xv"Game theory has become an enormously important field of study. It is now a vital methodology
for researchers and teachers in many disciplines, including economics, political science, biology, and law. This book provides
a thorough introduction to the subject and its applications, at the intermediate level of instruction."
p.24"The most important concept in the theory of games is the notion of a strategy. The
formal definition is simple:
A strategy is a complete contingent plan for a player in the game.
... By complete contingent plan I mean a full specification of a player's behavior, which
describes the actions that the player would take at each of his possible decision points... a player's strategy describes
what he will do at each of his information sets."
p.39,40"It is important for players to think about each other's strategic choices. We use the term
belief for a player's assessment about the strategies of the others in the game... Related to a belief is the notion
of a mixed strategy. A mixed strategy for a player is the act of selecting a strategy according to a probability
distribution... If a player uses a mixed strategy and/or assigns positive probability to multiple strategies of the other
player, then this player does not expect a particular payoff for sure. We can extend the definition of a payoff function to
mixed strategies and beliefs by using the concept of expected value."
p.58"I am trying to convince you that the most substantive component of behavior is the formation
of beliefs. Indeed, herein lies the real art of game theory. Success in games often hinges on whether you understand your
opponent better than he understands you. We often speak of someone 'outfoxing' others, after all. In fact, beliefs are subject
to scientific study as well. the bulk of our work in the remainder of this text deals with determining what beliefs are rational
in games... we can continue our study of strategic behavior by placing the beliefs of players at the center of attention."
p.69"The procedure just illustrated is called iterative removal of strictly dominated strategies
(or iterated dominance, for short). We can apply the procedure to any normal-form game as follows. First, delete all of the
dominated strategies for each player, because no rational player would adopt one of them. When these strategies have been
deleted, a new 'smaller' game is formed. Then, delete strategies that are dominated in this smaller game, forming an even
smaller game on which the deletion process is repeated. Continue this process until no strategies can be deleted."
p.72"In other words, strategic uncertainty sometimes hinders attainment of an efficient outcome...
Strategic uncertainty is a part of life, but there are devices in the world that help us coordinate our behavior and avoid
inefficiency."
p.168"Players ought to demonstrate rationality whenever they are called on to make decisions. This
is called sequential rationality.
Sequential rationality: An optimal strategy for a player should maximize his or her expected payoff,
conditional on every information set at which this player has the move. That is, player i's strategy should specify
an optimal action from each of player i's information sets, even those that player i does not believe (ex
ante [JLJ - ex ante: before the event]) will be reached in the game.
If sequential rationality is common knowledge between the players (at every information set), then
each player will 'look ahead' to consider what players will do in the future in response to her move at a particular information
set."
