Game Theory

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Studying through applying mathematical models how people interact and make decisions. Explanation of Game Theory of Von Neumann, Morgenstern, and Nash.

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What is Game Theory? Description

Game Theory is a special branch of mathematics which has been developed for studying decision-making in complex circumstances. Game theory tries to predict outcomes based on interactive models in which the decisions of each party affect the decisions of the other parties. The meaning of "Game" here is: a move by one player will result in moves by others. The idea historically dates back to the Talmud and Sun Tzu's writings. However, the contemporary codification is attributed to John von Neumann and Oskar Morgenstern. They published the Theory of Games and Economic Behavior in 1944. In the early 1950s, John Nash generalized their results and provided the basis of the modern field of Game Theory. A rapid rise in theoretical developments led to the founding of the first academic magazine devoted to the field by Oskar Morgenstern in 1972. Few corporations nowadays think about their strategy without adding some game theory models or game elements into their strategy process.

Game theory can be defined as the study of how people interact and make decisions. This broad definition applies to most of the social sciences, but game theory applies mathematical models to this interaction under the assumption that each person's behavior impacts the well-being of all other participants in the game. These models are often quite simplified abstractions of real-world interactions. While many game theorists certainly enjoy playing games, a "game" is an abstract representation of many serious situations and has a serious purpose.

Usage of Game Theory. Applications

Preparing business negotiations.
Analyzing future market conditions.
Strategic decision-making.
Assess the viability of a new venture, business model, program, project, product, service or technology.

Assumptions in Game Theory

A major issue with game theory is: it is necessary to make assumptions. Any model of the real world must make assumptions that simplify the reality, because the real world is too complex to analyze with any precision. There is a constant tradeoff between realism and the technical capability to solve problems. Even if one could write down a model that accurately describes how people make decisions in general, no amount of computers would be able to calculate it.

What assumptions are made normally? The usual assumptions are:

Rationality. People take whatever actions are likely to make them more happy. And they know what makes them happy.
Common knowledge. We know that everyone is trying to make himself as happy as possible, potentially at our expense.

These assumptions take many mathematical forms, from very strong (and likely unrealistic) towards much weaker forms in the study of behavioral game theory.

Experimental economics examines the validity of these assumptions by seeing how real people act in controlled environments.

Example of Game Theory

The most widely known example of game theory is probably the Prisoner's Dilemma: A zero-sum game cooperation game that got its name from the following hypothetical situation: imagine two criminals arrested under the suspicion of having committed a crime together. However, the police does not have sufficient proof to have them convicted. The two prisoners are being isolated from each other, and the police offers each of them a deal: the person that offers evidence against the other one will be freed. If none of them accepts the offer, they are in fact cooperating against the police, and both of them will get only a small punishment because of lack of proof. They will both win. However, if one person betrays the other, by confessing to the police, he will gain more, since he is freed. The one who remained silent, on the other hand, will receive the full punishment, since he did not help the police, and there is sufficient proof. If both betray, both will be punished, but less severely than if they had refused to talk. The dilemma resides in the fact that each prisoner has a choice between only two options. But they can not make a good decision, without knowing what the other person will do.

Game Theory Special Interest Group

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Game Theory Forum

Recent User Comments

    			 
             Mutua Fred - Kenya
  	       
  		     Dominance Theory
  	  		 "Can anybody explain to me the concepts of dominance theory vs. the prisoners dilemma?"
  			   
    	  		 0

    			 
             Aziz - India
  	       
  		     Using Game Theory for Making Investments
  	  		 "How can we use Game Theory in making investment decisions? How can it be useful in this?"
  			   
    	  		 2

    			 
  			   Kim Warren - UK
  	       
  		     Game Theory Cases in Strategy?
  	  		 "Though I have heard of game theory being used in a few particular and special cases (e.g. the auctioning of 3G cellphone licenses) I have not seen anything of it being used in general strategy or business planning. The strategy textbooks dismiss it as too uni-dimensional and limited to special cases to be useful, and I can find virtually no articles in e.g. Harvard Business Review or McKinsey Quarterly giving any encouraging cases where it has been helpful. 
Does anyone know otherwise?"
  			   
    	  		 8

    			 
  			   Ryan - USA
  	       
  		     Can Game Theory deal with Bounded Rationality?
  	  		 "A key assumption of Game Theory, as mentioned in the article, is rationality. In reality of course  individuals and companies may differ from each other in terms of how effectively they can observe a situation, analyze it, plan a strategy and execute their strategy. Their rationality is bounded.

(How) can Game Theory deal with Bounded Rationality?"
  			   
    	  		 0

    			 
  			   Ryan - USA
  	       
  		     Is Business Strategy a Non-Zero-Sum Game?
  	  		 "I found that a ZERO-SUM GAME is a game with a clear winner and one or more clear losers. The more outcomes or results one player receives, the fewer outcomes or results are available for the other players. In other words, in zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero.

