bsp1005 lecture notes 10 - game theory ii- strategic thinking in dynamic games

1Lecture Notes 10

GAME THEORY AND STRATEGIC THINKING II:

Game Theory in Dynamic Settings and

Strategic Moves

Semester II, AY2013-2014NUS Business School

BSP1005 Managerial Economics

By Jo Seung-Gyu

Outline

Introduction: Sequential Games Equilibrium Concepts

Backward Induction/Subgame Perfection Centipede Game 21 flags from Survivor?

Strategic Moves Credibility and Importance of Commitment Chicken Game and Strategic Moves Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence Strategic Trade Policy in Air War between Airbus

and Boeing Repeated Games and Folk Theorems

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sequential game Game in which players move in turn,responding to each others actions and reactions.

Introduction

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We now extend our analysis to include dynamic features of the strategic decision.

Example:

You are one of a few global chipmakers competing for market shares. You threaten your rivals:

I am going to double my supply, so youd better reduce yours!

- Would they listen to you?- How would you make your threat credible?

To formalize such situations, we need to model a game in a sequential way and incorporate the following factors:

- Different timing in moves- Thinking out how your rival will react to your actions- How to manipulate your rivals choice to your favor

Introduction-cont

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Sequential (or Extensive Form) Games: Dynamic Games

Sequential games or extensive form games are useful when players move sequentially or a player moves multiple times.

Extensive form games are represented through a game tree as the following examples illustrate:

EXAMPLE : HIJACKING GAME Payoffs are (Pilots, Hijackers) (- , - ) Explode HIJACKER Schiphol Give In PILOT Cuba (1 million, - 100) (- 100, 1 million)

5Outline


Backward Induction/SubgamePerfection

Centipede Game 21 flags from Survivor?

Strategic Moves Credibility and Importance of Commitment Chicken Game and Strategic Moves Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence Strategic Trade Policy in Airwar between

Airbus and Boeing Repeated Games and Folk Theorems

Equilibrium Concepts in Sequential Games

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Nash Equilibrium?

Nash equilibrium concept is still valid in extensive form games.

However, in many instances, Nash equilibrium is not unique.

If we are trying to predict as accurately as possible how the players will behave, we will need a new equilibrium selection mechanism for the most reasonable one among the multiple Nash equilibriums.

Equilibrium Concepts in Sequential Games

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(- , - ) Explode HIJACKER Schiphol Give In PILOT Cuba (100, - 50) (- 100, 10 million)

(You had better see the game in a strategic form always to solve for Nash equilibrium):

Two Nash equilibriums: (Schiphol, Give In) and (Cuba, Explode).

(Cuba, Explode) is a poor predictor of how the players behave since it incorporates a non-credible threat of Hijacker.

Pilots choice of Cuba is justifiable only when the airplane is to be exploded if Pilot dares to head to Schiphol. But Give In is in Hijackers best interest in this case. That is, Hijackers threat to explode is simply not credible. Knowing this, with mutual rationality assumed, Pilot will head to Schiphol. And then Hijacker Gives in.

In conclusion, (Schiphol, Give in) makes more sense than (Cuba, Explode).

HIJACKER Explode Give In Schiphol (- , - ) (100, - 50 ) PILOT Cuba ( -100, 10 m) ( -100, 10 m)

Backward Induction and Subgame Perfect Nash Equilibrium

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(Schiphol, Give in) can be selected when we start from the Hijackers decision node and move backward to Pilots decision node.

Play forward but think backward!

Backward induction is about ruling out the actions that players would not play if they were actually given a chance to choose.

- This is how backward induction rules out non-credible threats/promises, thereby eliminating bad Nash equilibrium.

Many refinements usually extremely complicated both conceptually and technically of Nashs concept exist in the game theory literature and each one has its own contribution both theoretically and practically

Among others, backward induction was the most important refinement of the Nash equilibrium

(- , - ) Explode HIJACKER Schiphol Give In PILOT Cuba (100, - 50) (- 100, 10 million)

Backward Induction and Subgame Perfect Nash Equilibrilum cont.

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In applying the backward induction principle to dynamic games, we start with the last period first and work backwards through successive nodes until we reach the beginning of the game.

What if the game doesnt have the end?

Professor Reinhard Selten formalized this idea by inventing the concept of a subgame and the solution concept called subgame perfection, which can be applied to a game of infinite horizon as well. This contribution awarded him the Nobel Prize in Economics in 1994 together with John Nash and John Harsanyi.

