scholarly journals General features of Nash equilibria in combinations of elementary interactions in symmetric two-person games

2021 ◽  
Vol 94 (5) ◽  
Author(s):  
György Szabó ◽  
Balázs Király
Keyword(s):  
Mathematical Models ◽  
Nash Equilibria ◽  
Matrix Decomposition ◽  
Payoff Matrix ◽  
Zero Eigenvalue ◽  
Macroscopic Behavior ◽  
Different Types ◽  
Multi Agent ◽  
Different Characteristics ◽  
Pair Interactions

AbstractTwo-person games are used in many multi-agent mathematical models to describe pair interactions. The type (pure or mixed) and the number of Nash equilibria affect fundamentally the macroscopic behavior of these systems. In this paper, the general features of Nash equilibria are investigated systematically within the framework of matrix decomposition for n strategies. This approach distinguishes four types of elementary interactions that each possess fundamentally different characteristics. The possible Nash equilibria are discussed separately for different types of interactions and also for their combinations. A relation is established between the existence of infinitely many mixed Nash equilibria and the zero-eigenvalue eigenvectors of the payoff matrix.

scholarly journals Design and Calibration of Moisture Sensor Based on Electromagnetic Field Measurement for Irrigation Monitoring

Chemosensors ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 251
Author(s):  
Daniel A. Basterrechea ◽  
Javier Rocher ◽  
Mar Parra ◽  
Lorena Parra ◽  
Jose F. Marin ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Absolute Error ◽  
Induced Voltage ◽  
Agricultural Field ◽  
Average Absolute Error ◽  
Moisture Sensor ◽  
Green Areas ◽  
Different Types ◽  
Dry Soil ◽  
Different Characteristics

Soil moisture control is crucial to assess irrigation efficiency in green areas and agriculture. In this paper, we propose the design and calibration of a sensor based on inductive coils and electromagnetic fields. The proposed prototypes should meet a series of requirements such as low power consumption, low relative error, and a high voltage difference between the minimum and maximum moisture. We tested different prototypes based on two copper coils divided into two different sets (P1–P15 and NP1–NP4). The prototypes have different characteristics: variations in the number and distribution of spires, existence or absence of casing, and copper wires with a diameter of 0.4 or 0.6 mm. In the first set of experiments carried out in commercial soil, the results showed that the best prototypes were P5, P8, and P9. These prototypes were used in different types of soils, and P8 was selected for the subsequent tests. We carried the second set of experiments using soil from an agricultural field. Based on the data gathered, mathematical models for the calibration of prototypes were obtained and verified. In some cases, two equations were used for different moisture intervals in a single prototype. According to the verification results, NP2 is the best prototype for monitoring the moisture in agricultural lands. It presented a difference in induced voltage of 1.8 V, at 500 kHz, between wet and dry soil with a maximum voltage of 5.12 V. The verification of the calibration determined that the calibration using two mathematical models offers better results, with an average absolute error of 2.1% of moisture.

scholarly journals Expressiveness and Nash Equilibrium in Iterated Boolean Games

2021 ◽  
Vol 22 (2) ◽  
pp. 1-38
Author(s):  
Julian Gutierrez ◽  
Paul Harrenstein ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Infinite Sequence ◽  
Multi Agent Systems ◽  
Temporal Logics ◽  
Agent Systems ◽  
Temporal Properties ◽  
Multi Agent ◽  
Game Theoretic ◽  
Boolean Games

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent  has a goal  , represented using (a fragment of) Linear Temporal Logic ( ) . The goal  captures agent  ’s preferences, in the sense that the models of  represent system behaviours that would satisfy  . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of  ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

scholarly journals Multi-Agent Reinforcement Learning: A Review of Challenges and Applications

2021 ◽  
Vol 11 (11) ◽  
pp. 4948
Author(s):  
Lorenzo Canese ◽  
Gian Carlo Cardarilli ◽  
Luca Di Di Nunzio ◽  
Rocco Fazzolari ◽  
Daniele Giardino ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Mathematical Models ◽  
Learning Algorithms ◽  
Single Agent ◽  
Critical Issues ◽  
Multi Agent ◽  
Pros And Cons ◽  
Application Fields

In this review, we present an analysis of the most used multi-agent reinforcement learning algorithms. Starting with the single-agent reinforcement learning algorithms, we focus on the most critical issues that must be taken into account in their extension to multi-agent scenarios. The analyzed algorithms were grouped according to their features. We present a detailed taxonomy of the main multi-agent approaches proposed in the literature, focusing on their related mathematical models. For each algorithm, we describe the possible application fields, while pointing out its pros and cons. The described multi-agent algorithms are compared in terms of the most important characteristics for multi-agent reinforcement learning applications—namely, nonstationarity, scalability, and observability. We also describe the most common benchmark environments used to evaluate the performances of the considered methods.

