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Summary - Game Theory Economics 318
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In-depth Summaries of the Game Theory component in Economics 318. Notes made from additional resources, class slides, lecture notes and examples.
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Introduction and TerminologyConventional microeconomics
• Price taken as given
• Individuals agents cannot influence prices
Game theory
Agents’ decisions impact on payoffs of others
Examples of Game theory
• Oligopoly pricing – not a zero-sum game
• « We can’t take this exam because we had a flat tyre».
• Note : the important element of looking ahead and reasoning backwards
• Economic policy (Central Bank vs National Treasury)
• Bribes
• Wage bargaining
• Auctions
• Insurance
• Signalling
Games of Strategy
• Most games include chance, skill, and strategy in varying proportions. Strategic thinking is
essentially about your interactions with others, as they do similar thinking at the same time
and about the same situation.
• When you think carefully before you act—when you are aware of your objectives or
preferences and of any limitations or constraints on your actions and choose your actions in
a calculated way to do the best according to your own criteria—you are said to be behaving
rationally.
• Game theory is the science of rational behaviour in interactive situations.
• Game theory provides some general principles for thinking about strategic interactions. You
may think that you have already acquired the art from your experience
• The science systematizes many general principles that are common to several contexts or
applications. The general principles of game theory provide you with a ready reference
point.
How to think about strategic games
Decisions vs Games
• When a person (or team or firm or government) decides how to act in dealings with
other people (or teams or firms or governments), there must be some cross-effect of
their actions; what one does must affect the outcome for the other.
• For the interaction to become a strategic game, however, we need something more—
namely, the participants’ mutual awareness of this cross-effect.
• What the other person does affects you; if you know this, you can react to his actions, or
take advance actions to forestall the bad effects his future actions may have on you and
to facilitate any good effects, or even take advance actions so as to alter his future
reactions to your advantage.
,• If you know that the other person knows that what you do affects him, you know that he
will be taking similar actions. And so on.
• This distinction is captured by reserving the label strategic games (or sometimes just
games, because we are not concerned with other types of games, such as those of pure
chance or pure skill) for interactions between mutually aware players and decisions for
action situations where each person can choose without concern for reaction or
response from others
• The simple rule is that unless there are two or more players, each of whom responds to
what others do (or what each thinks the others might do), it is not a game.
• Strategic games arise most prominently in head-to-head confrontations of two
participants. In contrast, interactions among a large number of participants seem less
susceptible to the issues raised by mutual awareness.
• Many situations that start out as impersonal markets with thousands of participants turn
into strategic interactions of two or just a few.
o This happens for one of two broad classes of reasons—mutual commitments or
private information.
• When each participant is significant in the interaction, either because each is a large
player to start with or because commitments or private information narrow the scope of
the relationship to a point where each is an important player within the relationship, we
must think of the interaction as a strategic game.
Sequential and Simultaneous Moves
• The distinction between sequential and simultaneous moves is important because the
two types of games require different types of interactive thinking.
• In a sequential-move game, each player must think: If I do this, how will my opponent
react? Your current move is governed by your calculation of its future consequences.
• With simultaneous moves, you have the trickier task of trying to figure out what your
opponent is going to do right now. But you must recognize that, in making his own
calculation, your opponent is also trying to figure out your current move, while at the
same time recognizing that you are doing the same with him. . . . Both of you have to
think your way out of this circle.
Players ’ Interests in Total Conflict or Some Commonality
• Where one player’s gain is the other’s loss, these situations are called zero-sum games.
The players’ interests are in complete conflict.
o Such conflict arises when players are dividing up any fixed amount of possible
gain, whether it be measured in yards, dollars, acres, or scoops of ice cream.
o Because the available gain need not always be exactly 0, the term constant-sum
game is often substituted for zero-sum game.
• Most economic and social games are not zero-sum.
o Economic activity offers scope for deals that benefit everyone.
o Joint ventures can combine the participants’ different skills and generate synergy
to produce more than the sum of what they could have produced separately.
o But the interests are not completely aligned either; the partners can cooperate
to create a larger total pie, but they will clash when it comes to deciding how to
split this pie among them.
,Is the Game Played Once or Repeatedly, and with the Same or Changing Opponents?
• A game played just once is in some respects simpler and in others more complicated
than one that includes many interactions.