Subgame Perfection requires players rationality at all subgames.

Simply describing, subgame perfection is similar to backward induction, extending the sequential rationality to infinite games.

Note that all subgame perfect equilibrium is a Nash equilibrium but the reverse is not true

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Outline


Backward Induction/Subgame Perfection

Centipede Game 21 flags from Survivor?

Strategic Moves Credibility and Importance of Commitment Chicken Game and Strategic Moves Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence Strategic Trade Policy in Airwar between


Experiment: Centipede Game

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Rosenthal (1981, Journal of Mathematical Psychology),

= As moves = Bs moves Payoffs: (As, Bs)

How would you play the game if you were A? How about B?

R R R R R R (8,6) D D D D D D (2, 0) (1, 3) (4, 2) (3, 5) (6, 4) (5, 7)

Centipede Game cont.

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Remarks on Centipede Game:. Sophisticated thinkers (like chess grandmasters) took the down step

in the first round.

But at the same time, experiments show that people actually chose R many times rather than D.

- Altruistic?

- Reputation-building incentive?

- Irrationality or calculation errors (a players own irrationality and a players expectation on the opponents irrationality)

- A repeated play of the game can unravel the situation, making a cooperative outcome evolve. (This result is known as folk theorem.)

Experiment: 21 Flags in Survivor

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Outline



Strategic Moves Credibility and Importance of

Commitment Chicken Game and Strategic Moves Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence Strategic Trade Policy in Airwar between


STRATEGIC MOVES

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Credibility and Importance of Commitment

You often want to influence threat or promise your competitors choice in a manner favorable to yourself.

But talk is cheap! Just telling that you are going to act in this or that way wont work if your threat or promise is non-credible (i.e. empty).

A strategic move refers to an action in game theory that influences other players expectations about how you will behave.

It involves a commitment from the player and the commitment has to be credible, meaning that once employed it must be in the interest of the player to follow through with the move.

Such concept was first introduced by Thomas Schelling, one of the two Nobel Prize laureates in Economics in 2005.

STRATEGIC MOVES cont.

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How did Wal-Mart Stores succeed where others failed? The key was Wal-Marts expansion strategy. To charge less than ordinary department stores and small retail stores, discount stores rely on size, no frills, and high inventory turnover.

Through the 1960s, the conventional wisdom held that a discount store could succeed only in a city with a population of 100,000 or more. Sam Walton disagreed and decided to open his stores in small Southwestern towns.

The stores succeeded because Wal-Mart had created 30 local monopolies. Discount stores that had opened in larger towns and cities were competing with other discount stores, which drove down prices and profit margins. These small towns, however, had room for only one discount operation. There are a lot of small towns in the United States, so the issue became who would get to each town first. Wal-Mart now found itself in a preemption game of the sort illustrated by the payoff matrix below.

WAL-MART STORES PREEMPTIVE INVESTMENT STRATEGY

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Jo Brothers

Enter Dont enter

Wal-MartEnter 10 , 10 20, 0Dont enter 0, 20 0, 0

WAL-MART STORES PREEMPTIVE INVESTMENT STRATEGY-cont.

This game has two Nash equilibria: (0, 20) and (20, 0)

Which equilibrium results depends on who moves first.

The trick, therefore, is to preempt - to set up stores in other small towns quickly, before Company Jo Brothers can do so: (20,0) is the only Subgame Perfect Nash equilibrium.

That is exactly what Wal-Mart did. By 1986, it had 1009 stores in operation and was earning an annual profit of $450 million. And while other discount chains were going under, Wal-Mart continued to grow. By 1999, Wal-Mart had become the worlds largest retailer, with 2454 stores in the United States and another 729 stores in the rest of the world, and had annual sales of $138 billion.

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Outline




Commitment

Chicken Game and Strategic Moves

Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence Strategic Trade Policy in Airwar between


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GAME OF CHICKEN AND STRATEGIC MOVES

Game of ChickenTwo players (say, teenage boys) decide to settle a dispute (over a girl) by way of near-death experiences. Each speeds an automobile towards a cliff (or at each other, in later adaptations).

A simple rule governs the challenge: the first to jump out of his automobile is the chicken and, by universally accepted social convention, concedes the object in dispute. The second to jump is victorious, and, depending on context, becomes the winner (gang leader or prom king etc).

