Critical mass (game theory)

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A critical mass in game theory means that it is not necessary to convince the entire group of a strategy, but that it is sufficient to convince only a certain number of participants of this strategy. If this threshold is exceeded, i.e. the critical mass is reached, this strategy will become self-sustaining.

Importance in game theory

In the context of game theory, a critical mass describes a threshold value. If this is achieved, a self-sustaining effect is triggered within a group dynamic process , in which one existing equilibrium can shift to another.

Conceptual classification

Originally, the concept of critical mass was developed as part of the analysis for the construction of telecommunications networks. The smallest number of participants in a network denotes the critical mass at which a network can be operated cost-effectively with a uniform, minimal connection fee. The formal analysis of the concept of critical mass goes back to Jeffrey Rohlfs.

Based on research from network economics, the phenomenon of critical mass became important for game theory. An economic analysis of networks is understood to mean the criteria for a decision by suppliers and buyers in a market for network goods and their impact on the equilibrium allocation. A network good represents a good, the use of which depends on the number of actors who have this good.

In other words, network externalities play a special role in describing the phenomenon of critical mass. They describe situations in which one person's consumption directly affects the benefit of another. Another property of network goods is that of complementarity or compatibility . This means that the consumption of a good is not only determined by its specific properties, but also by the consumption of other market participants and the corresponding supplementary components.

An example to illustrate this: “A consumer's demand for fax machines.” A fax machine is used to communicate with other market participants. Buying such a device is only worthwhile if other market participants also own a fax machine. The benefit therefore depends on other market participants and their consumption. In order for such a technology system of fax machines to prevail, it is necessary that the critical mass of subscribers is reached. If a sufficiently large number of subscribers have a fax machine, this system will become self-supporting.

Critical masses can result from a variety of effects from an economic ( economies of scale , composite effects , network effects ) or psychological ( herd instinct , learning effect) point of view.

Example: standard change

Assuming there are two competing technical systems; if one of them is technologically better than the other, the technologically better system will probably prevail on the market. The following example of the VHS and Betamax video cassette systems and formats shows that this does not always have to be the case . The Betamax format from Sony, although the technologically better system, could not prevail over the VHS from JVC . The benefit of a technological system therefore not only depends on the product-specific properties, but also on which system other users are using. A critical mass of users was enough for one system to prevail over the other.

Why one standard has prevailed over another is therefore less important in game theory. But if a standard has prevailed and a group of players is in the situation of a lock-in effect , a critical mass of participants is required to shift the existing balance to another. The follower effect then ensures that the new equilibrium is stabilized.

See also

literature

  • Avinash Kamalakar Dixit , Barry J. Nalebuff: Game Theory for Beginners - Strategic Know-How for Winners. Schäffer-Poeschel, Stuttgart 1997, ISBN 978-3-7910-1239-1 .
  • Alfred Endres, Jörn Martiensen: Microeconomics - An integrated presentation of traditional practice and modern concepts in theory and practice . Kohlhammer, Stuttgart 2007, ISBN 978-3-17-019778-7 .
  • Ulrich Blum , Simone Müller, Andreas Weiske: Applied industrial economics - theories - models - applications . Gabler, Dresden 2006, ISBN 978-3-8349-0215-3 .
  • Varian: Fundamentals of Microeconomics . 6th edition. Oldenbourg, Munich 2004, ISBN 3-486-27453-8 .
  • Samuel S. Oren, Stephen A. Smith: Critical Mass and Tariff structure in Electronic Communications Markets . In: Bell Journal of Economics , 1981, 12/2, pp. 467-487.
  • Jeffrey Rohlfs: A theory of interdependent demand for a communications service . In: Bell Journal of Economics and Management science , New Jersey 1974, 5/1, pp. 16-37.
  • Günter Knieps: Network Economy: Basics - Strategies - Competition Policy . Gabler, Wiesbaden 2007, ISBN 978-3-8349-0107-1 .

Individual evidence

  1. ↑ Oren, Smith: Critical Mass and Tariff structure in Electronic Communications Markets . P. 472
  2. ^ Rohlfs: A theory of interdependent demand for a communications service . P. 29
  3. ↑ Knieps: Netzökonomie . P. 125
  4. ↑ Endres, Martiensen: Microeconomics . P. 602
  5. ↑ Endres, Martiensen: Microeconomics . P. 603
  6. ↑ Endres, Martiensen: Microeconomics . P. 607
  7. ↑ Varian: Fundamentals of Microeconomics . P. 648
  8. ↑ Blum, Müller, Weiske: Applied Industrial Economics . P. 219
  9. ↑ based on Dixit, Nalebuff: Game theory for beginners . P. 247