• You can think about a one-shot game without worrying about its repercussions on other
games you might play in the future against the same person or against others who might
hear of your actions in this one.
• Therefore actions in one-shot games are more likely to be unscrupulous or ruthless.
• Games with ongoing relationships require the opposite considerations. You have an
opportunity to build a reputation (for toughness, fairness, honesty, reliability, and so
forth, depending on the circumstances) and to find out more about your opponent.
• A game may be zero-sum in the short run but have scope for mutual benefit in the long
run.
Do the Players Have Full or Equal Information?
• In games, the players face some limitation of information. Such limitations come in two
kinds.
• First, a player may not know all the information that is pertinent for the choice that he
has to make at every point in the game.
o This type of information problem arises because of the player’s uncertainty
about relevant variables, both internal and external to the game
• If a game has neither external nor strategic uncertainty, we say that the game is one of
perfect information; otherwise the game has imperfect information.
• Trickier strategic situations arise when one player knows more than another does; they
are called situations of incomplete or, better, asymmetric information.
• In such situations, the players’ attempts to infer, conceal, or sometimes convey their
private information become an important part of the game and the strategies.
• The general principle here is that you want to release your information selectively
o You want to reveal the good information (the kind that will draw responses from
the other players that work to your advantage) and conceal the bad (the kind
that may work to your disadvantage).
• This raises a problem. Your opponents in a strategic game are purposive, rational
players, and they know that you are, too. They will recognize your incentive to
exaggerate or even to lie.
o Therefore, they are not going to accept your unsupported declarations about
your progress or capabilities. They can be convinced only by objective evidence
or by actions that are credible proof of your information.
o Such actions on the part of the more-informed player are called signals, and
strategies that use them are called signalling.
• Conversely, the less informed party can create situations in which the more-informed
player will have to take some action that credibly reveals his information; such strategies
are called screening, and the methods they use are called screening devices.
• The word screening is used here in the sense of testing in order to sift or separate, not in
the sense of concealing.
Are the Rules of the Game Fixed or Manipulable?
• In games of business, politics, and ordinary life, the players can make their own rules to
a greater or lesser extent.
, • In such situations, the real game is the “pregame” where rules are made, and your
strategic skill must be deployed at that point.
• The actual playing out of the subsequent game can be more mechanical; you could even
delegate it to someone else.
o However, if you “sleep” through the pregame, you might find that you have lost
the game before it ever began.
• The distinction between changing rules and acting within the chosen rules will be most
important for us in our study of strategic moves, such as threats and promises.
• Often the pregame is one of incomplete or asymmetric information, requiring more
subtle strategies and occasionally resulting in some big surprises.
Are Agreements to Cooperate Enforceable?
• Agreements to cooperate can succeed if all players act immediately and in the presence
of the whole group, but agreements with such immediate implementation are quite
rare.
• More often the participants disperse after the agreement has been reached and then
take their actions in private.
• Still, if these actions are observable to the others, and a third party—for example, a
court of law—can enforce compliance, then the agreement of joint action can prevail.
• However, in many other instances individual actions are neither directly observable nor
enforceable by external forces.
• Without enforceability, agreements will stand only if it is in all participants’ individual
interests to abide by them.
• Games where agreements for joint action are not enforceable constitute a vast majority
of strategic interactions.
• Game theory uses a special terminology to capture the distinction between situations in
which agreements are enforceable and those in which they are not.
o Games in which joint-action agreements are enforceable are called cooperative
games.
o Those in which such enforcement is not possible, and individual participants
must be allowed to act in their own interests, are called non-cooperative games.
• The important distinction is that in so-called non-cooperative games, cooperation will
emerge only if it is in the participants’ separate and individual interests to continue to
take the prescribed actions.
• The terms cooperative and non-cooperative refer to the way in which actions are
implemented or enforced—collectively in the former mode and individually in the latter
—and not to the nature of the outcomes.
Terminology and Background Assumptions
Strategies
• Strategies are simply the choices available to the players, but even this basic notion
requires some further study and elaboration.
o If a game has purely simultaneous moves made only once, then each player’s
strategy is just the action taken on that single occasion.
o But if a game has sequential moves, then a player who moves later in the game
can respond to what other players have done (or what he himself has done) at
earlier points.
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