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Not only boys play the game. Check out the girls real story below. In their case, even the winners lose. (Winners Curse)

Teens Run Over During Game of 'Chicken' (The Lufkin Daily News, October 12, 2005)

HUDSON, Texas Two Hudson girls, age 13 and 14, were attending a slumber party Friday night at a house along state Highway 103 west of Hudson when they decided to lie in the road. The two were the first girls to play the game, lying along the center stripe on the highway 103, according to another family member, who asked not to be identified. Just before 9 p.m., a dark-colored SUV with chrome wheels passed, running over both girls. The girls remained in Lufkin hospitals Tuesday, one suffering internal injuries, the other having a broken collarbone and several lost teeth, Bass said. Updated information on the girls' conditions was not available. State police are withholding the girls' names because they are juveniles.

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Chicken Game in Broadway Musical

Recall a scene from West Side Story, in which two gangsters are to race their cars toward each other and the first one to chicken out loses. Lets assign numerical payoffs as below:

Gang B Straight Swerve

Straight (-100, -100) (10, -2) Gang A

Swerve (-2, 10) (0,0)

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Chicken Game in West Side Story cont.

How many (pure strategy) Nash equilibriums do we have here?- We have two Nash equilibriums, in which one player swerves

and the other doesn't (lower left and upper right).

What actually happens when this game is played? - It is hard to say. Under Nash theory, either of the two equilibrium

points is an equally rational outcome.


Straight (-100, -100) (10, -2) Gang A

Swerve (-2, 10) (0,0)

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Chicken Game in Broadway Musical cont.

What can you do to win?

(i) Create your own fog.

Put a weirdo in the driver seat than a smart member(The key is randomizing your behavior so that your rivals cannot outguess yourself.)

An irrational rationally irrational player has the upper hand in chicken game.


Straight (-100, -100) (10, - 2) Gang A Swerve (- 2, 10) (0,0)

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(ii) Reduce temptation

Life as a chicken is like no life(The key is reducing your own payoff from the options you might be tempted to.)


Straight (-100, -100) (10, -2) Gang A Swerve (-101, 10) (0,0)



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(iii) Add carrots to the options you want to be committed to

Ill die for the honor of my family.(The key is increasing your own incentive to play the options you want to be committed to.)

Example: Put a suicidal guy in the driver seat. Gang B Straight Swerve




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(iV) Remove your own options you might be tempted to play

Tie up your steering wheel.(The key is getting rid of the options you might be tempted to play.)

More options are not necessarily better. Fewer options might be better sometimes.




Gang A Straight ( -100 -100) (10, - 2)

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Chicken Game in Film: Rebel Without a CauseThe game of chicken has been featured in many films.

Remember Jimmie (acted by James Dean) and Buzz in Rebel Without A Cause? Probably it has set the standard. (http://www.youtube.com/watch?v=u7hZ9jKrwvo)

Jimmie (James Dean), to settle a dispute with Buzz, the leader of a local gang, agrees to a "Chickie Run." Both race stolen cars towards the edge of a cliff. The first to eject out of his car is branded a "chickie."

Seconds into the race, Buzz discovers that his jacket is stuck on the door handle, making jumping out of the car somewhat difficult. Jimmie jumps out an instant before the cars reach the edge of the cliff.

Buzz, still unable to free his jacket from the door handle, fails to escape. While he won't be branded a "chickie," he suffers a worse fate.

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A Textbook Example: Production Choice Problem

Race Car MotorsSmall cars Big Cars

Far Out Engines

Small engines 3, 6 3, 0

Big engines 1, 1 8, 3

Two Nash equilibriums if simultaneous game: (Small, Small) and (Big, Big).

If Race Car moves first: (Small, Small).

What can Far Out do then?

o threat to produce Big Engines but it is non-credible

o Thus, need to make its threats credible. Example: destroying (shutting down) small engine production capacity

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Outline



Strategic Moves Credibility and Importance of Commitment Chicken Game and Strategic Moves

Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence Strategic Trade Policy in Airwar between Airbus and

Boeing Repeated Games and Folk Theorems

Brinkmanship as a Commitment

Examples: During the Cold War, the threat of nuclear

force was often used as a measure. Creating powerful nuclear weapons is more efficient in avoiding nuclear war than destroying them. (Kim Jeong Eun from North Korea is the real example.)

Burning ships when Spanish ConquistadorHernando Corts attacked the Aztec Empire in 16th century. (Note: Sometimes you need to build bridges for the enemies to retreat.)

