**Theory**

**Game**

**A presentation**

by Group 13

by Group 13

Game Theory is a mathematical study of strategic decision making and analyses the nature of competitive behaviour.

It is the evaluation of the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences of those agents.

A brief history OF GAME THEORY

features and forms

Types of games

Applications of game theory

APPLICATION OF GAME THEORY

TO BUSINESS

Nash Equilibrium

Navitas vrs. Kaplan

Private forces in the education industry

Links to further READING/viewing:

References

(known as IBT until 2007)

Had become a leader in university pathway education in Australia

Specifically focused on the international student market.

Between 1993 and 2000, Kaplan diversified beyond test preparation to:

Higher Education

Professional (licensing, training and professional development programs)

Kids and schools

Navitas

acquired two new companies, allowed integrating through the offering of vocational and education courses.

“Not overly concerned”

Kaplan

entered the Australian market in December 2005, although not entering into direct competition with Navitas in the university pathway and English language sectors, Kaplan’s strength and capabilities in both of those areas

had not been overlooked by Navitas

.

Navitas diversifies

Value net

Kaplan

observed that its focus in Australia was concentrated in both ‘professional education and international student pathway education’. Chief executive of Kaplan Australia, Warren Jacobson, pointed out that Kaplan would be both a

collaborator

and

competitor

to the universities and that its education offerings were unique and unmatched.

Tactics: Signalling

Navitas

commented that the company’s growth in the years ahead was going to come from the UK and Canada and that the company was not ‘actively pursuing’ any more relationships with Australian universities.

However

, two weeks after, Curtin University of Technology announced that it was partnering with Navitas to build a $30 million campus in Singapore.

Dynamic Competitive strategy

Consider the expected reactions of competitors to any move

Surprising competitors with strategic moves

Kaplan

acquired The Financial Services Institute of Australia (Finsia Education), followed by Bradford College and Grange Business School. Based in Adelaide Bradford provided pathway programs for international students who, at the completion of their studies, gained direct entry into the University of Adelaide (

Go8 Universities across Australia

).

Kaplan borned in USA

Navitas borned in Australia

Both have conquered the education market in their own countries and are now competing internationally, establishing connections with well known universities and professional bodies.

The Main Principles

Consider the expected reactions of competitors through backward reasoning.

Know your competitor as well as you know yourself.

Consider the appropriate strategy for one-period or repeated interaction games

The most well-known Game Theory example is the ‘

Prisoner’s Dilemma

’.

It is often used to describe decision problems involving positive and negative externalities.

Prisoners Dilemma describes a wide variety of business decisions made where the resulting payoffs depends on competitors responses.

Positive and cohesive management promotes cooperation.

Use any existing dominant strategy.

Seek stable situations.

Prisoners Dilemma demonstrates why two individuals may not cooperate and helps explain what governs the balance between cooperation and competition in business, politics, and in social settings.

Consider Coca-Cola and Pepsi, both of these companies sell similar products.

Both Coca-Cola and Pepsi would be better off if they charged regular prices and could be assured that their competitor would do the same. However, by charging regular prices each company is confronted with the possibility of earning decreased profits if its competitor decides on a discount price strategy.

This uncertainty creates a Prisoner’s Dilemma for Coca-Cola and Pepsi.

Forms

In the case of Coca-Cola, the worst possible profit scenario of $2 billion results when it charges regular prices while Pepsi charges discount prices.

In the case of Pepsi, the worst possible profit scenario of $1 billion results when it charges regular prices, while Coca-Cola charges discount prices.

For both Coca-Cola and Pepsi the secure strategy is to offer discount prices, therefore assuring customers of discount prices and themselves profits of $4 billion and $2 billion.

Ultimately Coca-Cola and Pepsi would be better off if they adopted a regular-price strategy, however the risk of low profit outcomes prevents that possibility.

•The number of players must be specified

•The expected outcomes must be quantifiable

•Whether or not information available about the issue is completely known

•Whether or not it is a one-off or multi-period game

•Whether or not actions by competitors are simultaneous or sequential

Parameters

Game theory was pioneered by John Von Numann and Oskar Morgenstern in 1944, however became popular in the 1990s through the publication of their book ‘Theory of Games and Economic Behaviour’.

