<p>Decision under uncertainty is sometimes called a &quot;game against chance&quot;, and can thus be modeled as a two-player normal form game: the decision-maker vs Nature/Chance. The possible states would form a set of pure strategies for Nature, and Nature commits to a publicly known mixed strategy that randomizes over those pure strategies (assume Nature is indifferent between all outcomes so that the mixed strategy is rational). The decision-maker's best response to this known mixed strategy is equivalent to the choice that maximizes his expected utility in the decision problem. In this sense, decision problems are really just a special case of a game.</p>
<p>The above suggests that your statement</p>
<blockquote>
<p>A decision problem deals with expected utility, whereas normal form games do not.</p>
</blockquote>
<p>is incorrect, since normal form games do deal with expected utility, especially when proper mixed strategies are involved.</p>

CC BY-SA 4.0
2021-03-25T05:06:56.857Z
2021-03-25T05:06:56.857Z
Herr K.
<p>I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.</p>

<game-theory><utility><definition><expected-utility><uncertainty>
Comparing & contrasting decision problems and normal games
Wivaviw
# Comparing & contrasting decision problems and normal games

(Asked by: username_0 on 2021-03-25)

I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.

**Tags:** game-theory, utility, definition, expected-utility, uncertainty

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## 1 answers

### Answer by username_1 on 2021-03-25. Score: 4

Decision under uncertainty is sometimes called a "game against chance", and can thus be modeled as a two-player normal form game: the decision-maker vs Nature/Chance. The possible states would form a set of pure strategies for Nature, and Nature commits to a publicly known mixed strategy that randomizes over those pure strategies (assume Nature is indifferent between all outcomes so that the mixed strategy is rational). The decision-maker's best response to this known mixed strategy is equivalent to the choice that maximizes his expected utility in the decision problem. In this sense, decision problems are really just a special case of a game.

The above suggests that your statement

> A decision problem deals with expected utility, whereas normal form games do not.

is incorrect, since normal form games do deal with expected utility, especially when proper mixed strategies are involved.


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