Unpredictability (game theory)

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The unpredictability of the game in game theory sense corresponds to the uncertainty which the players (and any spectators) of a parlor game in terms of the process and the result are exposed to a lot. The terms unpredictability and uncertainty - like the term game - are used with inconsistent meanings in specialist literature depending on the context (mathematical game theory, sociology , political science ).

causes

In almost all games, the unpredictability of the course of the game results from only three different causes, the differentiation of which enables games to be classified:

Causes of the uncertainty in parlor games as the basis for a game classification

Within this classification scheme, the proportions with which the three causes for a specific game determine the game result can usually only be assessed qualitatively. To visualize a comparison of different games, a triangle (also referred to as Bewersdorff triangle , tension triangle or luck-logic-and-bluff triangle ), occasionally also a point scale, is used.

1. Coincidence

This characteristic is mainly caused in parlor games by rolling the dice or shuffling playing cards and stones. The respective game is then determined within the framework of the rules of the game both by the decisions of the players and by random events. If the influence of chance dominates, it is a game of chance . In pure games of chance, the decision of the player about participation and the size of the stake is already the most important. Games of chance that are played for assets are traditionally subject to statutory regulations , in Germany in the form of a gaming monopoly .

2. Various combinations of possible moves

The rules of the game give the players the opportunity to act within a precisely defined framework. The sequence of player actions, a single one of which is referred to as a move, combine to form a usually large number of moves, making the outcome of a game de facto unpredictable. Games in which the uncertainty is based exclusively on this phenomenon are called combinatorial games (such games for two players are sometimes examined in combinatorial game theory ).

3. Different levels of information of the individual players

Another cause of the unpredictability is based on different levels of information of the acting players, as they come about through hidden cards, hidden or simultaneous moves. Games, the uncertainty of which mainly results from different levels of information, are called strategic games .

Mathematical approaches

Mathematics is used to try to overcome the unpredictability in games to a certain extent. We are looking for optimal behavior for the players. Depending on the cause of the unpredictability, the relevant methods can be assigned to different disciplines of mathematics and computer science :

Game theory studies are based on a formal model for games in which strategies are examined.

Example: heads or tails (matching pennies)

Two players independently choose the side of a coin to flip, i.e. either heads (K) or tails (Z). The first player wins one euro if there is a match. If different results are achieved, the second player wins one euro. In order to make the strategic behavior unpredictable (calculable), a player should randomly choose between the given alternatives and thus use a so-called mixed strategy .

Payout matrix

Explanations:

  • N = {player 1, player 2}
  • Possible strategy S1: head
  • Strategy rooms S1 = S2 = {heads, tails}
  • Possible profile: s = (number, number)
  • Set of all strategy profiles: S = {(head, tails); (head, head); (tails, heads); (tails, tails)}

Mathematical game theory

In their game theory book, Dixit and Nalebuff explain mixed strategies in games in a chapter titled Unpredictability . A mixed strategy is a random selection with a probability distribution determined at the beginning of the game , with which a complete action plan of the player is “rolled out”, which contains a decision for every possible decision situation in the game. In this case, the unpredictability does not result directly from the game, but from the behavior of the corresponding players, which may be motivated by the game.

In a two-person zero-sum game , which is characterized by the fact that the profit of one player is always equal to the loss of his opponent, there is always an equilibrium with a clearly determined game result based on mixed strategies ( Min-Max theorem ). In principle, such minimax strategies can be calculated using methods of linear optimization . For games with more than two people or two-person games without a zero-sum character, there can be several equilibria with different game results (so-called Nash equilibria ).

Economic Applications of Game Theory

The actual focus of game theory studies is not the optimization of behavior in parlor games. As early as 1928, the founder of game theory John v. Neumann : "... there is hardly a question of everyday life in which this problem did not play a role."

However, the practical relevance of game theory is political scientists as Joachim Raschke and Ralf Tils because of their "realistätsfernen reductionism denied": ". Game theory is - except in marginal areas - consequences for practice" . Regarding unpredictability, the authors remark on their non-game theoretical level: “The assumption of fundamental unpredictability is wrong - then strategy would not be possible either. There are degrees of predictability. Strategy becomes more unpredictable, the more leeway an institution allows ... Strategy refers to the predictable dimensions of external actors. One can ... anticipate possible opponent behavior and build up reaction reserves for it ” .

In general, it is beneficial to be able to correctly predict the unpredictability of the counterparty and to be able to act accordingly. The unpredictability becomes a crucial part of the strategy when one of the players wants a simultaneous approach and the other player would rather prevent this.

Thus, the unpredictability is an indispensable part of reality and thus forms a starting point for entrepreneurial activity, it is not a disadvantageous component that must be eliminated by the planning and acting person, he must be able to deal with it and draw the corresponding added value for himself.

