Transcript
GAME THEORY
NATURE AND SCOPE OF GAME THEORY
The essential nature of game theory is that it involves strategic behavior, which
means interdependent decision-making
ELEMENTS OF A GAME PLAYERS:
These are the relevant decision-making identities, whose utilities are interdependent.
STRATEGIES:
These are complete plans of action for playing the game.
PAYOFFS:
These represent changes in welfare or utility at the end of the game, and are determined by the choices of strategy of each player.
PRISONER’S DILEMMA (PD).
AT THIS STAGE WHAT THE TYPE OF SITUATION DESCRIBED ABOVE HAS TO DO WITH BUSINESS STRATEGY
To illustrate this, let us consider the situation
Of Coke and Pepsi.
At any given time period each firm has to decide
whether to maintain their existing price or to offer a
discount to the retailers who buy from them.
PRISONER’S DILEMMA FOR COKE AND PEPSI
PEPSI
Maintain Price Discount
Maintain Price
COKE
Discount
50 50
70 -10
-10 70
10 10
STRUCTURE OF PAYOFFS IN PRISONER’S DILEMMA
Strategy pair (self/other) Name of payoff
Defect/co-operate Temptation (70)Co-operate/co-operate Reward (50)Defect/defect Punishment (10)Co-operate/defect Sucker’s payoff (10)
TYPES OF GAME
Co-operative and non-cooperative games Two-player and multi-player games Zero-sum and non-zero-sum games Perfect and imperfect information Static and dynamic games Discrete and continuous strategies ‘One-off’ and repetitive games
STATIC GAMES
The nature of this type of game raises the following
questions:
How does a firm determine strategy in this type of situation?
What do we mean by an equilibrium strategy?
Is there anything that firms can do to change the equilibrium to a more favorable one, meaning to ensure co-operation?
EQUILIBRIUM
We can now consider three types of equilibrium and
appropriate strategies in situations involving
different payoffs.
Dominant strategy equilibrium, Iterated dominant strategy equilibrium, Nash equilibrium
DOMINANT STRATEGY EQUILIBRIUM
Strictly dominant strategy in a situation, will
always give at least as high a payoff as any other
strategy, whatever player other does
DOMINANT STRATEGY EQUILIBRIUM
PEPSI
Maintain Price Discount
Maintain Price
COKE
Discount
50 50
70 -10
-10 70
10 10
PARETO DOMINATED SITUATION
This means that there is some other outcome where
at least one of the players is better off while no other
player is worse off.
ITERATED DOMINANT STRATEGY EQUILIBRIUM
What would happen if one firm did not have a
dominant strategy?
CONT….. PEPSI
Maintain Price Discount
Maintain Price
COKE
Discount
80 50
70 -10
-10 70
10 10
NASH EQUILIBRIUM
The situation becomes more complicated when
neither player has a dominant strategy.
CONT…….
75 10
PEPSI
Maintain Price Discount
Maintain Price
COKE
Discount
60 50
15 10
10 15
CONTI……
If Coke maintains price, Pepsi will discount; and, given this best response, Coke’s best reply is to maintain price.
If Coke discounts, Pepsi will maintain price; and, given this best response, Coke’s best reply is to discount.
CONTI…….The same equilibrium could also be expressed from
Pepsi’s point of view:
If Pepsi discounts, Coke will maintain price; and, given this best response, Pepsi’s best reply is to discount.
If Pepsi maintains price, Coke will discount; and, given this best response, Pepsi’s best reply is to maintain price
OLIGOPOLY MODELS
Cournot model Bertrand model Contestable markets model
THE COURNOT MODEL There are few firms in the market and many
buyers.
The firms produce homogeneous products; therefore each firm has to charge the same market price (the model can be extended to cover differentiated products).
Competition is in the form of output, meaning that each firm determines its level of output based on its estimate of the level of output of the other firm.
Each firm believes that its own output strategy does not affect the strategy of its rival(s).
Barriers to entry exist.
Each firm aims to maximize profit, and assumes that the other firms do the same.
THE BERTRAND MODEL
There are few firms in the market and many buyers.
The firms produce homogeneous or differentiated products; therefore each firm has to charge the same market price in the case of homogeneous products, but there is some scope for charging different prices for differentiated products.
CONTI… Competition is in the form of price, meaning that
each firm determines its level of price based on its estimate of the level of price of the other firm. Each firm believes that its own pricing strategy does not affect the strategy of its rival(s).
Barriers to entry exist. Each firm has sufficient capacity to supply the
whole market. Each firm aims to maximize profit, and assumes
that the other firms do the same.
CONTESTABLE MARKETS
There are an unlimited number of potential firms that can produce a homogeneous product, with identical technology.
Consumers respond quickly to price changes. Incumbent firms cannot respond quickly to entry
by reducing price. Entry into the market does not involve any sunk
costs. Firms are price-setting Bertrand competitors.
DYNAMIC GAMES
Many business scenarios tend to involve
sequential moves rather than simultaneous
moves.
Example: Decision to invest in new plant
EQUILIBRIUM
Dynamic games are best examined by drawing a game tree.
An extensive-form game not only specifies the
players, possible strategies, and payoffs, as in the
normal-form game, but also specifies when players can move, and what information they have at the time of each move.
CONTI…….
In order to analyze this game tree we must derive the sub game perfect Nash equilibrium (SPNE).
This is the situation where each player selects an
optimal action at each stage of the game that it might reach, believing the other player(s) will act in the same way.
CONT…….
70 40
FIRM B
Expand No change
Expand
FIRM A
No change
50 20
85 25
95 30
LIMITATIONS OF GAME THEORY
As game theory applications have become more widespread throughout economics and the other social and natural sciences, certain criticisms have arisen regarding the validity of its conclusions
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