Focal point (game theory)
A focal point ( Schelling point or focal equilibrium) provides in game theory is a solution, select the player if they can not communicate with each other because this solution seems to them natural or outstanding. The concept was introduced in 1960 by Nobel Prize winner Thomas Schelling in his book The Strategy of Conflict.
Introductory example
Two businessmen make an appointment over the phone that they want to meet at 12 clock in Paris. Suddenly, the connection breaks off, without being able to make a closer meeting place. Since the two were to meet exactly at 12 clock, they must now find a point at which they expect to encounter the other, because this also expected to find her there. The choice may fall, for example, the Eiffel Tower in Paris, not because it represents a better meeting place than other places, but because it stands out from many possible solutions.
The successful solution depends on how well already know the business in Paris. For someone who is better versed in Paris, the Louvre, the Arc de Triomphe and the Eiffel Tower can be three equally probable solutions.
Classification in game theory
The focal point is a coordination strategy for simultaneous, strategic games with multiple equilibrium situations (see Nash equilibrium ) and the requirement that all (or the majority ) of the players decide simultaneously for the same balance in order to win the game. In non- cooperative games, a Nash equilibrium is a stable solution, since no player has motivation to deviate the only one of the even broader balance.
Because in this game, no communication is permitted or possible among the participants, it is important to anticipate which equilibrium is assumed by all players than expected result.
The expected equilibrium, the focal point is different from all other equilibria by an outstanding property. His selection is thus likely than the selection of another equilibrium and it is therefore preferred by all players. This means that not always the best balance, but often the most striking equilibrium has the best chance.
Once a focal equilibrium is established in the game, there is no player for a better strategy than just that which leads to this equilibrium outcome.
Importance of convention and context
The selection of the focal equilibrium occurs less often according to the rules of logic as by those of the prevailing conventions and the context of the players.
The context is described by the respective personal backgrounds, experiences and imagination of all participants. The prevailing convention, ie the social and cultural norm, as relevant to the choice of the focal outcome.
If players participate with similar contexts and conventions in the game, they will also prefer a common focal point. The more diverse the backgrounds of the players, the lower the probability that they choose the same focal point.
Game theory includes cultural influences, with a few possible equilibria, often from.
Application examples for focal equilibria
Best Result
Is there in game three Nash equilibria with the amounts paid out € 30, € 20 and € 10 for each player, so all players will choose strategies without a vote to preserve the € 30. If a balance for all players brings the best result at the same time, this is automatically a focal point.
Secure result
Two players have the task to decide between three Nash equilibria with the amounts paid out € 10, € 20 and € 20. Only if they decide at the same time for the same balance, they will receive the respective payout. Without agreement, they get nothing.
The payment of € 20 is the highest result achieved for both players. However, since there are two equilibria that pay this amount, there is a risk in choosing. No player white sure which of the two equilibria will be decided by the other. This deal both, by opting for the balance with the bank € 10.
In this example, does not lead the best result, but the unique, safe result as a focal equilibrium to success.
Fair result
Two players in the same context given the task independently and without a vote split an amount of 10 € by determining their own share in the whole euro. If both play in the total yield 10 €, so the amount in the money is paid. If the sum is not 10 €, no profit is paid.
This game has eleven Nash equilibria: 0-10, 1-9, 2-8, 3-7, 4-6, 5-5, 6-4, 7-3, 8-2, 9-1, 10 - 0
Both players will engage with a high probability to a fair 50-50 strategy. This focal equilibrium also leads to a Pareto- efficient outcome.
A change in the context of the players, other results are considered fair. For example, plays a woman against a man may be, depending on the culture room, a ratio of 40:60 or 20:80 as focal establish equilibrium.
Unusual result
Each player has a group select the task from a sequence of numbers, a number of which he thinks that she gets the most votes. Typing the player correctly he receives a payout of 10 €, he is wrong, there is no gain.
Sequence of numbers: 8, 12, 11, 16, 14, 15
Many players will choose the number 8 because it is on the one hand, the first number in the sequence and also that the only single-digit number. Thus, the focal equilibrium lies in the number 8