Introduction to Game Theory and Strategic Interactions

Introduction to Game Theory andIntroduction to Game Theory andStrategic InteractionsStrategic Interactions

• With extreme market structures, no need to consider rival actions:– Monopoly: no rivals– Perfect competition

• Intermediate case: Oligopoly or concentrated industry– Need to consider rivals’ reactions– Impossible to fully control your own destiny

• Can be at competitor’s mercy no matter how good you are– Can the current environment be made more attractive?

• If the rules of the game change, the outcome can also change(i.e. the structure of competition may not be fixed)

Market Structure and Competition

• Game Theory:– Formal study of strategic behavior, relation between interdependent agents (firms, trade authorities, armies, litigation, athletes, nuclear deterrence between countries,…)

– Teaches us how to think about strategic interactions

– Rivalry/cooperation, commitment, investment, signaling• Provides insight into effect of changing/choosing the game

– Is the only formal tool for analyzing strategic interactions• Requires explicit assumptions about timing and payoffs • Provides predictions about behavior under full rationality

What is Game Theory?

• Anticipate actions and reactions– Must analyze competitors’ situation carefully

• i.e., put yourself in their shoes

– Must consider whether they are going through the same process

• acting rational• determining the likely payoff structure

– When these things hold, game theory can predict the likely responses to various strategies

Important Principle: Anticipation

• Direct applicability for business strategic decision-making limited by strong rationality assumptions

– Sometimes people behave irrationally• Perhaps they do not think through their problem• Their objectives may not be profit maximization

– However, rationality can be achieved by being empirically attentive

• People may not solve complex optimization problems but use heuristics that they update every so often.• More successful agents are selected by markets

– survivor explanation

– Can be sensitive to information and timing structure

– Small change may make big difference

– Often there is not a unique answer

WARNING:WARNING: Exercise Caution with Game Theory in Business Situations

• Use game theory to think about strategic interactions on a broad level

– Get insight into strategic interaction• Explains many real world observations that cannot otherwise be rationalized (e.g. both competitors would rather not be undertaking their actions, but cannot help themselves)

– Get insight into effect of changing the game

• Adopt strategies that account for anticipated responses when maximizing value

– Can you induce rivals to take actions beneficial to you?– Can you change the game in a favorable way?– If game is good now, can you prevent it from getting bad?

• Problems of technological innovation, mobile strategic assets

Applicability to Business Situations

– You are managing a line of fashion garment and it is the end of the season

• Should I discount to liquidate stock?

– Decision: start discounting now or wait?

– Setup• You face one competitor in exactly same situation you are in.

– Fashion Sensitive customers buy only the items they like• 2m additional profits from fashion customers if you keep prices high• 1m if you discount now.

– Bargain Hunters buy any discounted item.• Split 2m if both discount now or both wait• 4m profits if you discount and competitor waits,• 0m profits if competitor discounts and you wait

Fashion Pricing: Example of Strategic Interaction

What is a game?– Players (e.g. Store 1 and Store 2)– Rules (e.g. simultaneously choose whether to start discounting)– Strategies (Discount or wait)– Payoffs (Profits from strategy)

• Convention has payoffs written as (Player on left, Player on top)

Game: A Model of Strategic Interactions

Fashion Pricing Game: Formal Approach To Analysis

Suppose Store 2 waits, what should 1 do?Suppose Store 2 discounts, what should 1 do?


Suppose Store 1 waits, what should 2 do?Suppose Store 1 discounts, what should 2 do?


Dominant strategy for both players is Discount.(Nash) Equilibrium is Discount/Discount.

• Idea: If the payoff for me under one action is highest for all possible actions of my opponent, then this highest payoff strategy is called a dominant strategy

• Discounting is the dominant strategy in this game for both players

• How to approach a game:-- if you have a dominant strategy, use it-- if there is a dominated strategy ignore it

Dominant Strategies

Nash Equilibrium: Concept of a “Reasonable” Outcome

Definition: Given what other players are doing, no player would want to change strategy unilaterally (i.e. each player’s strategy is an optimal response to the other players’ strategies)

No Dominant Strategy but, Multiple Nash Equilibria

Sometimes no solution (i.e. no Nash Equilibrium)

• Avoid thinking only in terms of ‘how does this move affect me’ (direct effects)

– Need to consider strategic effects:• How does this move affect me through the impact on the game and on the other players?

– Can I change the game in a favorable way?

Thinking Strategically

Strategic CommitmentStrategic Commitment• Strategic commitments are decisions that have long run

impact and are hard to reverse (Example: Installation of additional production capacity)

• These differ from tactical moves which are easy to reverse and have only a short run impact (Example: A store cutting the price on certain items)

• To achieve the desired result, the commitment should be– Visible– Understandable– Credible

• To be credible, the commitment should be irreversible

Two Effects of Commitments

• A commitment may have a direct and a strategic effect on the firm’s profitability

– Direct effect is the change in the present value of profits assuming that the rival’s tactics are unaffected by the commitment

– The strategic effect is the further change in the present value of the firm’s profits due to the rival adjusting its tactics

Credible CommitmentsCredible CommitmentsStrategic moves signal competitors about behavior.

Moves must be meaningful, not seen as random.

ExampleExample: Wal-Mart opens stores in small towns that can only support one store. If Wal-Mart enters first, other firm will not, but Wal-Mart will enter regardless of its competitor, to show commitment even if it means taking a lose.

-- Action -- Enter Don’t Enter

Enter -10, -10 20, 0

Don’t Enter 0, 20 0, 0Wal-Mart

Wal-Mart Competitor

Politics Intrudes

-- Action -- Produce Don’t Produce

Produce -10, -10 100, 0

Don’t Produce 0, 100 0, 0Boeing

Airbus

Governments often engage in strategic behavior to try to create an advantage over competitors, such as by giving a subsidy to domestic producer.

Suppose the market for a new model of aircraft is expected to support only one maker—Boeing or Airbus—but not both. If both produce the aircraft, both will lose money as the matrix shows.

Politics Intrudes

-- Action -- Produce Don’t Produce

Produce -10, 10 100, 0

Don’t Produce 0, 120 0, 0Boeing

Airbus

Now, suppose European governments, for political reasons, want to be sure Airbus does build aircrafts.

The governments announce a subsidy to Airbus of 20. The subsidy will be paid regardless of what Boeing does.

This reduces the incentive for Boeing to build, Airbus cannot lose—thanks to the subsidy.

Problem can be tit-for-tat—U.S. government gives Boeing subsidy or retaliates elsewhere.

Jack and Jill Oligopoly Game

Copyright©2003 Southwestern/Thomson Learning

Jack’s Decision

Sell 40Gallons

Sell 40 Gallons

Jack gets$1,600 profit

Jill gets$1,600 profit







Sell 30 Gallons

Sell 30Gallons

Jill’sDecision

What type of game is this?What type of game is this?

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Introduction to Game Theory and Strategic Interactions