Game Theory Applications Ian Larkin Evan Rawley MBA

Game Theory & Applications Ian Larkin & Evan Rawley MBA 299: Strategy April 15 th, 2004 1

Agenda for today Hand back case write-ups Round 5 of the CSG Game theory and applications 2

Grading philosophy and approach Philosophy Approach Grades matter – I take them seriously 1 st pass to establish independent grade My strong presumption is that you will write very intelligent papers 2 nd pass to ensure rank order is right Grading is more lenient on mid-term work than on the final Final typically makes up a lot of the variability in grades 3 rd read for anyone on the margin 3

Grades 20: Outstanding 19: Very strong analysis; no major flaws 18: Very good analysis w/clear thesis; some problems 17: Good analysis overall; at least one major issue 16: Some good analysis, but at least 2 major problems <15: A few good points, but problems tend to dominate n n 10 -15% 10 -20% 25 -35% 10 -20% <10% Very good performance overall The only time a letter grade will be assigned is for your final course grade 4

Thinking ahead to the final WE NEED MORE OF: n n Establishing an organization or framework for analysis that supports a thesis Work on quant. Analysis q q n n n More of it + going deeper Better justifications for assumptions Deeper thinking about dynamics Consistent logic Clarity around predictions WE NEED LESS OF: n n n 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) 5

Agenda for today Hand back case write-ups Round 5 of the CSG Game theory and applications 6

Update on CSG n 4 rounds complete; round 5 due by Monday at noon n Round 5 is THE MOST important round of the game! n 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 7

Am I on a path to make money? n If you had done nothing, by end of Round 5 you would have had in the bank $1, 000*(1. 02)^4= $1, 082, 500 n 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 n Question: Why is this calculation simplistic? 8

You should do better in Rounds 6 -9 n n 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: q Have better information q Sent signals to competitors, q Reinvested along the way q Hopefully won’t make as many mistakes Most teams do STILL have the chance to beat “break even” which is $1, 000*(1. 02)^8= $1, 172, 000 9

Thinking about Round 6 -9 strategy If you DIDN’T make money in a market, why would you choose to rebuild your factory? q You expect fewer entrants in Round 6 (Why? ) q You expect better pricing in Rounds 6 -9, even with the same number of entrants (Why? ) q 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 q Assuming you lost money in your initial market in Rounds 15, a big part of your CSG memo needs to be why you did (or didn’t) choose to rebuild capacity for Rounds 6 -9 10

Additional thoughts n 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? n 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? 11

Agenda for today Hand back case write-ups Round 5 of the CSG Game theory and applications 12

What is game theory? n n 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: q q n Much of traditional operations management Neo-classical micro-economics Game theory is usually most applicable when there are limited numbers of players 13

Some Examples n Areas where game theory can (has) been fruitfully applied: q q q n Price competition between oligopolists Entry decisions Product differentiation and marketing decisions Areas that are not game theory q q Optimizing factory line performance Monopoly pricing (maybe)… 14

Why is game theory useful? n Provides predictions for what should happen q q q 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 15

What is a game? Four elements q Players q Payoffs (or Outcomes) q Choices q Rules Given all of this information players try to determine what their best course of action should be given: q The possible actions they can take q What they think other players will do q What their payoffs are Nash equilibrium occurs when all players have taken the previous factors into account and take their actions 16

A Simple Game: The Prisoner’s Dilemma B Confess Don’t Confess 0, 0 4, -3 -3, 4 1, 1 A Don’t Confess Players Three Key Components Outcomes Choices 17

Nash Equilibrium of the Prisoner’s Dilemma (AKA what should everyone do) Confess B Don’t Confess 0, 0 4, -3 -3, 4 1, 1 A Don’t Confess Nash Equilibrium: Given what the other guy doing, you can’t do better 18

Application of Prisoner’s Dilemma: Price War Fight B Accommodate 0, 0 4, -3 -3, 4 1, 1 A Accommodate 19

A few comments & caveats n Equilibria are not necessarily socially efficient; they are just in some sense “stable” q n Do we ever see inefficient equilibria in real life? Better outcomes for the players could be achieved through coordination and commitment q q Mergers Collusion 20

Coordination Games: Divide the Market B Segment A Segment B -1, -1 1, 3 3, 1 -1, -1 A Segment B 21

Coordination Games: Divide the Market B Segment A Segment B -1, -1 1, 3 3, 1 -1, -1 A Segment B 22

Some examples of the coordination games & prisoner’s dilemmas n Prisoner's dilemma q n Coordination games q q n Pricing decisions when there are only a few firms 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 23

What about repeated games? What happens when we play the price war game over and over again? Fight B Accommodate 0, 0 4, -3 -3, 4 1, 1 A Accommodate 24

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. . =4 1+1+1. . =n 25

Thinking about price wars n Why do price wars stop? PV (nice payoffs) > PV (bitter competition) n Why do price wars start? How do you credibly signal commitment to fight forever? n What happens if it’s not an infinite game? Would you ever cooperate? 26

Sequential games n In sequential games, players move in a predetermined order, and can observe moves of other players that happened before they move n This type of game is useful in developing predictions in situations where one firm moves first and others follow q q q Firms with a dominant player (e. g. , AB/Bud advertising) Capacity decisions (e. g. , Nutraweet) Patent games (e. g. , Pharmaceuticals) 27

Capacity Expansion and Entry is one relevant example n n n 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 28

Strategies n Incumbent: Expand capacity or not n Rival: Enter or not 29

Game Tree In Expand 1, 1 R 3, 2 Out I In Do not expand 2, 4 R Out 4, 2 30

Game is solved using Backward Induction n 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 31

What will rival do? In Expand 1, 1 R 3, 2 Out I In Do not expand 2, 4 R Out 4, 2 32

Rival’s Choice In Expand 1, 1 R 3, 2 Out I In Do not expand 2, 4 R Out 4, 2 33

What will incumbent do? In Expand 1, 1 R 3, 2 Out I In Do not expand 2, 4 R Out 4, 2 34

Incumbent’s Choice In Expand 1, 1 R 3, 2 Out I In Do not expand 2, 4 R Out 4, 2 35

Equilibrium Prediction n n 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. q By thinking dynamically, game theory allows a refinement of the typical economics monopoly prediction of MR=MC 36

Is Flexibility an Advantage? n n 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? 37

Game Tree – Rival moves first Expand In 1, 1 I 4, 2 Not expand R Expand Out 2, 3 I Not expand 2, 4 38

Backwards Induction – Rival moves first Expand In 1, 1 I 4, 2 Not expand R Expand Out 2, 3 I 2, 4 Not expand 39

Equilibrium Prediction n n 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 q n 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? 40

Defining the Rules Properly is Critical: An Example of What Can Go Wrong 1=B 2=U 3=T 4=S 5=E 5 4 Abstain 2 Abstain Don’t buy 0, 0, 0 6, 6, 6 Abstain 3 Buy 1 Join 4, 4, 0 2, 2, 2, 0, 0, 0 -10, 0, 0 What do you think happened? 41

Next time More sophisticated game theory More on repeated games Cournot vs. Stackelberg games 42