also reconsider all the methods known so far by classifying them according to which properties they satisfy and giving the first non-trivial lower bounds on their price of stability. Finally, we propose a new method, namely the free-riders method, which admits a polynomial time algorithm for computing a pure Nash equilibrium whose cost is at most twice the optimal one. Some of the ideas characterizing our approach have been independently proposed in Ref. 10.

Analysis of a two-dimensional stair-case warranty policy with preventive maintenance

2020 ◽  
Vol 32 (1) ◽  
pp. 51-67
Author(s):  
Jinting Wang ◽  
Sheng Zhu ◽  
Simiao Du
Keyword(s):  
Mathematical Model ◽  
Preventive Maintenance ◽  
Optimal Strategy ◽  
Optimal Solution ◽  
Two Dimensional ◽  
Rectangular Region ◽  
Numerical Example ◽  
Warranty Cost

Abstract We develop a mathematical model to study optimal preventive maintenance (PM) strategy under a two-dimensional stair-case warranty policy considering both age and usage of a product. During the warranty term, sellers implement preventive maintenance within the stair-case region of the warranty policy and upon failure a product is repaired minimally and immediately. Our objective is to find the optimal PM strategy that minimizes the seller’s cost of warranty while jointly considering the age and usage intervals of the PM policy and the level of PM executed. We also discuss how our results compare to those in a two-dimensional warranty policy with a rectangular region, and we find that the stair-case policy is preferable for sellers. An algorithm is provided to find the optimal solution and a numerical example is presented to illustrate how to find an optimal strategy with our proposed method. We show numerically that the expected total warranty cost is convex both in the age and the usage of the product under certain conditions.

scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (04) ◽  
pp. 1165-1172
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

scholarly journals METHODS OF SYSTEM ANALYSIS IN THE FORMATION OF INFORMATION SECURITY POLICY ON TRANSPORT

2021 ◽  
Vol 1 (13) ◽  
pp. 81-91
Author(s):  
Valerii Lakhno ◽  
Borys Husiev ◽  
Victor Smolii ◽  
Andrii Blozva ◽  
Dmytro Kasatkin ◽  
...  
Keyword(s):  
Information Security ◽  
Optimal Strategy ◽  
Security Policy ◽  
System Analysis ◽  
System Development ◽  
Optimal Solution ◽  
Security System ◽  
Enterprise Management ◽  
Final Decision ◽  
Advantages And Disadvantages

Approaches to the application of methods of system analysis to solve problems related to information security of enterprises in transport, which have a complex IT structure with a large number of components. It is shown that the active expansion of the areas of informatization of the transport industry, especially in the segment of mobile, distributed and wireless technologies, is accompanied by the emergence of new threats to information security. It is shown that in order to build an effective information security system, the selection and implementation of adequate technical means of protection should be preceded by a stage of description, analysis and modeling of threats, vulnerabilities, followed by calculation of risks for IS and determining the optimal strategy for information security system. After evaluating the different NIB options according to several criteria, a decision is made: if the recommendations coincide, the optimal solution is chosen with greater confidence. If there is a contradiction of recommendations, the final decision is made taking into account its advantages and disadvantages, for example, the strategy of information security system development is chosen, which turned out to be optimal for at least two criteria. If different NIB development strategies are obtained for all three criteria, it is necessary to vary the values of pessimism-optimism in the Hurwitz criterion or change the data, for example, about possible threats to IP or automated enterprise management system. An algorithm for modeling the decision-making process for selecting the optimal strategy for managing investment design components of the information security system for the transport business entity is proposed.

scholarly journals Resource-Saving Methods for Growing Rice in the Krasnodar Territory

2021 ◽  
Vol 37 ◽  
pp. 00151
Author(s):  
Igor Prikhodko ◽  
Stanislav Vladimirov ◽  
Daniil Alexandrov
Keyword(s):  
Drip Irrigation ◽  
Optimal Solution ◽  
Sprinkler Irrigation ◽  
Climatic Conditions ◽  
Rice Production ◽  
Rice Cultivation ◽  
Resource Saving ◽  
Traditional Methods ◽  
The World ◽  
New Generation

The world practice of rice cultivation has shown that rice cultivation by traditional methods for Russia is labor-intensive, resource-intensive, ineffective with low profitability, and often unprofitable production. As a result, traditional methods of flooding rice paddies in Russia are faced with a shortage and high cost of irrigation water and a reduction in rice irrigation systems, i.e., areas suitable for rice cultivation. For solving the problem of unprofitable rice production, an analysis of the world practice of rice production has been implemented. The analysis showed that the most optimal solution for the natural and climatic conditions of the Krasnodar Territory is the cultivation of rice using sprinkler irrigation and drip irrigation. Further analysis showed that drip irrigation is the most promising way of growing rice, which has many undeniable advantages. The main advantages of drip irrigation are the low irrigation rate, labor intensity, and energy intensity of rice production. Therefore, the article proposes a pioneering Russian ridge cultivation method for rice cultivation on the lands of the irrigated rice fund with drip irrigation under plastic and/or biodegradable perforated film. This method will make it possible to radically revise the principles of rice cultivation, form a new generation of rice crop rotations with the inclusion of melons and vegetables in them, and carry out rice production on previously rainfed lands. The implementation of the method has proven the effectiveness and feasibility of our research.

scholarly journals Decision Analysis of E-commerce Closed-loop Supply Chain with Different Recycling Modes

2021 ◽  
Vol 257 ◽  
pp. 02019
Author(s):  
Sijia Liu ◽  
Yanting Huang
Keyword(s):  
Supply Chain ◽  
Optimal Strategy ◽  
Mixed Mode ◽  
Closed Loop ◽  
Optimal Solution ◽  
The Other ◽  
Price Sensitivity ◽  
Closed Loop Supply Chain ◽  
Closed Loop Supply Chains ◽  
The Game Theory

