Exponential Families and Game Dynamics

1982 ◽  
Vol 34 (2) ◽  
pp. 374-405 ◽  
Author(s):  
Ethan Akin
Keyword(s):  
Game Theory ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Exponential Families ◽  
Von Neumann ◽  
Rational Player ◽  
Large Populations ◽  
Pure Strategies ◽  
Classical Game ◽  
Classical Game Theory

A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in units of some desirable good, e.g. money. The problem of game theory is that of a rational player who seeks to choose a strategy or mixture of strategies which will maximize his return. In evolutionary game theory of Maynard Smith and Price [13] we look at large populations of game players. Each player's opponents are selected randomly from the population, and no information about the opponent is available to the player. For each one the choice of strategy is a fixed inherited characteristic.

scholarly journals Nonlinear parametric excitation of an evolutionary dynamical system

2011 ◽  
Vol 226 (8) ◽  
pp. 1912-1920 ◽  
Author(s):  
Rocio E Ruelas ◽  
David G Rand ◽  
Richard H Rand
Keyword(s):  
Game Theory ◽  
Differential Equations ◽  
Parametric Excitation ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Periodic Coefficients ◽  
The Stability ◽  
Social Applications ◽  
Classical Game ◽  
Classical Game Theory

Nonlinear parametric excitation refers to the nonlinear analysis of a system of ordinary differential equations with periodic coefficients. In contrast to linear parametric excitation, which offers determinations of the stability of equilibria, nonlinear parametric excitation has as its goal the structure of the phase space, as given by a portrait of the Poincare map. In this article, perturbation methods and numerical integration are applied to the replicator equation with periodic coefficients, being a model from evolutionary game theory where evolutionary dynamics are added to classical game theory using differential equations. In particular, we study evolution in the Rock–Paper–Scissors game, which has biological and social applications. Here, periodic coefficients could represent seasonal variation.

scholarly journals The evolution of strategy in bacterial warfare via the regulation of bacteriocins and antibiotics

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Rene Niehus ◽  
Nuno M Oliveira ◽  
Aming Li ◽  
Alexander G Fletcher ◽  
Kevin R Foster
Keyword(s):  
Game Theory ◽  
Stress Responses ◽  
Regulatory Networks ◽  
Cell Damage ◽  
Evolutionary Game ◽  
Toxin Production ◽  
Clear Understanding ◽  
Bacterial Competition ◽  
Classical Game ◽  
Classical Game Theory

Bacteria inhibit and kill one another with a diverse array of compounds, including bacteriocins and antibiotics. These attacks are highly regulated, but we lack a clear understanding of the evolutionary logic underlying this regulation. Here, we combine a detailed dynamic model of bacterial competition with evolutionary game theory to study the rules of bacterial warfare. We model a large range of possible combat strategies based upon the molecular biology of bacterial regulatory networks. Our model predicts that regulated strategies, which use quorum sensing or stress responses to regulate toxin production, will readily evolve as they outcompete constitutive toxin production. Amongst regulated strategies, we show that a particularly successful strategy is to upregulate toxin production in response to an incoming competitor’s toxin, which can be achieved via stress responses that detect cell damage (competition sensing). Mirroring classical game theory, our work suggests a fundamental advantage to reciprocation. However, in contrast to classical results, we argue that reciprocation in bacteria serves not to promote peaceful outcomes but to enable efficient and effective attacks.

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.

An Analysis of Quality Liability Insurance for Prefabricated Components Using Evolutionary Game Theory

2021 ◽  
Author(s):  
Yan Liu ◽  
Chenyao Lv ◽  
Hong Xian Li ◽  
Yan Li ◽  
Zhen Lei ◽  
...  
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Liability Insurance ◽  
Insurance Companies ◽  
Social Benefits ◽  
Simulation Calculation ◽  
The Government

Managing quality risks of prefabricated components is one of the challenges for prefabricated construction. The Quality Liability Insurance for Prefabricated Components (QLIPC) is an effective approach to transfer such risks; however, limited research has been conducted regarding the development of QLIPC. This study introduces an Evolutionary Game Theory (EGT)-based approach incorporating decisions from both the government and insurance companies. In the EGT model, a payoff matrix under disparate strategies is constructed, and the evolutionary stable strategies (ESS) are deduced. The simulation calculation is then carried out by MATLAB using sample virtual data to demonstrate the analysis. The results show that the government should act as the game promoter because the QLIPC can reduce governance cost and has significant social benefits. This research contributes a theoretical framework to analyze the QLIPC development using the EGT theory, and it could help the government to make long-term strategies for developing the QLIPC market.

Fuzzy Optimal Approaches to 2-P Cooperative Games

2016 ◽  
Vol 3 (2) ◽  
pp. 22-35
Author(s):  
Mubarak S. Al-Mutairi
Keyword(s):  
Game Theory ◽  
Favourable Outcome ◽  
Decision Makers ◽  
Fuzzy Approach ◽  
Fuzzy Information ◽  
Missing Information ◽  
Conflicting Objectives ◽  
Potential Benefits ◽  
Classical Game ◽  
Classical Game Theory

In game theory, two or more parties need to make decisions with fully or partially conflicting objectives. In situations where reaching a more favourable outcome depends upon cooperation between the two conflicting parties, some of the mental and subjective attitudes of the decision makers must be considered. While the decision to cooperate with others bears some risks due to uncertainty and loss of control, not cooperating means giving up potential benefits. In practice, decisions must be made under risk, uncertainty, and incomplete or fuzzy information. Because it is able to work well with vague, ambiguous, imprecise, noisy or missing information, the fuzzy approach is effective for modeling such multicriteria conflicting situations. The well-known game of Prisoner's Dilemma, which reflects a basic situation in which one must decide whether to cooperate or not with a competitor, is systematically solved using a fuzzy approach. The fuzzy procedure is used to incorporate some of the subjective attitudes of the decision makers that are difficult to model using classical game theory. Furthermore, it permits researchers to consider the subjective attitudes of the decision makers and make better decisions in subjective, uncertain, and risky situations.

scholarly journals Quantum Conditional Strategies and Automata for Prisoners’ Dilemmata under the EWL Scheme

2019 ◽  
Vol 9 (13) ◽  
pp. 2635 ◽  
Author(s):  
Konstantinos Giannakis ◽  
Georgia Theocharopoulou ◽  
Christos Papalitsas ◽  
Sofia Fanarioti ◽  
Theodore Andronikos
Keyword(s):  
Game Theory ◽  
Finite Automata ◽  
State Machines ◽  
Conditional Strategy ◽  
Abstract Machines ◽  
Quantum Finite Automata ◽  
Quantum Version ◽  
Important Field ◽  
Classical Game ◽  
Classical Game Theory

Classical game theory is an important field with a long tradition of useful results. Recently, the quantum versions of classical games, such as the prisoner’s dilemma (PD), have attracted a lot of attention. This game variant can be considered as a specific type of game where the player’s actions and strategies are formed using notions from quantum computation. Similarly, state machines, and specifically finite automata, have also been under constant and thorough study for plenty of reasons. The quantum analogues of these abstract machines, like the quantum finite automata, have been studied extensively. In this work, we examine well-known conditional strategies that have been studied within the framework of the classical repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with a probability of 1, achieving some interesting results. We also study the quantum version of PD under the Eisert–Wilkens–Lewenstein scheme, proposing a novel conditional strategy for the repeated version of this game.

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