Lecture 5B
Complete Information Games
This lecture analyzes complete
information games, before turning to a
discussion of Home Depot.
Imperfect monitoring
If the actions of those paid to make decisions on your
behalf are hidden from you, whether you retain them
or not cannot directly depend on what they do.
This creates a situation of moral hazard, because you
cannot directly reward them for following your
instructions.
In that case their employment contract with you
typically depends on signals that are correlated with
their behavior.
These issues are taken up in depth in 45-976:
Bargaining, Contracts and Strategic Investment.
Investment broker
This game is neither a
simultaneous move
game, nor a perfect
information game.
However the second
mover, the client, knows
more than the first
mover, her broker.
For that reason, this is
an example of a
complete information
game.
Strategic form of investment broker
The easiest way of solving this
game is to directly analyze its
strategic form.
The strategies for each player are
shown in the matrix.
To obtain the payoffs suppose, for
example, the broker chooses
“tech” and the client’s strategy is
“continue with broker”. Then the
broker’s expected compensation
is:
0.5*3 + 0.5*9 = 6
Solution to investment broker
This game is dominance solvable.
The broker should choose “tech” because it is a
dominant strategy.
The investor should use the signal she receives
about the economy, picking the strategy
“continue if new, liquidate if bubble”.
Complete information games
Games where each player knows at least as much as
everyone who has moved before him/her are called
complete information games.
Complete information games include simultaneous move
and perfect information games.
The solution to any complete information game is
typically found by decomposing it into a sequence of
solutions to smaller reduced games, and using the tools
developed for perfect information games and
simultaneous move games.
Read Chapter 11, “Complete Information Games” in
Strategic Play.
Unrest down under
Coal miners rank amongst the highest paid workers
Australia, and the media are not shy about
broadcasting this fact.
Encouraged by a conservative government, several
years ago a major coal exporter in Australia began to
negotiate with its workers individually.
In this way the exporter hoped to undermine the
power of the union representing the workers, and
ultimately reduce the miner’s wages by encouraging
entry into that profession.
Industrial Dispute
This game can be
solved by combining
the dominance
principle used in
simultaneous move
games and the roll
back rule used in
perfect information
games.
Subgame for industrial dispute
Consider what would happen if
management chose “Continue to
de-unionize”.
Having reached the second choice
node of the union, the remainder of
the game could be considered a
game in its own right.
This is why we call it a subgame.
In this case the subgame is itself a
simultaneous move game.
The reduced game
Having solved the subgame,
we now substitute its
solution into the main game,
to form a reduced game
Notice that this procedure
mimics the roll back method
we used to solve perfect
information games.
Strategic form for industrial dispute
Other Nash equilibrium in this game
There are two other Nash
equilibrium in this game, top
right and bottom left, but
both involve playing weakly
dominated strategies.
Considering the top right cell,
the union’s strategy of “go on
strike, continue with strike” is
an incredible threat to the
employer, and is dominated
by “go on strike, settle the
dispute”.
Just in time
3/20*50+17/20*50=50
3/20*2+17/20*2=2
3/20*400-17/20*60=9
3/20*248-17/20*12=27
Reduced game for component
supplier
Taking the
expected value
over the nodes
that involve nature
(and the possibility
of breakdown), we
obtain the reduced
game depicted on
the right.
Subgame for component supplier
Here we see that a
subgame begins at
the node reached by
Pratt & Whitney
choosing “Wait” and
Boeing choosing
“Wants part”.
The subgame is itself
a perfect information
game, and trivially
solved by the choice
“Make part”.
Strategic form for the reduced game
Folding the
solution of the
subgame into
the extensive
form, we see
the resulting is
a 2 by 2
simultaneous
move game
with the
strategic form
depicted.
Alliance
Strategic form of a subgame for Alliance
If GM does pursue a
formal relationship
with Hyundai, then it
would enter a
simultaneous move
subgame in which
each company
determined its effort
level informally.
The value of a formal
relationship, incurring
the costs of lawyers,
is evident.
Solution to Alliance
In the subgame
modeling an informal
alliance, both players
have a dominant
strategy of exerting
“minimal effort”.
The value of a formal
relationship, incurring
the costs of lawyers,
becomes evident.
Background to Home Depot case
Games where each player knows at least as much as
everyone who has moved before him/her are called
complete information games.
Complete information games include simultaneous move
and perfect information games.
The solution to any complete information game is found
by decomposing it into a sequence of solutions to smaller
reduced games, and using the tools developed for perfect
information games and simultaneous move games.
Read Chapter 11, “Complete Information Games” in
Strategic Play.
Who are the main players
in the Home Depot case?
Robert Nardelli, CEO of Home Depot.
Shareholders in Home Depot.
Shareholders in Lowe’s. (Note that Lowe’s
are smaller than Home Depot.)
Board of directors of Home Depot
What can they do?
Robert Nardelli, can refashion Home Depot
stores, for example orienting towards building
contractors and away from homeowners.
The Board sets CEO compensation, and his
term of office.
Shareholders in Home Depot can call for proxy
votes to change the composition of the Board.
What do they they know?
Robert Nardelli knows where his strengths
lie, and maybe able to hide his actions from
the Board, at least initially.
The Board knows the plans of Nardelli, and
is privy to early indicators of how
successful his strategy is.
Shareholders see the financial results after
the strategy has been implemented , along
with those of Lowe’s.
How do the players evaluate
the consequences?
Robert Nardelli cares about his
compensation and future job opportunities.
Shareholders in Home Depot care about
capital gains and dividends.
Shareholders in Lowe’s care about capital
gains and dividends.
Board of directors of Home Depot can be
voted in or out of office. Their networking
opportunities help shape their financial
portfolios and other lifestyle.
Home Depot in extensive form
There are several ways of reconstructing
this business scenario.
One intriguing question is whether Nardelli
could foresee the solution outcome at the
beginning of the game or not?
Lecture summary
In games of complete information where
there is more than one pure strategy
equilibrium, we showed how to extend the
roll back solution to find the solution, and
showed why some of the other Nash
equilibrium involve making threats that are
not credible.