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 going to 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 expected 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.