1 game theory & applications ian larkin & evan rawley mba 299: strategy april 15 th, 2004
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Game Theory & Applications
Ian Larkin & Evan Rawley
MBA 299: Strategy
April 15th, 2004
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Agenda for today
Hand back case write-ups
Round 5 of the CSG
Game theory and applications
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Grading philosophy and approach
1st pass to establish independent grade
2nd pass to ensure rank order is right
3rd read for anyone on the margin
Grades matter – I take them seriously
My strong presumption is that you will write very intelligent papers
Grading is more lenient on mid-term work than on the final
Final typically makes up a lot of the variability in grades
Philosophy Approach
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Grades20: Outstanding 10-15%19: Very strong analysis; no major flaws 10-
20%18: Very good analysis w/clear thesis; some problems 10-
20%17: Good analysis overall; at least one major issue 25-35%16: Some good analysis, but at least 2 major problems 10-
20%<15: A few good points, but problems tend to dominate
<10%
Very good performance overall The only time a letter grade will be assigned is for your final course
grade
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Thinking ahead to the finalWE NEED MORE OF: Establishing an
organization or framework for analysis that supports a thesis
Work on quant. Analysis More of it + going deeper Better justifications for
assumptions Deeper thinking about
dynamics Consistent logic Clarity around predictions
WE NEED LESS OF: Summarization of case facts Mechanical/exhaustive
application of “standard” frameworks
Bullet pointed lists Approaching it as “building a
business plan” rather than analyzing a case
Exhibits without quantitative analysis (save these for the boardroom)
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Agenda for today
Hand back case write-ups
Round 5 of the CSG
Game theory and applications
7
Update on CSG
4 rounds complete; round 5 due by Monday at noon
Round 5 is THE MOST important round of the game!
Why? You have to decide where you’re going to play in the second half, and you have MUCH more info than you did when you made your initial decision in Round 1
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Am I on a path to make money? If you had done nothing, by end of Round 5 you
would have had in the bank $1,000,000*(1.02)^4= $1,082,500
You’ll have to re-spend your capacity costs to “play” in the remaining rounds, so in order to be “on track” to make money, you should have MORE THAN
$1,082,500 – .5*(total EC spent) in the bank by the end of Round 5
Question: Why is this calculation simplistic?
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You should do better in Rounds 6-9 It’s not unexpected that few teams will have the “break
even” amount of money in the bank at the end of Round 5. Rounds 6-9 are the chance to take advantage of what you gained in the earlier rounds: Have better information Sent signals to competitors, Reinvested along the way Hopefully won’t make as many mistakes
Most teams do STILL have the chance to beat “break even” which is $1,000,000*(1.02)^8=
$1,172,000
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Thinking about Round 6-9 strategyIf you DIDN’T make money in a market, why would you choose to rebuild your factory?
You expect fewer entrants in Round 6 (Why?) You expect better pricing in Rounds 6-9, even with the same
number of entrants (Why?) You expect the Magic CSG Fairy to bless your team
Staying in a market because you’re “committed” to it is NOT a valid reason
Assuming you lost money in your initial market in Rounds 1-5, a big part of your CSG memo needs to be why you did (or didn’t) choose to rebuild capacity for Rounds 6-9
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Additional thoughts Some teams are doing very well! Can you figure
out who? What happens in the real world when there are “profit pools” out there? Does it make sense to go after them?
If you’re one of the “lucky ones,” did you capture as much value as you could have? What will you do if you are attacked?
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Agenda for today
Hand back case write-ups
Round 5 of the CSG
Game theory and applications
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What is game theory?
Game theory is about how individual decisions are made strategically by taking into consideration the actions and interests of competitors
What isn’t game theory: Much of traditional operations management Neo-classical micro-economics
Game theory is usually most applicable when there are limited numbers of players
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Some Examples
Areas where game theory can (has) been fruitfully applied: Price competition between oligopolists Entry decisions Product differentiation and marketing decisions
Areas that are not game theory Optimizing factory line performance Monopoly pricing (maybe)…
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Why is game theory useful?
Provides predictions for what should happen This means using estimates of payoffs to deduce
behavior in advance Explicitly considers what other players’ strategies
are (or are likely to be), making it a more dynamic view than traditional economics
Moves away from the world of post-modern strategy where “anything goes” and much is rationalized ex-post
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What is a game?Four elements
Players Payoffs (or Outcomes) Choices Rules
Given all of this information players try to determine what their best course of action should be given:
The possible actions they can take What they think other players will do What their payoffs are
Nash equilibrium occurs when all players have taken the previous factors into account and take their actions
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A Simple Game: The Prisoner’s Dilemma
0,0 4,-3
1,1-3,4
Confess
Don’t Confess
Confess Don’t Confess
A
B
Three Key ComponentsPlayers Outcomes Choices
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Nash Equilibrium of the Prisoner’s Dilemma (AKA what should everyone do)
0,0 4,-3
1,1-3,4
Confess
Don’t Confess
Confess Don’t Confess
A
B
Nash Equilibrium: Given what the other guy doing, you can’t do better
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Application of Prisoner’s Dilemma: Price War
0,0 4,-3
1,1-3,4
Fight
Accommodate
Fight Accommodate
A
B
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A few comments & caveats
Equilibria are not necessarily socially efficient; they are just in some sense “stable” Do we ever see inefficient equilibria in real life?
