Pelé Meets John Von Neumann in the Penalty Area

2014 ◽  
Author(s):  
Ignacio Palacios-Huerta
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
General Theory ◽  
Minimax Theorem ◽  
Common Interest ◽  
John Von Neumann ◽  
Von Neumann ◽  
Complete Test ◽  
Zero Sum ◽  
Special Case

The movie A Beautiful Mind (2001) portrays the life and work of John F. Nash Jr., who received the Nobel Prize in Economics in 1994. A class of his theories deals with how people should behave in strategic situations that involve what are known as “mixed strategies,” that is, choosing among various possible strategies when no single one is always the best when you face a rational opponent. This chapter uses data from a specific play in soccer (a penalty kick) with professional players to provide the first complete test of a fundamental theorem in game theory: the minimax theorem. The minimax theorem can be regarded as a special case of the more general theory of Nash. It applies only to two-person, zero-sum or constant-sum games, whereas the Nash equilibrium concept can be used with any number of players and any mixture of conflict and common interest in the game.

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.

Game Theory vs. Business Ethics

2015 ◽  
pp. 1849-1872
Author(s):  
Ben Tran
Keyword(s):  
Game Theory ◽  
Business Ethics ◽  
Emerging Economies ◽  
Moral Philosopher ◽  
John Von Neumann ◽  
Von Neumann ◽  
Economic Behaviour ◽  
History Of ◽  
The Moment ◽  
The Relationship

In 1954, the British philosopher Richard Braithwaite gave his inaugural lecture, Theory of Games as a Tool for the Moral Philosopher. Braithwaite predicted game theory would fundamentally change moral philosophy. However, in hindsight, John von Neumann and Oskar Morgenstern's publication of Theory of Games and Economic Behaviour was the moment modern game theory entered the discipline of ethics. The purpose of this chapter is to analyze the relationship between game theory and business ethics. In other words, this chapter explains how game theory plays a role in business ethics and affects business ethics for emerging economies and covers in detail: 1) the history of game theory; 2) types of/definition(s) of games; 3) business ethics; 4) business; and 5) ethics. The chapter concludes with the role that game theory and business ethics play in emerging economies.

‘If They Say Bomb at One O’clock …’

2019 ◽  
pp. 199-230
Author(s):  
Alan Bollard
Keyword(s):  
Game Theory ◽  
Cold War ◽  
Manhattan Project ◽  
Mathematical Approach ◽  
John Von Neumann ◽  
Von Neumann ◽  
Dynamic Economy ◽  
Atom Bomb ◽  
Post War ◽  
The Cold War

In Japan conventional bombing had not proved sufficient: it was the atom bomb that ultimately brought surrender. The brilliant Hungarian mathematician John von Neumann had worked on the Manhattan Project and identified Hiroshima as a bombing target. He went on to design computers that helped build bigger bombs. In addition he developed an original mathematical approach to modelling a dynamic economy that helped economists advance their modelling. With the Cold War looming, he and colleague Oskar Morgenstern pioneered the new subject of game theory which the big powers used to model their post-war defence tactics, and led to the classic 1950s strategy of ‘mutually-assured destruction’.

Explaining the Long Peace

2019 ◽  
pp. 145-160
Author(s):  
Frank C. Zagare
Keyword(s):  
Game Theory ◽  
Interstate Conflict ◽  
Security Studies ◽  
Conflict Behavior ◽  
John Von Neumann ◽  
Von Neumann ◽  
Incorrect Prediction ◽  
Game Theoretic ◽  
The Cold War ◽  
Thomas Schelling

This chapter addresses the charge made by some behavioral economists (and many strategic analysts) that game theory is of limited utility for understanding interstate conflict behavior. Using one of perfect deterrence theory’s constituent models, a logically consistent game-theoretic explanation for the absence of a superpower conflict during the Cold War era is provided. As well, the chapter discusses a prescription based on an incorrect prediction attributed to John von Neumann, one of the cofounders of game theory. It also examines a logically inconsistent explanation of the long peace offered by Thomas Schelling, the game theorist many consider the most important strategic thinker in the field of security studies. The argument is made that a predictively inaccurate or logically inconsistent game model in no way undermines the utility of game theory as a potentially powerful methodological tool.