Game Theory can be classified into two main strands:

1.Non-cooperative game theory

2.Cooperative game theory

Non-cooperative game theory

Focus is on the individual players strategies and their influence on payoffs and try to predict what strategies players will choose.

Cooperative game theory

Focus is on the alliances players may form. Assumptions that each alliance may attain some payoffs, and then attempt to predict which alliances will form.

In business a game would rarely be as simple as that of the 'prisoner's dilemma'. Once there is more than two players, more than one period of play and unknown information the game would become much more complex.

Normal Form

Represented by a matrix, the normal form game displays a payoff for each player and every possible combination of actions. Players, strategies and payoffs are usually shown.

Nalebuff & Branenburger's PARTS model provides a framework for considering which elements to most effectively employ.

PARTS model

Players

A game's players are determined by a value net that maps all relationships including competitors and complementors.

added value

Defined as "the total value of the industry with the organisation, less the total value of the industry without the organisation"(Hubbard 2011, p. 226).

Rules of the game

Rules are important as innovative organisations can use the rules to determine industry standards or change implicit rules to their best advantage.

tactics

Defined as "actions that are taken to carry out or support a business or functional strategy (Hubbard 2011, p. 226)".

Tactics are designed to have their own effect ans well as an affect on competitors perceptions.

scope

Scope defines a range of categories that the game can be played in. It can encompass the typical geographical scope as well as customer types or functional use, etc.

Dufwenberg (2010) argues that the name ‘game theory’ is derived from parlor games such as poker, chess and bridge.

“However, game theory’s main applications concern society: economists study, for example,auctions, bargaining, market competition, or family formation;military strategists examine conflict: biologists model natural selection: political scientists analyze voting, etc (p. 1)”.

D'Aventi argued that "frequency, boldness and aggressiveness of dynamic movement" (Hubbard 2011, p. 229)amongst players created constant disequilibrium and rapid change in industry that he called hypercompetition. He identified four "competitive arenas" where this could occur.

cost-quality competition

timing-know-how competition

stronghold competition

deep pockets competition

The organisation with the deepest pockets will start a price-based war to drive smaller organisations out of the industry.

Organisations build geographical, product or customer type entry barriers to deter new entrants from entering the industry.

When an organisation is able to avoid the cost-quality arena by finding a new or emerging market, or by creating a technological advantage.

Where cost and quality are two fundamental bases of competition an organisation will attempt to differentiate on quality following a price-war and leading to segment competition.

cooperative vs non-cooperative

Cooperative players form binding commitments.

Non-cooperative players focus on their individual strategies and resultant influence on payoffs.

symeteric vs asymeteric

In a symmetric game the opposing players can change without the payoff changing. The player can focus solely on the other strategies employed.

The previously demonstrated 'prisoner's dilemma' is an example of a symmetric game.

Within most asymmetric games both sets of players do not have identical strategy sets.

zero sum vs non-zero sum

In zero-sum games the winner always benefits at the expense of the others such as poker or chess. The total benefit to all players in the game, for every combination of strategies, always adds to zero.

The outcome of non-zero-sum games is a net result greater or less than zero. A win by one player does not necessarily have to result in a loss by another.

simultanEous and sequential

As the name suggests in simultaneous games both players are able to move simultaneously.

Sequential games are governed by time. A later player will have some knowledge of the first players actions.

Perfect information vs imperfect information

If all players know the previous moves of all the other players it will be one of perfect information. An example being sequential games such as chess.

Many games are of imperfect information such as poker where a player may not know other players actions or strategy.

extensive form

An extensive form game allows the sequencing of players moves. Able to be governed by time the game can be viewed as a multi-player generalization of a decision tree.

BUT WHAT IS IT?

HISTORY OF THE NASH EQUILIBRIUM

John Forbes Nash Jr.

