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| Utility is taken to be an absolute, accurate measurement of how desirable something is; in particular, it differs from money in three key ways. |
Utility is taken to be an absolute, accurate measurement of how desirable something is; in particular, it differs from money in three key ways. |
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First, desire for it is linear (generally in economics and game \PMlinkescapetext{theory} a person with a lot of money receives less utility from an additional \PMlinkescapetext{fixed} amount of utility than someone with very little money). |
| First, desire for it is linear (generally in economics and game \PMlinkescapetext{theory} a person with a lot of money receives less utility from an additional \PMlinkescapetext{fixed} amount of money than someone with very little money). |
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| Second, when modeling a \PMlinkescapetext{real} situation, utility should include all external \PMlinkescapetext{factors} (the happiness received from doing a good deed, for instance). |
Second, when modeling a \PMlinkescapetext{real} situation, utility should include all external \PMlinkescapetext{factors} (the happiness received from doing a good deed, for instance). |
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| Third, different people's utility is incomparable. It is meaningless to ask whether one person gets more utility from a situation than another person does. Utilities for a given person can be compared only to other utilities for that person. |
Third, different people's utility is incomparable. It is meaningless to ask whether one person gets more utility from a situation than another person does. Utilities for a given person can be compared only to other utilities for that person. |
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| A utility function is a function which specifies how much utility a player gets for a particular outcome. It maps the space $S$ of all possible strategy profiles to $\mathbb{R}$. |
A utility function is a function which specifies how much utility a player gets for a particular outcome. It maps the space $S$ of all possible strategy profiles to $\mathbb{R}$. |