In a NON-ZERO-SUM GAME on the other hand, there is not a fixed pie of outcomes or possible results, there is an opportunity for all players to maximize their outcomes simultaneously. In a worst-case scenario the outcomes of one player do not remove outcomes from any other player. And in a best-case scenario, the outcomes of one player may be interdependenty linked to the maximization of the other players' outcomes.

Often (typically) business strategy is seen as a zero-sum game, but it has elements of both game types ... What are NON-zero game characteristics of business strategy?"
  			   
    	  		 4

Best User Comments

    			   
    			     Editor - NL
  	         
  				   Game Theory in Business
  				   "Issue #46 of S+B has an interview with Prof. Nalebuff, well known for bringing game theory into the realm of business. According to N. there are 2 reasons why extending game theory to business requires an intellectual leap: 1. The game of business is not a zero-sum game (the success of one company does not require others to fail). 2. There are no explicitely defined rules in business (each firm can change the game/rules). Moreover, Nalebuf warns that the behavior of businesspeople is not always rational, and inertia can be a powerful force to overcome."
    			   
        	  		 22

    			   
    			     Nick Bailey - USA
  	         
  				   Game Theory vs. SWOT Analysis
  				   "A major advantage of Game Theory over SWOT analysis when preparing a business strategy is the possibility of INTERACTION between your own firm and other firms. Reactions of competitors on a potential strategic move can be studied and predicted. This allows us to anticipate in our strategy on the reactions of the competitors. We can use certain characteristics of our competitors to our own advantage."
    			   
        	  		 4

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	└► Sekar Vedaraman (India)	Game Theory and Strategy	"The Right Game: Use Game Theory to Shape Strategy by Adam M. Brandenburger and Barry J. Nalebuff HBR - July August 1995."
	└► Abraham (Netherlands)	Boeing and Airbus	"What is the dilemma for Boeing and Airbus in developing a super jumbo?"

                     
                      └► Y Kerbelker (S Africa)
                      
                    Game Theory
                    "Please read the book:   "Game Changer" by A G Lafley (chairman and CEO of Procter & gamble) and Ram Charam (Coauther of the New York Times bestseller Execution) 2008 First Edition ISBN 978-0-307-38173-6 Published in US by Crown Business."

	└► Ian Sutherland (UK)	Rational or not	"As I understand it, game theory persumes that players on the same side have the same motivation. In business this is rarely true and often it is hard to find anything other than a superficial commonality of purpose. Instead there is a great tendency in this world of short term views for each person to promote their own personal agenda, often at the expense of the greater good. This may what was meant by the comment that not all behaviour is rational. I would argue that it is usually rational in the framework used by the individual, but that there is rarely a similar "framework" for the group or business. This means look at the individuals if you want to truly understand. Or as is often said in my field "follow the money!""
	└► Mary (USA)	Assumption of Utility	"Indeed Ian, another game theory assumption is that all participants are motivated inherently to maximize their utility (economic measure of desired outcomes). Von Neumann and Morgenstern understood this distinction; to accommodate all players, whatever their goals, they constructed a theory of utility. They began by listing certain axioms that they thought all rational decision makers would follow (for example, if a person likes tea better than coffee, and coffee better than milk, then that person should like tea better than milk). They then proved that it was possible to define a utility function for such decision makers that would reflect their preferences."
	└► Editor (Netherlands)	Utility variations	"Note that there could be conflicting group and individual utilities and short-term and long-term utilities."
	└► srikanth (India)	Business is a NON-zero sum game	"I think the definition of "ZERO SUM GAME" by Ryan is slightly wrong. A "ZERO SUM GAME " is a game in which the total of all the gains and losses is zero and not the total benefits of all players in the game. So in a real market scenario, when one player tries to gain (the player could be a STAR OR A CASH COW as the case may be), it has to be at the expense of another player. The case varies if the players are competing in different domains and these players are not on the same page. A "NON ZERO SUM GAME" is a different concept, where players are all benefitting from a situation without cutting each other. All real-life business situations are NON ZERO SUM GAMES. Any differences of opinion are always welcome!"
	└► Richard D. Cushing (USA)	Free Market Exchanges	"I would add to and extend srikanth's (India) statement to say this: All real-life business exchanges in a free market are non zero-sum games. The assumption in a "free market" exchange is that none of the participants in the exchange are employing fraud or coercion to effect the outcome of the exchange."
	└► Gillion Utens (The Netherlands)	Game Theory literature	"Recommended literature on this subject: Robert Axelrod - The evolution of cooperation (1981). Or watch the BBC documentary "Nice guys finish first" on YouTube (Richard Dawkins 1987)."
	└► Bas (Netherlands)	Differentiation	"As was said in the article, this is just a simplification. In the real world, no two consumers are the same. Companies can differentiate on hundreds of details and change the mental image that consumers have of a company or product. Therefore, one company's gain does not necessarily mean another companies loss."

                       
                        └► Kim Warren (UK)
                        
                      Game theory article by Nalebuff
                      "BTW - the S+B article mentioned may not be easy to find, so here's a link."