# 1-2 Self-Interested Agents and Utility Theory

0 (0 Likes / 0 Dislikes)

We will be talking about self interested agents and their interactions. So let's
first speak about what we mean by self interested agents. We don't mean
necessarily that agents are adversarial or don't care about what happened to other
agents. What we mean by that is that agents have opinions, have preferences,
and so there's some. Description of the world how the world could be, and in
different descriptions, the agents have different Preferences and different
utilities as we'll see. And so what we mean by utility function is, a
mathematical measure that tells you how much the agent likes or does not like a
given situation. It describes not only their attitude towards a definite of
events, so for example, tomorrow the temperature will be exactly 25 degrees
centigrade. But, But, in fact, it'll describe the preferences towards a, a
distribution of such, outcomes. So it really captures their, attitude towards,
uncertainty about events. So, for example, if I tell you that it will be, 25 degrees
with, probability 7.. And 24 degrees with probability.3. you might have an opinion
about how much you like that versus some other distributions. And the decision
theoretic approach which is what underlies modern game theory, says that you're gonna
try to act in the way that maximizes your expected or average utility. And so, this
is the concept we need to get comfortable with. And, and its not obvious that one
would want to use such an approach. For example we are going to look at a single
dimension, so your. Preferences will all be on a scale. As we'll see, the scale is
not that important. Unlike probability, utilities don't have to lie in the zero,
one scale. But they will lie in the linear dimension, and maybe that's inappropriate.
For example, you might have some level of wealth and some degree of health. And for
a certain level of each one, you have some. A notion of well being, but is it
appropriate to put the two together and have a single scale? You might, you might
question that. similarly, why is looking at the exp ected value when you're looking
at your uncertainty, why looking at the expected value an appropriate way to
capture your attitude? And so these are not trivial statements in fact on
topological they make a substantive claim, but there is a very long tradition and
maybe the most famous references to von Neuman named Morgenstern seminal book on,
on which is really, in some ways, the introduction to modern day game theory.
That derives the these utility functions from more basic assumptions one makes. And
we won't go into that but we just wanted to flag this issue as something that will
underlie everything we say about game theory, and which really underlays one
game theory.