According to an e-commerce closed-loop supply chain dominated by manufacturers, which is composed of manufacturers and e-commerce platforms, divided into three different recovery mode: manufacturers recycling mode alone, electric business platform recycling mode alone, and manufacturers and electric business platform mixed mode, using the game theory to solve, compares three closed-loop supply chains found: (1)When the recycling price sensitivity is high, the optimal strategy of the manufacturer is the manufacturers recycling mode alone; when the price sensitivity of recycling is low, the manufacturer’s best strategy is the independent recycling mode of the e-commerce platform. No matter how sensitive the recycling price is, the profits of the manufacturer under the mixed recycling mode are always lower than those under the other two recycling modes. (2) When the recycling price sensitivity is high, the optimal strategy of the electric business platform is the mixed recycling mode; when the price sensitivity of recycling is low, the optimal solution of the electric business platform is the independent recycling mode of the electric business platform. (3) When the recovery price sensitivity is low, the best strategy of both is the separate recycling mode of the electric business platform.

scholarly journals A Novel Zero-Sum Polymatrix Game Theory Bidding Strategy for Power Supply Market

2019 ◽  
Vol 8 (2) ◽  
pp. 5669-5675
Keyword(s):  
Game Theory ◽  
Financial Risk ◽  
Optimal Solution ◽  
Theoretic Approach ◽  
Bidding Strategies ◽  
Load Demand ◽  
Novel Approach ◽  
Game Theoretic ◽  
Player Game ◽  
Zero Sum

The competitive power system market involves very high financial risk due to the essential requirements of real-time bidding decision making. Decisions once taken cannot be altered easily because multiple generators participate in bidding process while simultaneously dispatching to meet the load demand most economically. In order to avoid such risks it becomes pertinent to re-structure the bidding strategies from time to time to meet upcoming techno-economical challenges. In this paper, three generating units are studied using Matrix Laboratory software with a novel approach for deciding the best strategy from the most economical strategy viewpoint. A scenario of different formulations is created for muti-player game, which then is solved with the help of zero-sum polymatrix game theory. A systematic tabular layout of revenues pertaining to each formulation in terms of mixed strategies is developed. The minimax and maximin revenues, identified using Game theoretic approach, gave the most economical strategy. Thus exact and self-enforcing generalized method for best bidding strategies of all three generators are logically derived for the most optimal solution.

Determining Optimal Strategy of a Micro-Grid through Hybrid Method of Nash Equilibrium –Genetic Algorithm

2019 ◽  
Vol 20 (3) ◽  
Author(s):  
Ehsan Jafari
Keyword(s):  
Genetic Algorithm ◽  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Hybrid Method ◽  
Optimal Strategy ◽  
Energy Resource ◽  
Energy Resources ◽  
Optimal Planning ◽  
Nash Equilibrium Point ◽  
Micro Grid

Abstract Increasing the fossil fuels consumption, pollution and rising prices of these fuels have led to the expansion of renewable resources and their replacement with conventional sources. In this paper, a robust algorithm for a micro-grid (MG) planning with the goal of maximizing profits is presented in day-ahead market. The energy resources in MG are wind farms (WFs), photovoltaic (PV), fuel cell (FC), combined heat and power(CHP) units, tidal steam turbine (TST) and energy storage devices (ESDs). This algorithm is divided into two main parts: (1) Optimal planning of each energy resource; (2) Using the Nash equilibrium –genetic algorithm (NE-GA) hybrid method to determine the optimal MG strategy. In energy resources optimal planning, using a stochastic formulation, the generation bids of each energy resource is determined in such a way that the profit of each one is maximized. Also, the constraints of renewable and load demands and selection the best method of demand response (DR) program are investigated. Then the Nash equilibrium point is determined using the primary population produced in the previous step using the NE-GA hybrid method to determine the optimal MG strategy. Thus, using the ability of the genetic algorithm method, the Nash equilibrium point of the generation units is obtained at an acceptable time, and This means that none of the units are willing to change their strategy and that the optimal strategy is extracted. Comparison of results with previous studies shows that the expected profit in the proposed method is more than other method.

Intermodal Hinterland Network Design Games

2020 ◽  
Vol 54 (5) ◽  
pp. 1272-1287
Author(s):  
Yann Bouchery ◽  
Marco Slikker ◽  
Jan C. Fransoo
Keyword(s):  
Nash Equilibrium ◽  
Network Design ◽  
Optimal Solution ◽  
Design Stage ◽  
Pure Nash Equilibrium ◽  
Design Problems ◽  
Distinctive Features ◽  
Multiple User ◽  
General Network ◽  
The Impact

Intermodal hinterland transportation is becoming increasingly critical for global container supply chains. Managing intermodal hinterland networks is challenging because multiple actors often interact in practice. The intermodal hinterland network design games that we propose enable assessing the impact of having noncooperative users in intermodal networks. The games fall into the class of network design games but have key distinctive features. We provide some general results as well as an instance without a pure Nash equilibrium for the general case. Subsequently, we focus on the special case with a single intermodal connection available. We show that a pure Nash equilibrium always exists but that this one is not always unique. We additionally identify key structural properties for this single-hub game. These properties enable us to identify all pure Nash equilibria and a system-optimal solution in polynomial time. We illustrate our results with an application related to the development of an extended gate in the Netherlands and derive a series of insights. Overall, the results show that the multiple user feature of intermodal hinterland networks is critical and needs to be accounted for at the network design stage. We believe that this latter statement holds for general network design problems with multiple users.

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