Better outcomes for the players could be achieved through coordination and commitment Mergers Collusion
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Coordination Games: Divide the Market
-1,-1 1,3
-1,-13,1
Segment A
Segment B
Segment A Segment B
A
B
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Coordination Games: Divide the Market
-1,-1 1,3
-1,-13,1
Segment A
Segment B
Segment A Segment B
A
B
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Some examples of the coordination games & prisoner’s dilemmas Prisoner's dilemma
Pricing decisions when there are only a few firms
Coordination games Timing of advertisements on TV/radio Entry into (CSG) markets
These games differ in the amount of commitment required and what communication can get you in terms of outcomes
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What about repeated games?What happens when we play the price war game over and over again?
0,0 4,-3
1,1-3,4
Fight
Accommodate
Fight Accommodate
A
B
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Equilibrium in repeated play
Consider the strategy: If you fought last round I will fight forever . . . If you accommodated in the last round I will accommodate until you fight
Assume no discounting for simplicity
4+0+0+0+0 . . . . =4
1+1+1+1+1 . . . . =n
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Thinking about price wars
Why do price wars stop?PV (nice payoffs) > PV (bitter competition)
Why do price wars start?How do you credibly signal commitment to fight forever?
What happens if it’s not an infinite game? Would you ever cooperate?
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Sequential games In sequential games, players move in a pre-
determined order, and can observe moves of other players that happened before they move
This type of game is useful in developing predictions in situations where one firm moves first and others follow Firms with a dominant player (e.g., AB/Bud advertising) Capacity decisions (e.g., Nutraweet) Patent games (e.g., Pharmaceuticals)
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Capacity Expansion and Entry is one relevant example An established manufacturer is facing
possible competition from a rival The established retailer can try to stave off
entry by engaging in a costly capacity expansion, which increases supply and lowers price charged to customers
Rival can observe whether incumbent expands capacity or not before deciding on entry
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Strategies
Incumbent: Expand capacity or not
Rival: Enter or not
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Game Tree
I
R
R
1,1
3,2
2,4
4,2
Expand
Do notexpand
In
Out
In
Out
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Game is solved using Backward Induction Look to the end of the game tree and prune
back Rationality assumption implies that players
choose the best strategy at each node There’s no incomplete information in this
game, so there’s no uncertainty in the prediction
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What will rival do?
I
R
R
1,1
3,2
2,4
4,2
Expand
Do notexpand
In
Out
In
Out
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Rival’s Choice
I
R
R
1,1
3,2
2,4
4,2
Expand
Do notexpand
In
Out
In
Out
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What will incumbent do?
I
R
R
1,1
3,2
2,4
4,2
Expand
Do notexpand
In
Out
In
Out
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Incumbent’s Choice
I
R
R
1,1
3,2
2,4
4,2
Expand
Do notexpand
In
Out
In
Out
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Equilibrium Prediction
The prediction from this model is that the incumbent will expand capacity and this will effectively forestall entry
Notice that even in absence of actual entry, the potential competition from the rival eats into the incumbent’s profits. By thinking dynamically, game theory allows a
refinement of the typical economics monopoly prediction of MR=MC
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Is Flexibility an Advantage? Preceding game assumed rival could move at
the last moment, after seeing incumbent’s decision
Suppose that the rival is less flexible in its management practices.
It must commit to enter or not before the capacity expansion decision of the incumbent.
How does this affect the outcome of the game?
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Game Tree – Rival moves first
R
I
I
1,1
4,2
2,3
2,4
In
Out
Expand
Not expand
Expand
Not expand
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Backwards Induction – Rival moves first
R
I
I
1,1
4,2
2,3
2,4
In
Out
Expand
Not expand
Expand
Not expand
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Equilibrium Prediction
The absence of flexibility on the part of the rival improves its outcome relative to the case where it retained flexibility.
This game has a first-mover advantage Sometimes “flexibility to commit” is more
important than “flexibility to wait and see” Is it always true in sequential move games
that there is a first-mover advantage?
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Defining the Rules Properly is Critical: An Example of What Can Go Wrong
Buy
Join
Join
Join
Join
Abstain
Abstain
Abstain
Abstain
Don’t buy
0,0,0,0,0
1
2
3
4
5
-10,0,0,0,0
0,0,0,0,0
2,2,2,0,0
4,4,4,4,0
6,6,6,6,61=B2=U3=T4=S5=E
What do you think happened?
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Next time
More sophisticated game theory
More on repeated games
Cournot vs. Stackelberg games