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Brinkmanship is the maneuver of pushing a situation to the verge of disaster brink, as the term reads in order to achieve the most advantageous outcome. This might be achieved by creating the impression in rivals mind that one is willing to use extreme methods rather than concede, thereby forcing the rival to back down and make concessions

Examples of Brinkmanship - cont

Canals surrounding the European fortress

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Doomsday Machine in Kubricks movie Dr. Strangelove.

- The Russians sought to deter American attack by building a "Doomsday Machine," a device that would trigger world annihilation if Russia was hit by nuclear weapons.

Dr. Strangelove says, Deterrence is the art of producing in the mind of the enemy the fear to attack.)

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Outline



Strategic Moves Credibility and Importance of Commitment Chicken Game and Strategic Moves Brinkmanship as a Commitment

Extra Capacity as an Entry Deterrence

Strategic Trade Policy in Airwar between Airbus and Boeing

Repeated Games and Folk Theorems

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STRATEGIC MOVE IN ENTRY-DETERRENCE

Extra Capacity as a Entry Deterrence(Avinash Dixit, The role of investment in Entry Deterrence, The Economic Journal 90)

Consider a pricing game for the Incumbent facing a potential entrant. Entrant decides first and Incumbent decides later, but the latter can behave strategically to deter the entry.

Potential Entrant

Enter Stay out

IncumbentHigh price (accommodation) 100, 20 200, 0Low price (warfare) 70, 10 130, 0

Incumbent has a dominant strategy of high price. But if the incumbent follows its dominant strategy, then entrant will enter (because 20 >

0) with the outcome of (100, 200). But incumbent wants to (200, 0).

A simple threat of I will charge low if you enter will not work. It is an empty threat. Incumbent needs to introduce a self-constraining idea to manipulate Entrants decision

to incumbents own favor. Lets consider some options below:

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Extra Capacity as a Entry Deterrence cont.

Potential Entrant

Enter Stay out

IncumbentHigh price (accommodation) 100, 20 200, 0Low price (warfare) 70, 10 130, 0

Strategy 1: Side Payment

What if the incumbent pays the entrant 20 (the most it could earn if it entered) to stay out and make 180 for itself? Not a bad idea, but illegal.

Strategy 2: Merge?.What about a merge with the potential entrant? This is truly an option yet all the relevant costs and benefits will have to be considered. (Its a shame that we dont have time for the economics of M & A.) Plus, it might be illegal again because of its anti-competitive effects

Strategy 3: Build a Reputation

We already have seen a case for the incentive to brink. Building a reputation for being irrational may be another strategy by which you can manipulate rivals choices to your advantage. (Let them believe you can do any crazy thing.)

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Strategy 4: How about making an irrevocable commitment that will force you to charge Low Price in case entry occurs?

Suppose that the incumbent makes a capacity investment - like extra production facility etc of, say, $50.

This will lower the profit in the High Price situation since at high price the sales is low and the new capacity investment is just waste of money.

But at the Low Price choice, the extra capacity becomes useful giving you a marginal cost advantage over the entrant and helps to shift profits away from the entrant. You can increase your profits while Entrants may lose more.

Potential Entrant Enter Stay Out High Price (10050=)50, 20 (20050=)150, 0 (Accommodation) Incumbent Low Price (7050+60=)80, 20 (13050+50=)130, 0 (Warfare)

Entrant stays out. The equilibrium is (150, 0).

Note that the extra capacity is solely for a strategic move and is going to be idled at the equilibrium.

Sometimes you want to constrain yourself to win.

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Real Life Application?

Chicken Game in Semiconductor Rivalry and Capacity Commitment

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Outline



Strategic Moves Credibility and Importance of Commitment Chicken Game and Strategic Moves Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence

Strategic Trade Policy in Air War between Airbus and Boeing


STRATEGIC TRADE POLICY(Air War between Airbus and Boeing)

Background: LCA industry is under significant economy of scale and large scale of

production is critical for survival as well as profitability. US enjoyed de facto monopoly in the LCA industry until 1970s. The Airbus

consortium created in 1969 and started competing effectively in the 1980s. US concerned about the alleged subsidies by European govts

Europe concerned about indirect subsidies through NASA and US defense programs

Mutually fatal damage was forthcoming without a coordination, leading to rounds of trade negotiations.

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In late 1970s and early 1980s, (American) Boeing and (European consortium based) Airbus were each considering developing a new aircraft. The situation can be simplified as below, in which the typical Chicken Game situation emerges

Now, what if Airbus is subsidized?

