Game Theory & Applications

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

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

Grading philosophy and approach Philosophy 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

Grades 20: 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

Thinking ahead to the final 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) WE 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

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

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?

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

Thinking about Round 6-9 strategy If 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

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?

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

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)…

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

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

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

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

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

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

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

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

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

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

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?

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)

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

Strategies • Incumbent: Expand capacity or not • Rival: Enter or not

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

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

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

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

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

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

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

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?

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

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

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?

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

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

Game Theory & Applications