An Overview of Game Theory and Some Applications

Journal of Applied Mathematics, 2014

Game theory, as a branch of the applied mathematics, contributes insight into economics, sociology, and many other disciplines. Game theory has outstanding effects on the theory of economics, and the literature on applying game theoretical and related approaches to economics is growing rapidly, and yet many theoretical and empirical challenges remain in this field. The focus of this special issue is the application of game theory to problems in economics, including economic theory, microeconomics, industrial economics, and other application fields. The publication of this special issue can efficiently extend the applications of game theory and attracts the attention of economists to game theory. This special issue received high-quality manuscripts from 23 countries all over the world. After a strict review process, 25 high-quality papers are published. These 25 papers cover the game theory and applications in all fields of economics, including microeconomics, industrial economics, and macroeconomics. Ten papers in this issue focus on the significant topics of game theory. Cooperative games are still challenging topics and four papers develop the theory about cooperative games. D. Hou and T. Driessen explored the cooperative game theory and applied it to data cost games. J. Pang and X. Chen developed the cooperative game theory under fuzzy environment. R. P. Arribillaga et al. compared the cooperative and competitive solution for generalized assignment game. J. Pang et al. further developed the Shapley values of fuzzy coalition game theory.

Journal of Economic Behavior & Organization, 1995

Game theoretic concepts apply whenever the actions of several agents are interdependent. These agents may be individuals, groups, firms, or any combination of these. The concepts of game theory provide a language to formulate, structure and analyze situations of interdependence between adaptive agents, out of which can emerge dynamics of conflict and cooperation. As a method of applied mathematics, game theory has been used to study a wide variety of human and animal behaviors. It was firstly developed in economics to understand a variety of economic behaviors, including behaviors of firms, markets, and consumers, but has since been used to model a myriad of phenomena, such as the interaction of nation states within international politics, crime, ecosystem dynamics, the routing of internet traffic and much more. Classical game theory describes the behavior of rational players. It attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others. 1 The limitations of this classical game theory 2 are long since know, but they are becoming more apparent as behavioral economics exposes them to real-world experiments and as we attempt to construct a more complex understanding of human motives and human interaction. The game theory of the past was focused on theory, mathematical elegance, closed form solutions, rigor and precise predictions, but in the process, it often ended up divorcing itself from the empirics of real-world socioeconomic interaction. Today developing models for the interaction between people is of critical importance within a wide variety of domains, both in the social sciences but also in management and design. Today there is a great demand for a game theory that puts empirics first; one that is grounded in real-world interaction and can accurately reflect the complexity of the many social interactions that we encounter on a daily basis and the motives of agents engaged in them. Achieving such a game theory framework will require a generalization of the existing game theory framework beyond its foundation. 3 As we move into the world of studying more complex systems there is an increasing demand for a more general conception of game theory. One that is capable of studying all forms of interaction between adaptive agents without the restrictive assumptions that are an inherent part of Classical Game Theory. In this paper, we look at the ongoing evolution of game theory, from its origins in classical game theory to more recent developments. We trace the past, present and potential future of game theory in search of an expanded formulation of game theory that would be relevant to the modeling of complex socioeconomic systems. Our primary focus here is on identifying the limitations within the existing game theory framework and how it can be expanded to accurately deal with more complex scenarios of socioeconomic interaction. At each step we try to identify and make explicit the assumptions inherent in standard game theory models and how these both enable and constrain the modeling process; how such assumptions may be revised in the light of new developments within complexity theory to better suit the modeling of interactions within complex socioeconomic systems.

This note reviews the game theoretic literature with the aim of highlighting the similarities and dissimilarities between what we term traditional game theory and evolutionary game theory. The focus is on the contributions of evolutionary game theory to the body of knowledge at the disposal of the game theorist. The note is intended for people with interests in economics and who are familiar with traditional game theory but not necessarily familiar with evolutionary game theory. The main objective is to reach out to the numerous economists and indeed, other social scientists, who are not as yet initiated in the basic theory of of evolutionary games. A major conclusion of this note is that, applications of evolutionary game theory in the analysis of economic problems, especially, in the areas of natural, environmental and development economics are long overdue.

Oxford Research Encyclopedia of International Studies

Game theory is the science of interactive decision making. It has been used in the field of international relations (IR) for over 50 years. Almost all of the early applications of game theory in international relations drew upon the theory of zero-sum games, but the first generation of applications was also developed during the most intense period of the Cold War. The theoretical foundations for the second wave of the game theory literature in international relations were laid by a mathematician, John Nash, a co-recipient of the 1994 Nobel Prize in economics. His major achievement was to generalize the minimax solution which emerged from the first wave. The result is the now famous Nash equilibrium—the accepted measure of rational behavior in strategic form games. During the third wave, from roughly the early to mid-1980s to the mid-1990s, there was a distinct move away from static strategic form games toward dynamic games depicted in extensive form. The assumption of complete infor...