An Overview of Game Theory
Game theory, or decision-making under competition, has its origins and applications in economics, operations research, and psychology. Game theory revolves around social interaction – what occurs depends on what others may be willing or unwilling to do. This section explains the basics of game theory, which studies optimal decision-making in a competitive circumstance where the decisions of one individual affect the situational outcome for every stakeholder. Game theory includes four major categories: classical game theory, combinatorial game theory, dynamic game theory, and other topics in game theory. Exposure to game theory benefits leaders who use critical thinking and logic to plan and manage growing industries and businesses.
Game theory is the study of decision-making under competition. More specifically, game theory studies optimal decision-making under competition when one individual's
decisions affect the outcome of a situation for all other individuals involved. You've naturally
encountered this phenomenon in your everyday life. When you play chess or Halo, chase
your baby brother in an attempt to wrestle him into his pajamas, or even negotiate the price on a car, your decisions and the decisions of those around you will affect the quality of the end
result for everyone.
Game theory is a broad discipline within applied mathematics that influences and is influenced by operations research, economics, control theory, computer science, psychology, biology, and sociology (to name a few disciplines).
Game theory is classified into four main sub-categories of study:
(1) Classical game theory focuses on optimal play in situations where one or more
people must decide, and the impact of that decision is known. Decisions may be made using a randomizing device (like
flipping a coin). Classical game theory has helped people understand everything
from the commanders in military engagements to the behavior of the car salesman
during negotiations.
(2) Combinatorial game theory focuses on optimal play in two-player games in which
each player takes turns changing in pre-defined ways. Combinatorial game theory
does not consider games with chance (no randomness). Combinatorial game theory
is used to investigate games like chess, checkers, or go. Of all branches, combinatorial game theory is the least directly related to real-life scenarios.
(3) Dynamic game theory focuses on the analysis of games where players must
make decisions over time that will affect the outcome during the
next moment in time. Dynamic game theory often relies on differential equations to
model the behavior of players. Dynamic game theory can help optimize
the behavior of unmanned vehicles or it can help you capture your baby sister who
has escaped from her playpen.
(4) Other topics in game theory. Game theory is broad. This category
captures topics that are derivative from the three other branches. Examples
include evolutionary game theory, which tries to
model evolution as competition between species, dual games where players choose from an infinite number of strategies, but time is not a factor, and experimental game theory, where people are studied to determine how accurately
classical game theoretic models truly explain their behavior.
In these notes, we focus primarily on Classical Game Theory. This work is relatively
young (under 70 years old) and was initiated by Von Neumann and Morgenstern. Major
contributors to this field include Nash (of A Beautiful Mind fame), and several other Nobel
Laureates.
Figure 1.1 A summary of various types of Game Theory.
There are several sub-disciplines within game theory. Each one has its
own unique sets of problems and applications. We will study classical game theory,
which focuses on questions like, "What is my best decision in a given economic
scenario, where a reward function provides a way for me to understand how my
decision will impact my result." We may also investigate combinatorial game theory, which is interested in games like chess or go.
Source: Christopher Griffin, https://learn.saylor.org/pluginfile.php/33552/mod_resource/content/8/BUS403-3.1.2-GameTheoryPennStateMath486LectureNotes-cc-nc-sa3.0-pdf..pdf
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