It shows how strategic trade policy can transfer profits from foreign country to home.

Air War- continued

Airbus Produce Dont Produce Produce -10, -10 100, 0 Boeing Dont Produce 0, 100 0, 0

Airbus Produce Dont Produce Produce -10, 10 100, 0 Boeing Dont Produce 0, 120 0, 0

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But retaliation is likely: If mutual subsidization:

Prisoners Dilemma again.o Mutually destructive trade was is likely, leading all countries to be worse off. o Implication: Both produce but subsidy expenditure may outweigh profits.

How to get out of the dilemma then?

o Its a cooperative game: Trade negotiations Bilateral agreement under Uruguay round 1992 government support is

limited

Multilateral level agreement associated with the Uruguay failed and remains under 1979 Tokyo GATT round context.

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Airbus Produce Dont Produce Produce 10, 10 120, 0 Boeing Dont Produce 0, 120 0, 0

Air War- continued

Real feature?

The United States initiated WTO dispute procedures then about subsidies to the European aircraft industry. In response, the EU launched similar proceedings against the US criticizing NASAs subtle procurement practice etc.

New 3-4 new players are expected in the next decade (such as Commercial Aircraft Corporation of China Ltd), and the game is to be more complicated.

(For a recent update: http://www.dw-world.de/dw/article/0,,6140280,00.html)

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Air War- continued

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Outline




Commitment Chicken Game and Strategic Moves Brinkmanship as a Commitment Extra Capacity as an Entry Deterrence Strategic Trade Policy in Airwar between

Airbus and Boeing


Consider the above pricing game: the inability to reach a cooperative agreement leads to a second-best outcome of (10,. 10).

What if the firms are interacting more than once? We call this a repeated game.

- If games are to be played many times, cooperative behavior may be fostered even if firms are competing in a non-cooperative way, leading to the cooperative outcome of (50, 50).

- The result is knows as Folk Theorems.

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REPEATED GAMES AND FOLK THEOREMFirm 2

Low price High price

Firm 1Low price 10, 10 100, 50High price 50, 100 50, 50

Folk Theorem

A cooperative outcome can be sustained as a subgame perfect Nash equilibrium of a repeated game usually infinitely repeated. (Such result may hold for a finitely repeated game as well, if rarely.)

(It has got its name of folk theorem because the result is fairly obvious common sense. Formal statements and proofs can be quite complex, but the intuition is clear and obvious; cooperation of a given sort is to help together by a threat to punish those who transgress. As long as the future looms large relative to the present time, such threatened punishments are effective. Because this result is something that game theorists feel they knew all along, it is part of the folk wisdom of the subject.

No one was brash enough to claim authorship of the general idea.)

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REPEATED GAMES AND FOLK THEOREM-cont.

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CONCLUDING REMARKS AND MANGERIAL IMPLICATIONS

The best way to learn how to use game theory as a management tool is to practice. Here is a seven step guide to using game theory in settings.

STEP 1: Calculate your profit as a function of what the other player(s) might doYou = f(Others Actions)

STEP 2: From your best guesses about your competitors demand and cost curves, calculate her profits as a function of what you might do

Opponent = g(Your Actions)STEP 3: Ask the question: Can we legally cooperate? Ask your lawyers; can we write a legally binding agreement to any deals we might do? If the answer is yes, then you want to make use of cooperative game theory. That is the theory of bargaining and negotiationsthat is trying to write mutually advantageous contracts. If the answer is no, then you want to make use of non-cooperative game theory. That is, the stuff we have been discussing in the last few game theory lectures.

STEP 4: Create the games payoffs in a form that helps you to understand the strategic interactions.(Normal form or Extensive form)

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CONCLUDING REMARKS AND MANGERIAL IMPLICATIONS - cont.

STEP 5: Can you recognize your game? Now you must pick your strategies. (Nash, Dominance, Maximin, Subgame Perfection, Repeated Interaction etc)

STEP 6: Can you change the game? To commit or not to commit? (Strategic Moves)

STEP 7: Make your moves: be cool!

Remember, if you get killed you still did the best you could, given the information you had. Being good at game theory doesnt guarantee you will make money, prevent a nuclear attack, or win at poker on Friday nights. You still need a good product and good information about your firm and your competitors demands and costs. But game theory will help you get the most of what are available.

Puzzle: How good is your game theoretic imagination?

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bsp1005 lecture notes 10 - game theory ii- strategic thinking in dynamic games

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