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

RELIABILITY ASSESSMENT OF AXIALLY COMPRESSED COMPOSITE CYLINDRICAL SHELLS WITH RANDOM IMPERFECTIONS

2011 ◽  
Vol 11 (02) ◽  
pp. 215-236 ◽  
Author(s):  
MATTEO BROGGI ◽  
ADRIANO CALVI ◽  
GERHART I. SCHUËLLER
Keyword(s):  
Mathematical Models ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Reliability Assessment ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Experimental Results ◽  
Drastic Decrease ◽  
Different Types ◽  
Probability And Statistics

Cylindrical shells under axial compression are susceptible to buckling and hence require the development of enhanced underlying mathematical models in order to accurately predict the buckling load. Imperfections of the geometry of the cylinders may cause a drastic decrease of the buckling load and give rise to the need of advanced techniques in order to consider these imperfections in a buckling analysis. A deterministic buckling analysis is based on the use of the so-called knockdown factors, which specifies the reduction of the buckling load of the perfect shell in order to account for the inherent uncertainties in the geometry. In this paper, it is shown that these knockdown factors are overly conservative and that the fields of probability and statistics provide a mathematical vehicle for realistically modeling the imperfections. Furthermore, the influence of different types of imperfection on the buckling load are examined and validated with experimental results.

scholarly journals An Algorithmic Procedure for Finding Nash Equilibrium

2020 ◽  
Vol 40 (1) ◽  
pp. 71-85
Author(s):  
HK Das ◽  
T Saha
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Payoff Matrix ◽  
Matrix Game ◽  
Perfect Equilibrium ◽  
Repeated Use ◽  
Definition Of ◽  
Zero Sum ◽  
Mathematical Construction ◽  
Algorithmic Procedure

This paper proposes a heuristic algorithm for the computation of Nash equilibrium of a bi-matrix game, which extends the idea of a single payoff matrix of two-person zero-sum game problems. As for auxiliary but making the comparison, we also introduce here the well-known definition of Nash equilibrium and a mathematical construction via a set-valued map for finding the Nash equilibrium and illustrates them. An important feature of our algorithm is that it finds a perfect equilibrium when at the start of all actions are played. Furthermore, we can find all Nash equilibria of repeated use of this algorithm. It is found from our illustrative examples and extensive experiment on the current phenomenon that some games have a single Nash equilibrium, some possess no Nash equilibrium, and others had many Nash equilibria. These suggest that our proposed algorithm is capable of solving all types of problems. Finally, we explore the economic behaviour of game theory and its social implications to draw a conclusion stating the privilege of our algorithm. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 71-85

scholarly journals Floral Consumption Values for Consumer Groups with Different Purchase Choices for Flowers

2009 ◽  
Vol 19 (3) ◽  
pp. 563-571 ◽  
Author(s):  
Li-Chun Huang ◽  
Tzu-Fang Yeh
Keyword(s):  
Information Search ◽  
Choice Behavior ◽  
Social Value ◽  
Evaluative Judgments ◽  
Consumption Values ◽  
The Social ◽  
Different Types ◽  
Commercial Communication ◽  
Different Characteristics ◽  
The Relationship

Consumption values are theoretically believed to be the antecedents of the outcomes of consumer purchase choice. In the floral market, even though the context of floral consumption values has been explored, the relationship between floral consumption values and consumer's purchase choice regarding floral products remains unknown. This study, however, seeks to address this deficiency by attempting to evaluate the differences in floral consumption values across consumer groups that have different purchase choices for floral products. After collecting data from a consumer survey, which yielded 615 valid questionnaires, the statistical results indicated that consumers who revealed different purchase choices in regard to flowers had different floral consumption values. In descending order, showing care to others, emotion conditioning, and sensory hedonics were the floral consumption values most strongly recognized by the majority of the consumers. However, heavy users of flowers revealed different characteristics in that they more strongly recognized the psychological value of emotion conditioning rather than the social value of showing care to others. The main difference across consumer groups that had purchased flowers with different frequencies or that preferred to buy different types of flowers had to do with the epistemic value (i.e., curiosity fulfillment). The results of this study imply that consumers who have different choice behavior toward flowers possess different evaluative judgments in regard to floral products. Such differences not only lead consumers to have different purchase choices in regard to flowers, but are also very likely to influence the consumer's behavior in regard to information search and variety seeking in the floral market, which in turn, impacts the effectiveness of commercial communication in the floral market.

Intelligent Traceability System of Containerized Goods

2013 ◽  
Vol 309 ◽  
pp. 241-251 ◽  
Author(s):  
Mourad Abed ◽  
Imen Charfeddine ◽  
Mounir Benaissa ◽  
Marta Starostka-Patyk
Keyword(s):  
Supply Chain ◽  
Intelligent System ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Traceability System ◽  
Transport Chain ◽  
Multimodal Transport ◽  
Literature Reviews ◽  
Different Types ◽  
Multi Agent

In recent year, many countries across in the world have made traceability a compulsory procedure in the Supply Chain. The Supply Chain is distributed collaborative environments involves the acquisition and use of extensive informational and physical flows. The flows management seems a complex task for the actors of the multimodal transport chain which the transport is the major driver in a Supply Chain. The literature reviews throws light on the traceability in the Supply Chain Management (SCM) shows the lack of interoperability and flexibility in data management systems hinders the work of traceability. And it introduces the importance and complexity of multimodal transport operations. To ensure effective traceability all along this chain, we relied on the agent paradigm and the ontology which facilitate the integration of goods data in order to exploit and reuse. Indeed, to ensure communication and interoperability of these data we relied on Multi-Agent Systems, due to their characteristics of autonomy, sociability and responsiveness that are generally associated. The Multi-Agent Systems can build flexible systems whose behaviors are complex and complicated due to the combination of different types of agents. With a focus on the importance of the concept of the traceability, the objective of this work is to propose an intelligent system for the traceability of containerized goods in the context of multimodal transport: Intelligent Traceability System of Containerized Goods (i-TSCG).

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