Lecture 1. Foundations
This lecture introduces the basic elements required to formally study games. The elements
combine to form models of strategic situations. The models, when correctly designed and
analyzed, can clarify the messy complexity of most situations. On occasion, casting a
situation in the language of game theory can dramatically revise your understanding. Even
when the models do little more than formalize your intuitions, they are extremely helpful
when you attempt to talk about strategic situations with other people. For this reason, the
language of game theory is widely employed in the social sciences and elsewhere.
As will be apparent below, the value of these tools depends crucially on getting some basic
assumptions correct, and it is not always the case that these assumptions can be easily “read
from reality”, that is, based on confirmable facts about the world. What distinguishes a good
from a poor game theorist is largely how well these basic modeling choices are made. Well
chosen assumptions lead to a tractable (i.e. feasibly solvable) model that captures the
important features of the situation under study. Of course, good game theorists are also
generally skillful solvers of games, and this is sometime not easy. But many extremely useful
games are not hard to solve, once specified correctly. The worst situation is a poorly chosen
set of assumptions, analyzed wrongly. This is more common than it should be.
For now we will focus on building models of games. In the next lecture we will see how
these can be solved.
Key terms: Choice, ordinal payoff, strategy, extensive form, normal (strategic) form.
Additional key terms are noted by
1. Choice Theory
of choice links a set of choices or
to a set of
. The link may be
, where each choice leads with certainty one
particular outcome, or
, where chance intervenes to help determine the outcome.
In simple choice theory we ignore strategic considerations and assume that no other
are involved. Sometimes, however, we speak as if the element of chance
were a choice made by
, as if nature was an actor. In such cases, we assume that
nature is not motivated by any interest in the outcome.
Example: Do you have another cup of coffee? Actions: another cup, not another cup.
Consequences: if you have another cup, you have some pleasure, perhaps, and face financial,
time and possible health costs; if you don’t you forego pleasure, possibly, but avoid those
negative costs. This may be entirely deterministic, or you may believe that 15 minutes more
or less at the lunch counter in Schwab’s Pharmacy (okay, Starbucks) can change your life
forever. Similarly, you might think the correct model is stochastic if you have never had a
cup of coffee before.