scholarly journals Research article game theory problems using interval parameters

2020 ◽  
Vol 7 (2) ◽  
pp. 123-129
Author(s):  
Radhakrishnan S ◽  
Saikeerthan D
Keyword(s):  
Game Theory ◽  
Mixed Strategy ◽  
Graphical Method ◽  
Pure Strategy ◽  
Payoff Matrix ◽  
Property A ◽  
Numerical Examples ◽  
Interval Parameters ◽  
Research Article

In this paper, we consider a game with imprecise values in the payoff matrix. All the imprecise values are taken as intervals. Here, we solve anintervalgame problem based on pure strategy, mixed strategy and using dominance property. A graphical method is also given for solving 2 x n and m x 2interval game problem.To illustrate this, numerical examples are provided.

Decision-making method based on game theory and grey theory in a single-value neutrosophic environment and its application to typhoon disaster assessment

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ruipu Tan ◽  
Lehua Yang ◽  
Shengqun Chen ◽  
Wende Zhang
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Mixed Strategy ◽  
Payoff Matrix ◽  
Neutrosophic Set ◽  
Grey Theory ◽  
Decision Matrix ◽  
Content Type ◽  
Disaster Assessment ◽  
Typhoon Disaster

PurposeThe Chinese believe that “man will conquer the sky” and “fighting with the sky brings endless joy”. Considering that disaster assessment can be regarded as a two-person, zero-sum game problem between nature and human beings, this paper proposes a multi-attribute decision-making method based on game theory and grey theory in a single-value neutrosophic set environment. Due to the complexity and uncertainty of the decision-making environment, the method builds a decision matrix based on single-valued neutrosophic numbers.Design/methodology/approachFirst, the authors use the single-value neutrosophic information entropy to calculate the attribute weights and the weighted decision matrix. Second, the optimal mixed strategy method based on linear programming solves the optimal mixed strategy for both sides of the game so that the expected payoff matrix can be obtained. Finally, grey correlation analysis is used to obtain the closeness coefficient of each alternative based on the expectation payoff matrix to identify the ranking result of the alternative.FindingsAn example is used to verify the effectiveness of the proposed method, and its rationality is verified through a comprehensive comparison and analysis of the various aspects.Practical implicationsThe proposed decision-making method can be applied to typhoon disaster assessment. Such assessment results can provide intelligent decision support to the relevant disaster management departments, thereby reducing the negative impact of typhoon disasters on society, stabilizing society and improving people's happiness. Further, the method can be used for decision-making, recommendation and evaluation in other fields.Originality/valueThe proposed method uses single-value neutrosophic numbers to solve the information representation problem of decision-making in a complex environment. Under a new perspective, game theory is used to handle the decision matrix, while grey relational analysis converts inexact numbers to exact numbers for comparison and sorting. Thus, the proposed method can be used to make reasonable decisions while preserving information to the extent possible.

On the Foundations of Nash Equilibrium

1996 ◽  
Vol 12 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Hans Jørgen Jacobsen
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Game Theory ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Mixed Strategies ◽  
Positive Theory ◽  
Equilibrium Concept ◽  
Strategy Equilibrium ◽  
Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

Generalized Replicator Dynamics as a Model of Specialization and Diversity in Societies

1998 ◽  
Vol 01 (04) ◽  
pp. 325-359 ◽  
Author(s):  
Vivek S. Borkar ◽  
Sanjay Jain ◽  
Govindan Rangarajan
Keyword(s):  
Mixed Strategy ◽  
Replicator Dynamics ◽  
Pure Strategy ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Theoretic Model ◽  
Final States ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
Pure Strategies

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community of N agents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors if N is sufficiently large, and be regarded as innovations that enhance the diversity of the community.

High-Dimensional Nash Equilibria Problems and Tensors Applications

2017 ◽  
Vol 19 (03) ◽  
pp. 1750015 ◽  
Author(s):  
J. E. Abdou ◽  
E. Safatly ◽  
B. Nakhle ◽  
A. El Khoury
Keyword(s):  
Game Theory ◽  
Normal Form ◽  
Nash Equilibria ◽  
Mixed Strategy ◽  
High Dimensional ◽  
Tensor Form ◽  
Numerical Examples ◽  
New Form

We propose, in this work, an overview on tensors application in game theory, and basically on Nash equilibria problems. In this paper, we extend the classic normal form of a game to a new form called Tensor form. We present some tensors concepts and operations with detailed examples and then we propose an efficient methodology to solve pure and mixed high-dimensional Nash equilibria problems using tensors operations. The efficiency of this methodology is shown in numerical examples for pure and mixed strategy. An algorithm based on tensors is also implemented to describe and solve these problems.

scholarly journals A Study of Taxi Service Mode Choice Based on Evolutionary Game Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Zhu Bai ◽  
Mingxia Huang ◽  
Shuai Bian ◽  
Huandong Wu
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Mode Choice ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Game Model ◽  
Stable States ◽  
Taxi Service ◽  
Service Mode ◽  
The Impact

The emergence of online car-hailing service provides an innovative approach to vehicle booking but has negatively influenced the taxi industry in China. This paper modeled taxi service mode choice based on evolutionary game theory (EGT). The modes included the dispatching and online car-hailing modes. We constructed an EGT framework, including determining the strategies and the payoff matrix. We introduced different behaviors, including taxi company management, driver operation, and passenger choice. This allowed us to model the impact of these behaviors on the evolving process of service mode choice. The results show that adjustments in taxi company, driver, and passenger behaviors impact the evolutionary path and convergence speed of our evolutionary game model. However, it also reveals that, regardless of adjustments, the stable states in the game model remain unchanged. The conclusion provides a basis for studying taxi system operation and management.

