Matching pennies

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

Causes

The unpredictability of the course of the game resulted in most games from three different causes, their differentiation allows a classification of games:

• Random as dice games,
• A high number of combinations to the combine, the possible moves of the players like chess,
• Concealed information, such as due to the fact that each player knows only his own cards.

1 random

This feature is mainly caused in society by playing dice or shuffling cards and stones. The relevant section is then determined under the rules of the game both by the decisions of the players as well as by random events. Dominating the influence of chance, it is a gamble. For pure games of chance the player on participation and on the bet the decision is already the most important. Gambling, which are played in assets are traditionally subjected to legal regulations in Germany in the form of a gambling monopoly.

• Examples of pure gambling: roulette, lottery, slot machines.

2 Various combinations of possible moves

The rule of the game gives the players the possibility to operate within a clearly defined framework. The sequence of his actions, of which an individual is referred to as a train, combine to create an usually large number of move sequences, whereby the result of a match is de facto unpredictable. Games where the uncertainty solely based on this phenomenon are called combinatorial games (those games for two players are sometimes in combinatorial game theory studies ).

• Examples of combinatorial games: chess, go, mill, lady and Halma.
• Examples of games with combinatorial and random elements: backgammon and Parcheesi.

3 Different information level of the individual player

Another cause of unpredictability based on different information stands of active players as they come through cards face down, face down permanent or simultaneous moves about. Games whose uncertainty mainly originating from different information stands are called strategic games.

• Example of a purely strategic game: rock-scissors- paper
• Games in which the players have different information stands: Poker, Bridge, speculation on the stock market, Sports Toto.

Mathematical approaches

By means of mathematics is an attempt to overcome the unpredictability in games to a certain extent. We are looking for best practices for the players. Depending on the cause of the unpredictability of the methods in question belong to different disciplines of mathematics and computer science:

• Probability,
• Combinatorial game theory and artificial intelligence (eg concerning Computer Chess )
• Game theory.

Basis of game theory studies is a formal model for games, under which strategies are investigated.

Example: Heads or Tails ( Matching Pennies )

Two players choose independently the side of a coin to be thrown, that is, either head ( K) or number (Z ). The first player wins a € if compliance is achieved. If different results are obtained, the second player wins one euro. In order not ( predictable ) to make the strategic behavior predict a player between the given alternatives should randomly select and thus use a so-called mixed strategy.

Notes:

• N = {Player 1 Player 2 }
• Possible strategy S1: Head
• Strategy spaces S1 = S2 = { head, number }
• Possible Profile: s = (number, number )
• Set of all strategy profiles: S = {( head count); (head, head); (number, head); (number, number ) }

Mathematical game theory

In their game theory book Dixit and Nalebuff explain in a chapter titled with Unberechbarkeit mixed strategies in games. A mixed strategy is a random sample with a specified probability distribution at the beginning of the game, with a full player's action plan " diced ", the possibly upcoming decision situation involves a decision for each in the game. So the unpredictability results in this case is not in the game, but on the possibly motivated by the play behaviors of the corresponding active players.

In a two -person zero- sum game, which is characterized in that the one player's gain is always equal to the loss of its counterparties exists based on mixed strategies always a balance with a clearly defined game result (Min -Max theorem). Such minimax strategies are computable in principle with linear optimization processes. For games with more than two persons or without zero-sum character of two-person games there may be multiple equilibria with different play results give (so-called Nash equilibria ).

Economic Applications of Game Theory

The real focus of game-theoretic investigations is not the behavior of optimization in games. So already formulated in 1928 the founder of game theory John von Neumann: " ... there is hardly a question of daily life, in the not played into this problem. "

However, the practical relevance of game theory to political experts like Joachim Raschke and Ralf Tils due to their will " realistätsfernen reductionism " denied: " Game theory remains - except in border areas - consequences for practice. ". Observed by the authors to unpredictability to their non- game theoretical view plane: "False is the assumption fundamental unpredictability - then would it be possible strategy. There are degrees of predictability. Strategy is unpredictable, ever greater scope allows an institution ... strategy refers to the predictable external dimensions Akteuere. You can ... anticipate possible enemy behavior and build up reserves for this reaction. "

In general, it is advantageous vorzuaussagen the unpredictability of the counterparty properly and to act accordingly. The unpredictability is a crucial part of the strategy, if one of the players wants a simultaneous approach and the other players that would rather avoid.

This unpredictability is an indispensable part of reality, and thus forms a point of entrepreneurship, there is no adverse part, must be what eliminated by the plan and acting people, he must be able to deal with it and pull the corresponding value for themselves.

• Example 1: unpredictability during strike

Within a strike by employees of the garbage disposal had to strike a new strategy should be developed, because until then six-week strike led to no result, and the participants vorwiesen first signs of fatigue. The strike strategy had to be changed so that it was not foreseeable for the opposite side, that is unpredictable. It was agreed to strike meetings on a resume amended strike activity. It was agreed as to develop a strategy that would make it difficult for the employer to use a private waste collection contractor. The strike tactic looked about to let by way of concerted agreement the employer in the dark when there is a strike and for how long. The workers were taken by surprise and literally could not react in time to the ever- moving situation. The change in unpredictable strike strategy was successful.

• Example 2: Tax Office

Review of taxpayers by the tax office if enough taxes have been paid, while the verifier would prefer to avoid this.

Sociological aspects

For Roger Caillois is the uncertainty in addition to voluntary, non-productivity, limitations in space and time, usually determination and fictitiousness one of the six characteristics of a game. In his building upon game typing in competition, chance, and noise masking is particularly randomly assigned to the unpredictability of " unpredictability means the structural feature of chance or luck ( alea ), which seems to make particularly the tension or even such can produce a permanent Whether something new succeed or who wins this time, behave tactically ... - This game appears to be infinitely repeatable, since they can not be calculated in advance and always "different" ".

Selected Quotations on the unpredictability

"You have to leave to chance his room, because you can never quite mastered it, but by seeking to restrict him, his territory rather extended ... " Gerhard von Scharnhorst

"Happiness does not help those who do not exerts himself " Leonardo da Vinci