  • Example 1: Unpredictability during a strike

A new strike strategy had to be developed within a strike by garbage disposal employees, as the six-week strike had not led to any result and those involved were showing signs of fatigue. The strike strategy had to be changed in such a way that it was unpredictable for the other side, that is, unpredictable. The employees agreed at the strike meetings to continue the strike activities in a changed manner. They developed a strategy to make it difficult for employers to use private garbage collectors. The strike tactic was to leave employers in the unclear when and how long the strike would take place by means of a coordinated arrangement. The employers were taken by surprise and could not react to the constantly changing situation in time. The changed, unpredictable strike strategy was successful.

  • Example 2: Tax office

Verification of taxpayers by the tax office whether enough taxes have been paid, while the person to be verified would prefer to avoid this.

Sociological Aspects

For Roger Caillois , uncertainty is one of the six characteristics of a game, along with voluntariness, unproductivity, limitation in space and time, rule-making and fiction. In his subsequent game typification of competition, chance, intoxication and masking, chance is assigned the unpredictability in particular: “Unpredictability means the structural characteristic of chance or luck (alea), which seems to make up the tension or can itself create such a permanent one : Whether something new succeeds or who wins this time, behaves tactically smart ... - Games seem to be infinitely repeatable because they cannot be calculated in advance and are always "different" .

Selected quotes on unpredictability

“You have to give chance its leeway, because you can never fully control it, but rather, by trying to limit it, expand your area…” Gerhard von Scharnhorst

"Happiness does not help those who do not make an effort" Leonardo da Vinci

Web links

literature

supporting documents

  1. ↑ Jörg Bewersdorff: Luck, Logic and Bluff: Mathematics in Play - Methods, Results and Limits , Wiesbaden 1998, ISBN 978-3-528-06997-1 , S. V-VIII ( Springer-Link )
  2. ↑ a b Hartmut Menzer, Ingo Althöfer: Number theory and number games: Seven selected topics , Munich 2014, ISBN 978-348672030-3 , p. 321 in the Google book search, doi : 10.1524 / 9783486720310.321
  3. ↑ Tom Verhoeff, The Mathematical Analysis of Games, Focusing on Variance ,: MaCHazine, 13 (3), March 2009. A detailed version was published in Dutch: Spelen met variantie , Pythagoras, 49 (3), January 2010, p. 20– 24.
  4. ↑ Jörg Bewersdorff: Luck, Logic and Bluff: Mathematics in Play - Methods, Results and Limits , Wiesbaden 1998, ISBN 978-3-528-06997-1 , p. VII ( Springer-Link )
  5. ↑ Dagmar de Cassan: The Book of Games 2005 ( online )
  6. ↑ Hartmut Menzer, Ingo Althöfer: Number theory and number games: Seven selected topics , Munich 2014, ISBN 978-348672030-3 , p. 322 in the Google book search, doi : 10.1524 / 9783486720310.321
  7. ^ Hugo Kastner: Learning with games: Advice for parents, educators and teachers , Hannover 2010, ISBN 978-3-86910-609-0 , p. 239 in the Google book search
  8. ↑ Nils Hesse: Win by playing: Winning strategies for the 50 most famous card, dice, board and prize games , Wiesbaden 2015, ISBN 978-3-658-04440-4 , p. X in the Google book search, doi : 10.1007 / 978-3-658-04441-1
  9. ↑ WIN, the games journal , January 2014, ISSN  0257-361X , p. 36 f. ( online )
  10. ↑ Peter-Jürgen Jost: The game theory in business administration , Stuttgart, 2001, p. 51 f.
  11. ↑ Avinash Dixit, Barry J. Nalebuff: Game Theory for Beginners. Strategic know-how for winners , Ulm 1997, p. 165 ff.
  12. ↑ Christian Rieck: Game Theory - An Introduction , Eschborn 2006, p. 95, p. 282
  13. ↑ J. v. Neumann: On the theory of parlor games , Mathematische Annalen, 100 (1928), pp. 295-320 ( Digi-Zeitschriften ).
  14. ↑ Joachim Raschke, Ralf Tils: Political Strategy: Eine Grundführung , Wiesbaden 2007, p. 77, doi : 10.1007 / 978-3-531-90410-8
  15. ↑ Joachim Raschke, Ralf Tils: Political Strategy: Eine Grundführung , Wiesbaden 2007, p. 153, doi : 10.1007 / 978-3-531-90410-8
  16. ↑ Avinash Dixit: Game Theory for Beginners. Strategic know-how for winners , Ulm 1997, p. 165
  17. ^ Hans H. Hinterhuber: Competitive Strategy , Berlin 1990, p. 82, doi : 10.1515 / 9783110854640
  18. ↑ Hans H. Hinterhuber: Competitive Strategy , Berlin 1990, p. 81, doi : 10.1515 / 9783110854640
  19. ↑ Plea for unpredictability on strike ( Memento from December 27, 2010 in the Internet Archive )
  20. ↑ Avinash Dixit: Game Theory for Beginners. Strategic know-how for winners , Ulm 1997. p. 165
  21. ↑ What is fun about the game? Future workshops annual meeting 2005 ( minutes )
  22. ↑ a b Hans H. Hinterhuber: Competitive Strategy , Berlin 1990, p. 66, doi : 10.1515 / 9783110854640