scholarly journals Entangled and correlated photon mixed strategy for social decision making

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shion Maeda ◽  
Nicolas Chauvet ◽  
Hayato Saigo ◽  
Hirokazu Hori ◽  
Guillaume Bachelier ◽  
...  
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Mixed Strategy ◽  
Evolutionary Game ◽  
Slot Machines ◽  
Decision Strategy ◽  
Social Infrastructure ◽  
Positive Effects ◽  
Social Decision Making ◽  
The Given

AbstractCollective decision making is important for maximizing total benefits while preserving equality among individuals in the competitive multi-armed bandit (CMAB) problem, wherein multiple players try to gain higher rewards from multiple slot machines. The CMAB problem represents an essential aspect of applications such as resource management in social infrastructure. In a previous study, we theoretically and experimentally demonstrated that entangled photons can physically resolve the difficulty of the CMAB problem. This decision-making strategy completely avoids decision conflicts while ensuring equality. However, decision conflicts can sometimes be beneficial if they yield greater rewards than non-conflicting decisions, indicating that greedy actions may provide positive effects depending on the given environment. In this study, we demonstrate a mixed strategy of entangled- and correlated-photon-based decision-making so that total rewards can be enhanced when compared to the entangled-photon-only decision strategy. We show that an optimal mixture of entangled- and correlated-photon-based strategies exists depending on the dynamics of the reward environment as well as the difficulty of the given problem. This study paves the way for utilizing both quantum and classical aspects of photons in a mixed manner for decision making and provides yet another example of the supremacy of mixed strategies known in game theory, especially in evolutionary game theory.

scholarly journals Game Theory in Molecular Nanosensing System for Rapid Detection of Hg2+ in Aqueous Solutions

2018 ◽  
Vol 8 (12) ◽  
pp. 2530
Author(s):  
Nan Nie ◽  
Xin Zhang ◽  
Chu Fang ◽  
Qiu Zhu ◽  
Jiao Lu ◽  
...  
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Pond Water ◽  
Payoff Matrix ◽  
Proof Of Concept ◽  
Decision Systems ◽  
Theoretical System ◽  
Intelligent Decision ◽  
Simple Molecules ◽  
Intelligent Decision Systems

Game theory—the scientific study of interactive, rational decision making—describes the interaction of two or more players from macroscopic organisms to microscopic cellular and subcellular levels. Life based on molecules is the highest and most complex expression of molecular interactions. However, using simple molecules to expand game theory for molecular decision-making remains challenging. Herein, we demonstrate a proof-of-concept molecular game-theoretical system (molecular prisoner’s dilemma) that relies on formation of the thymine–Hg2+–thymine hairpin structure specifically induced by Hg2+ and fluorescence quenching and molecular adsorption capacities of cobalt oxyhydroxide (CoOOH) nanosheets, resulting in fluorescence intensity and distribution change of polythymine oligonucleotide 33-repeat thymines (T33). The “bait” molecule, T33, interacted with two molecular players, CoOOH and Hg2+, in different states (absence = silence and presence = betrayal), regarded as strategies. We created conflicts (sharing or self-interest) of fluorescence distribution of T33, quantifiable in a 2 × 2 payoff matrix. In addition, the molecular game-theoretical-system based on T33 and CoOOH was used for sensing Hg2+ over the range of 20 to 600 nM with the detection limit of 7.94 nM (3σ) and for determination of Hg2+ in pond water. Inspired by the proof-of-concept for molecular game theory, various molecular decision-making systems could be developed, which would help promote molecular information processing and generating novel molecular intelligent decision systems for environmental monitoring and molecular diagnosis and therapy.

MONTE CARLO METHODS IN FUZZY GAME THEORY

2007 ◽  
Vol 03 (02) ◽  
pp. 259-269 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Game Theory ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Mixed Strategy ◽  
Minimax Theorem ◽  
Approximate Solutions ◽  
Mixed Strategies ◽  
Fuzzy Game ◽  
Zero Sum

In this paper, we consider a two-person zero-sum game with fuzzy payoffs and fuzzy mixed strategies for both players. We define the fuzzy value of the game for both players [Formula: see text] and also define an optimal fuzzy mixed strategy for both players. We then employ our fuzzy Monte Carlo method to produce approximate solutions, to an example fuzzy game, for the fuzzy values [Formula: see text] for Player I and [Formula: see text] for Player II; and also approximate solutions for the optimal fuzzy mixed strategies for both players. We then look at [Formula: see text] and [Formula: see text] to see if there is a Minimax theorem [Formula: see text] for this fuzzy game.

Model of Urban Road Congestion Pricing Based on Game Theory

2012 ◽  
Vol 253-255 ◽  
pp. 1895-1899 ◽  
Author(s):  
Li Li Ding ◽  
Zheng Wei Wang ◽  
Lu Yan Li
Keyword(s):  
Game Theory ◽  
Ride Comfort ◽  
Congestion Pricing ◽  
Travel Cost ◽  
Numerical Examples ◽  
Traffic System ◽  
Urban Road ◽  
Road Congestion ◽  
Charge Rate ◽  
The Government

This paper proposes a game-based model to conduct the issue of road congestion pricing. The ride comfort of travel modes, e.g., cars or buses, is introduced into the travel cost function of the traditional bottleneck model. Furthermore, based on different travel cost functions of various travel modes, the Nash equilibriums are achieved among the government and various travelers. The results can be employed to describe internality and externality of traffic system respectively. Finally, numerical examples are presented. The findings of our work indicate a relationship between the government’s goal and the charge rate and that the emergence of ride comfort obviously is a key determinant of travelers’ behavior.

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