Do Prudent Agents Play Lotteries? Von Neumann's Contribution to the Theory of Rational Behavior

2006 ◽  
Vol 28 (1) ◽  
pp. 95-109 ◽  
Author(s):  
Nicola Giocoli
Keyword(s):  
Game Theory ◽  
Set Theory ◽  
100Th Anniversary ◽  
Economic Behavior ◽  
Rational Behavior ◽  
John Von Neumann ◽  
Von Neumann ◽  
Balanced Growth ◽  
The Relationship ◽  
Fixed Point Techniques

The year 2003 marked the 100th anniversary of the birth of John von Neumann (1903–1957), one of greatest geniuses of the last century. Beyond contributing to fields as diverse as set theory, quantum mechanics, atomic energy, and automatic computing, von Neumann has also had a decisive influence upon modern economics. From the invention of game theory to the axiomatization of expected utility, from the introduction of convex analysis and fixed-point techniques to the development of the balanced growth model, the von Neumann heritage can be clearly traced in several areas of our discipline. The aim of this paper is to clarify the relationship between the two concepts of rationality he devised in his classic 1944 book Theory of Games and Economic Behavior, written with the collaboration of the Austrian economist Oskar Morgenstern (von Neumann and Morgenstern 1953).

scholarly journals Game Theory: An approach through history and its applications

2019 ◽  
Vol 12 (1) ◽  
pp. 138
Author(s):  
W. A. V. Souza ◽  
M. C. Malavazi
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Nobel Prize ◽  
Economic Behavior ◽  
Mathematical Approach ◽  
John Von Neumann ◽  
Von Neumann ◽  
Knowing That ◽  
The Game Theory ◽  
Arbitrary Decision

Game Theory is a mathematical approach to the study of decision making between individuals when each outcome depends on the decisions of others, ie, one should not make an arbitrary decision, but decide based on what they think the decision of their "opponent" will be, knowing that they think the same. Developed by John von Neumann and Oskar Morgenstern in 1944 in the book Theory of Games and Economic Behavior, it had been very contested since its launch, but the works of a genius named John Nash, winner of the Nobel Prize in economics in 1994, ended these contestations. This work shows that the Game Theory was not limited to the field of economics, but expanded to other areas, such as biology, explaining strategies used by species to survive. As results are presented more than ten models based on the principles of Game Theory, among them the Prisoner's Dilemma, Ice Cream Vendors Game, Clean City Law and Warning Song between Bird.

Abstraction

2020 ◽  
pp. 38-48
Author(s):  
Stephen K. Reed
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Visual Images ◽  
Abstract Thinking ◽  
John Von Neumann ◽  
Von Neumann ◽  
Definition Of ◽  
The Mind

The power of abstract thinking is captured by the brilliance of John von Neumann who made many contributions to mathematics, computer science, and game theory. One definition of abstraction is that an instance exists only in the mind (the word truth) rather than in the environment (the word car). An advantage of the latter, concrete examples is they support the formation of visual images to aid recall. A second definition of abstraction is a focus on the most important attributes of an instance. These attributes include those that differentiate one object from another or one category from another. A third definition of abstraction is that an abstract idea applies to many particular instances of a category. Prototypes, rules, and schema are examples.

Unlocking the Mystery of the Origins of John von Neumann’s Growth Model

2021 ◽  
Vol 53 (4) ◽  
pp. 595-631
Author(s):  
Juan Carvajalino
Keyword(s):  
Linear Equations ◽  
Minimax Theorem ◽  
Theoretical Models ◽  
Von Neumann ◽  
Systems Of Linear Equations ◽  
National Boundaries ◽  
And Mathematics ◽  
Zero Sum ◽  
General Economic Equilibrium ◽  
Local Perspectives

In his famous “A Model of General Economic Equilibrium,” von Neumann wrote that it was “obvious to what kind of theoretical models [his] assumptions correspond.” To date, however, his sources of economic insights about the functioning of the continuously growing price-economy that he modeled have remained a total mystery. Based on archival material, this mystery is solved in this account by making visible the specific influences from economics and mathematics that inspired him. I argue that von Neumann’s 1937 paper resulted from a deep engagement with economics as it was emerging at the beginning of the 1930s and that this happened as he was travelling and crossing national boundaries while bridging distinct branches of mathematics with different local perspectives in economics. His encounters with Jacob Marschak in Berlin, Nicolas Kaldor in Budapest, and Frank Graham in Princeton as well as his reading of Walras’s, Wicksell’s and Cassel’s work would be key. I also explain how he came to realize that there existed a formal analogy between systems of linear equations and inequalities with which he characterized (stationary and dynamic) economies and the minimax theorem for two-person zero-sum games that he had conceived and proved in 1928.

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