The Informal Background of Mathematics

Studies in Contemporary Economics, 1982

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...

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.

Philosophy of Economics, 2012

Philosophy of the Social Sciences, 2008

The mathematical tools of game theory are frequently used in the social sci-ences and economic consultancy. But how do they explain social phenomena and support prescriptive judgments? And is the use of game theory really necessary? I analyze the logical form of ...

Journal of Education, Humanities and Social Sciences

Game theory implies the logic of problematic situations with solutions through mathematical calculation. Since 1944, the game theory has been applied to military decisions, educational materials, and to find methods for complicated circumstances. The equilibria, different strategies to maximize surplus, and analysis of games could be inferred to assist players. The dominant strategy is the esse.ntial portion of the research to the game where the choice results in the best payoffs not affected by the other players' decisions. Closely connected to the dominant strategy, the Nash equilibrium represents the idea of the stable point where there is no profitable deviation for any player. Moreover, through calculation, the mixed strategy could be acquired, in situations when the probability of choices of all players is random, in the probability distribution. Finally, studies of shading the bid in auctions could maximize the surplus of bidders in partial auctions. The research could ac...

Erkenntnis, 1997

In its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player's decision problem, a solution valid for all real-world instantiations, regardless of context. "Permissiveness" would constrain the theory to designate as admissible for a player any conjecture consistent with the function's designation of admissible strategies for the other players. Given permissiveness and other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms.

Frontiers of Economics, edited by K. Arrow and S. …, 1985

The paper presents an approach to the philosophy of Game Theory; it is not a survey. The examples and references are an eclectic, largely haphazard selection-strongly skewed towards applications-from a truly enormous literature. The idea was merely to illustrate some of the points in the text; the references are neither representative nor systematically chosen, even within the particular subjects actually discussed.