Game theory focuses not only on player versus player games, but instead goes beyond that to focus on larger events. Some of the situation have been covered previously including the Jamaican fishing example and in the case of war. However, sometimes the real world is not that drastic but you are still faced with a problem. The problem could be something as simple as what you should do on a given day without knowing what the weather could turn out to be. Now, it is possible to simply check ones local new change for the whether, but…whats the fun in that?
Methods:
Laplace: In a given Matrix, select the row option with the highest average entry or highest row sum.
Wald: Take the minimax of the rows, meaning to select the row with the smallest number out of the largest values of each row.
Hurwicz: Involves the use of alpha to signify the coefficient of optimism which will be a value between 0 and 1. Then use the equation,
α(row max) + (1- α)(row min). From there the largest value is selected.
Savage: The values of the matrix are subtracted from the largest number in their column then replaced by the difference. This new matrix is known as a regret matrix and the maximin is taken from the largest values in the new rows.
Why are these important? Each of the given models helps to make decisions when faced against nature. However, they each reveal something different which can help someone make the best choice based on their personal preferences. Each method offers the best of a given criteria. Laplace’s method offers the highest average payoff while Wald’s focuses instead on the certainty that the worst option won’t be awful. It is clear to see the difference in choices someone may make based on whether they are an optimist or a pessimist. This continues with the second two methods, as Hurwicz ensures the possibility for the best of the options. On the other hand, Savage’s method focuses on not having too much regret based on one’s choice. Each method is able to target a specific focus which can better appeal to someone based on their attitude and/or view of the world.
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