An example of the Nash equilibrium taken from the movie

'A Beautiful Mind' (based on the life and work of John Forbes Nash).

• The Nash equilibrium is named after John Forbes Nash Jr. who developed the theory as a talented young graduate student at Princeton.

• A version of the concept was in existence prior to his development of the theory, with the first notable example coming from Antoine Augustin Cournot’s work (1838) on oligopolists and perfect competitors as limiting extremes. Further work by Emile Borel (1921) and John von Neumann and Oskar Morgenstern (1944) expanded on the theory, but none of these researchers focused specifically on finding a methodology of equilibrium analysis in the way that Nash did, and they were also unable to combine all of their concepts into one universal theory (Myerson, 1999).

• While these theories worked with pure strategy and gave some insight into the rational decision-making process of producers and consumers, it was Nash’s work on non-cooperative games that provided the breakthrough for a concept that could be applied to the rational-choice analysis in general competitive situations. Some believe that the impact of this theory on economics and social sciences is on par with the discovery of the DNA double helix in biological sciences (Myerson, 1999). In fact, this

theory lead to John Nash becoming a Nobel Laureate

(in Economics).

• While game theory can be applied to many different situations, perhaps the most important for the business and economics fields is the application of game theory to non-cooperative games (which exist when players make decisions independently).

• The Nash equilibrium is an important tool in these situations, as it is a solution concept that can be used in non-cooperative games involving two or more players (Osborne & Rubinstein, 1994). The players in the game are assumed to know the equilibrium strategies of the other players and have no incentive to deviate their strategy unilaterally, as this would lead to a less than perfect outcome (Myerson, 1999).

• The actual equilibrium point is found when all of the players in the game have chosen a strategy and no one can benefit from changing their strategy if the others keep theirs unchanged (The European Financial Review, 2012).

NASH EQUILIBRIUM AND ITS

APPLICATION TO BUSINESS

Binmore, K. (2007). 'Game Theory: A Very Short Introduction', Oxford University Press, UK.

Dufwenberg, M. (2010). 'Game Theory', John Wiley & Sons Ltd,page 167 - 172.

Dwyerson, R.B. (1999). Nash equilibrium and the history of economic theory, 'Journal of Economic Literature', 36, p.1067-1082.

Hirshcey, M. (2009). 'Managerial Economics', 12th Edition, Cengage learning.

Hubbard, G. & Beamish, P. (2011). 'Strategic Management: Thinking, Analysis, Action', 4th Edition, Pearson Education.

Osborne, M. & Rubinstein, A. (1994). 'A course in game theory', Cambridge, MIT:MA.

The European Financial Review. (2012, February 15). 'Options Games: Balancing the trade-off between flexibility and commitment'. Retrieved July 5, 2012 from http://www.europeanfinancialreview.com/?p=4645.

Thanks for watching, we hope you have enjoyed learning more about Game Theory!

EXAMPLE: THE PRISONERS' DILEMMA

• While the Nash equilibrium can be used for many situations (e.g. for war or arms races), it has been most predominantly used in the fields of economics and business.

• Institutions use the Nash equilibrium as a strategic decision-making tool by comparing the competition’s potential strategies against their own strategies, and then finding the point of maximum payoff (Myerson, 1999).

• The key point to realise (as noted in the previous video sample from ‘A Beautiful Mind’), is that the outcomes of competition cannot be predicted if the strategies of competitors are analysed in isolation; instead, strategies must be chosen by taking the actions of other decision-makers into account (Osborne & Rubinstein, 1994).

Here's a good example of the Nash equilibrium and how it is applied

to strategic decision-making (using Coke and Pepsi as examples again):

EXAMPLE: Coke vs Pepsi

READING

VIDEOS

Game theory and business applications:

http://finance.wharton.upenn.edu/~allenf/download/Vita/game.pdf

Nash equilibrium and the history of economic theory:

http://home.uchicago.edu/rmyerson/research/jelnash.pdf

Game theory online learning resource:

www.gametheory.net

Open Yale Course on

Game Theory (Part 1/5)

How to use game theory for negotations and strategic decisions

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