Fundamentals of Evolutionary Game Theory and its Applications

verfasst von: Jun Tanimoto

Verlag: Springer Japan

Buchreihe : Evolutionary Economics and Social Complexity Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book both summarizes the basic theory of evolutionary games and explains their developing applications, giving special attention to the 2-player, 2-strategy game. This game, usually termed a "2×2 game” in the jargon, has been deemed most important because it makes it possible to posit an archetype framework that can be extended to various applications for engineering, the social sciences, and even pure science fields spanning theoretical biology, physics, economics, politics, and information science. The 2×2 game is in fact one of the hottest issues in the field of statistical physics. The book first shows how the fundamental theory of the 2×2 game, based on so-called replicator dynamics, highlights its potential relation with nonlinear dynamical systems. This analytical approach implies that there is a gap between theoretical and reality-based prognoses observed in social systems of humans as well as in those of animal species. The book explains that this perceived gap is the result of an underlying reciprocity mechanism called social viscosity. As a second major point, the book puts a sharp focus on network reciprocity, one of the five fundamental mechanisms for adding social viscosity to a system and one that has been a great concern for study by statistical physicists in the past decade. The book explains how network reciprocity works for emerging cooperation, and readers can clearly understand the existence of substantial mechanics when the term "network reciprocity" is used. In the latter part of the book, readers will find several interesting examples in which evolutionary game theory is applied. One such example is traffic flow analysis. Traffic flow is one of the subjects that fluid dynamics can deal with, although flowing objects do not comprise a pure fluid but, rather, are a set of many particles. Applying the framework of evolutionary games to realistic traffic flows, the book reveals that social dilemma structures lie behind traffic flow.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Human–Environment–Social System and Evolutionary Game Theory

Abstract

In this chapter, we discuss both the definition of an environmental system as one of the typical dynamical systems and its relation to evolutionary game theory. We also outline the structure of each chapter in this book.

Jun Tanimoto

Chapter 2. Fundamental Theory for Evolutionary Games

Abstract

In this chapter, we take a look at the appropriate treatment of linear dynamical systems, which you may be familiar with if you have taken some standard engineering undergraduate classes. The discussion is then extended to non-linear systems and their general dynamic properties. In this discussion, we introduce the 2-player and 2-strategy (2 × 2) game, which is the most important archetype among evolutionary games. Multi-player and 2-strategy games are also introduced. In the latter parts of this chapter, we define the dilemma strength, which is useful for the universal comparison of the various reciprocity mechanisms supported by different models.

Jun Tanimoto

Chapter 3. Network Reciprocity

Abstract

In the previous chapter, we discussed Nowak’s five fundamental reciprocity mechanisms for adding social viscosity: kin selection, direct reciprocity, indirect reciprocity, network reciprocity, and group selection. In this chapter, we focus specifically on network reciprocity, as this mechanism has received the most attention in communities of statistical physicists and theoretical biologists who specialize in evolutionary game theory. Since 1992, when the first study of the spatial prisoner’s dilemma (SPD) was conducted by Nowak and May (1992), the number of papers dealing with network reciprocity has increased to several thousand. The main reason for this is that network reciprocity is regarded as the most important and interesting of the mechanisms from an application point of view. In fact, we can observe a lot of evidence in real life of network reciprocity working to establish mutual cooperation not only in human social systems but also in those of other animal species. The network reciprocity mechanism relies on two effects. The first is limiting the number of game opponents (that is, “depressing anonymity,” rather than having an infinite and well-mixed population), and the second is a local adaptation mechanism, in which an agent copies a strategy from a neighbor linked by a network. These two effects explain how cooperators survive in a social dilemma system, even though it requires agents to use only the simplest strategy—either cooperation (C) or defection (D), and this has attracted biologists who guess that network reciprocity may explain the evolution of cooperation even among primitive organisms without any sophisticated intelligence.

Jun Tanimoto

Chapter 4. Evolution of Communication

Abstract

In this chapter, we discuss several interesting applications of evolutionary game theory. The chapter first takes up one possible scenario for why and how animal communication evolves. A series of numerical experiments based on an evolutionary game elucidates that one of the key points is time flexibility in the evolutionary trail. A social dilemma situation in a static environment only requires time-constant -reciprocity that can be emulated by Prisoner’s Dilemma (PD) games, which does not give rise to any communication at all. On the other hand, a dynamic environment needs -reciprocity to solve a social dilemma. This compels communication to emerge among agents so that they can obtain a high payoff, leading to Fair Pareto optimum. This kind of constructivist approach suggests that a PD game seems less appropriate as an argument for the inception of communication, but Leader or Hero might be better.

Jun Tanimoto

Chapter 5. Traffic Flow Analysis Dovetailed with Evolutionary Game Theory

Abstract

In this chapter, we concern ourselves with traffic flow as another meaningful example of a situation in which evolutionary game theory can be applied. Although the study of traffic flow was originally thought to be best explained using fluid dynamics, a multi-agent simulation technique that has been widely used in the field of evolutionary games has been applied to the problem, under the name of cellular automaton (CA). In this chapter, we first explain how traffic flow can be modeled. Next, we discuss how evolutionary game theory can be applied to this traffic flow. One can consider the dynamics of traffic flow to be like a multi-player game, with vehicles being controlled by drivers who compete to access to a road as a finite resource in order to reduce their personal travel time. This implies that traffic flow may change its phase depending on traffic density, and that it entails a social dilemma that might also change its game class, depending on the density. We reveal that various social dilemmas are hidden behind different aspects of traffic flows, which may be considered remarkable. Traffic flow is a game committed by agents – drivers, which seems some sort of human drama unlike we naturally think that traffic flow is governed by rigid physics because the theory of fluid dynamics, one of the representative hard-core physics fields, has been applied to it.

Jun Tanimoto

Chapter 6. Pandemic Analysis and Evolutionary Games

Abstract

Human social networks are a central theme to which evolutionary game theory has been applied because the complexity of the underlying network serves as the key factor in determining game equilibrium. The spread of an epidemic throughout such a network is mathematically described by percolation theory, which is an archetype of the physics of diffusion processes. Vaccination, which is driven by individual decision making, inhibits the spread of infectious diseases. In addition, if the so-called herd immunity is established, a free-rider, who pays no cost for vaccination, can escape infection. Obviously, there is a conflict between individual and social benefits; in short, a conflict between individual rational choices: trying to avoid vaccination, or everyone taking the vaccine achieving the fair Pareto optimum. This conflict is why we introduce evolutionary game theory into epidemiology; vaccination can be viewed as a game in a complex social network. In this chapter, we examine pandemic analysis as another application to which evolutionary game theory can be applied.

Jun Tanimoto

Backmatter

Titel: Fundamentals of Evolutionary Game Theory and its Applications
verfasst von: Jun Tanimoto
Verlag: Springer Japan
Electronic ISBN: 978-4-431-54962-8
Print ISBN: 978-4-431-54961-1
DOI: https://doi.org/10.1007/978-4-431-54962-8