game theory von neuman and morgenstern the theory of games3120

8/6/2019 Game Theory Von Neuman and Morgenstern the Theory of Games3120

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Game Theory Von Neuman and Morgenstern (The Theory

of Games and Economic Behavior, 1944)

Conceptual Framework

Game strategy

Components of a game


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Two Person, Zero Sum Games Each person knows own and opponents

alternatives

All preferences are known

Single period game

Sum of payoffs zero

Equilibrium reached when neither of the

participants can improve payoff


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Strategies Dominant strategy

Best regardless what others do

Maximin strategy

Choice that maximizes across the set of

minimum possible payoffs

Best of the worst


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Unstable Games

No equilibrium found

Strategy chosen leads to solution

Each player then has incentive to switch


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Two Person, Non-Zero Sum

Games The Prisoners Dilemma

Bonnie and Clyde are caught

Dilemma: Confess or not

1 period game

Non-cooperative solution: Both confess Cooperative solution: Both do not confess

Off diagonal represents double cross


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Duopoly as a Prisoners Dilemma Even if both agree to a cooperative solution,

one may double cross

Two firms: decision on amount of output

{Small or Large}

{L,L} represents normal profits


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Repeated Games

Single period game predicts competition,

but there are likely to be multiple periods.

Multiple periods allow for retribution, not

found in single period games

Duopoly as a Multiperiod Game

More likely to collude


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N-Person Games Extend to more than 2 players

Complications:

Coalitions

Cooperation and duplicity

Solutions can be difficult

Still gives insight into nature of conflict,

posturing, and resolution


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Best Pricing Practices Shift attention to tactics and strategy to

achieve competitive advantage

Examine rival firm behavior as if it were a

game

First-mover advantages

Credible threats to alter rival behavior

Stresses interdependency in oligopoly


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Business Strategy Games When rivals alter products or pricing, react

or adapt

Anticipate actions; be proactive

Sequential game--specific order of play

E.g.; One firm announces a price cut; decision

is to respond or not respond

Simultaneous game--all players choose

actions at same time


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Business Rivalry as a Sequential

Game The first to introduce a product, lower price,

etc. often achieve recognition and

advantage--first-mover advantage

When games last several periods, actions

can be rewarded or punished in subsequent

periods Entry of a new firm often discouraged by threat

of existing firms dropping prices to

unprofitable levels.


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First-Mover Games Game with military and civilian markets for

Hum Vs.


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Game Tree--Illustrating

Sequential Games Game tree is like a decision tree

Schematic diagram of decision nodes (or

focal outcomes)

Solutions parallel board games like chess

One approach to solution--end-game

reasoning--start with the final decision and

use backward induction to find the best

starting point.


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1999 South-Western College Publishing

A Credible Threat

A credible threat--an action perceived as a

possible penalty in a noncooperative game.

Its existence sometimes induces cooperativebehavior.

A credible commitment--a mechanism for

establishing trust

Such as a reward for good behavior in a

noncooperative game.


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Mechanisms for Credible Threats and

Commitments

Contractual side payments, but these may violate

antitrust laws.

Use of nonredeployable assets such as reputation.

Entering alliance relationships which may fall

apart if any party violated their commitments.

Using a "hostage mechanism--irreversible and

irrevocable can deter breaking commitments.

Examples: "double your money back

guarantees," and "most favored nation"

clauses.


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1999 South-Western College Publishing1999 South-Western College Publishing

Hostage Mechanisms in

Oligopoly

Best Buys offer: If you find a lower advertised

price, youll get the difference back

This makes Best Buy cut prices whenever local

stores cuts prices

Local stores realize they cant undercut Best Buy

Customers realize it is unlikely to find lower prices

If potential entrants think they can get a foothold in area,

they know that Best Buys pricing is a credible

commitment.


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Excess Capacity, Scale of Entry,

and Entry Deterrence Building excess capacity can deter entry.

Potential entrants know that the price can

be driven down to unprofitable levels upon entryof new firms.

The building of extra capacity is an action in a

sequential game, often with the intent of

forestalling entry. This is called a

precommitment game.


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Size Barriers

Sometimes market entry requires large scale

Incumbents may accommodate entrant,

allowing a niche

Incumbents may take entry deterring

actions, such as cutting prices at the threat

of entry


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SortingR

ules

Brand loyalty

Efficient rationing

Random rationing

Inverse intensity rationing


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Theory of Contestable Markets

High prices encourage entry

When barriers are low, even monopolist

must be careful about raising prices too

high.

Contestable markets tend to have

competitive prices and low or zeroeconomic profits

Potential entry matters more than actual

number of firms


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Simultaneous Games A sealed bid auction is a simultaneous game

A dominant strategy is the best decision, no

matter what anyone else does.

When no Nash equilibrium exists, it is

useful to hide ones strategy by randomly

changing strategies. Called a mixed Nashequilibrium strategy


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Nash Equilibrium When all players make their best reply

responses (so changing their choices cannot

improve their situation) then the game is in

Nash Equilibrium

Since game trees have several branches, we

can examine the concept in each part of thetree, called a subgame.


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Repeated Games

Escape from the prisoners dilemma

If games are repeated, there is a greater

expectation that firms will achieve a

cooperative solution

Firms signal by their behavior whether they

want to cooperate or not

Firms that expand output show that they do

not want to cooperate


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Repeated Game Strategies

Grim trigger strategy--violations never

forgotten

Alternatively, punishment can be short-lived

For multiperiod games, usually some period of

punishment that can induce cooperation

Trembling hand trigger--when slightdefections go unpunished

One non-cooperative act may be forgiven, but

not two

game theory von neuman and morgenstern the theory of games3120

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