Chapter 7 a market structure game theory part a

CHAPTER 7A
Market Structure
Game Theory

What will you learn in this module?
In this module, you will learn the following:
• Explain the concept of game theory and strategy.
• Explain the difference between the dominant
strategy and Nash equilibrium strategy
• Distinguish cooperative (collusive) game and
non-cooperative game
2-3

What is GameTheory?
• The essential nature of game theory is that it involves
strategic behaviour, which means interdependent
decision-making.
• Game theory is a general framework to help decision
making when agents’ payoffs depends on the actions
taken by other players.
• For more information on “Game Theory”
• Watch this video
• https://www.youtube.com/watch?v=PCcVODWm-oY
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What is GameTheory?
• The following are the key elements of any game:
• Players or agents who make decisions.
• Strategies are complete plans of action for playing the
game.
• Payoff of players represent changes in welfare or utility
at the end of the game, and are determined by the
choices of strategy of each player
• Outcome of optimal strategy: Strategy that maximizes
a player’s expected payoff A description of the order of
play.

Players
The rules describe the setting of the game, the actions
the players may take, and the consequences of those
actions
• There are two players, if one of them confesses,
he will get a 1-year sentence for cooperating while
his accomplice will get a 10-year sentence for both
crimes.
• If both confess to the more serious crime, each
receives 3 years in jail for both crimes.
• If neither confesses, each receives a 2-year
sentence for the minor crime only.
2-6

Strategies
• There are two players Art and Bob. The strategies are
all the possible actions of each player.
• Art and Bob each have two possible actions:
1. Confess to the larger crime.
2. Deny having committed the larger crime.
 With two players and two actions for each player, there
are four possible outcomes:
1. Both confess.
2. Both deny.
3. Art confesses and Bob denies.
4. Bob confesses and Art denies.
2-7

Payoff
 Each prisoner can work out what happens to him—can
work out his payoff—in each of the four possible
outcomes.
2-8

Payoff – Con’t
 A payoff matrix is a table that shows the payoffs for
every possible action by each player for every possible
action by the other player.

Types of Game
• Different types of game according to certain important characteristics.
• Simultaneous-move game
• In this game each player makes decisions without the knowledge of the
other players’ decisions.
• Sequential-move game
• In this game one player makes a move after observing the other player’s
move. Playing chess is one the example of sequential-move game
• One-shot games and repeated games
• One-shot game is played only once while repeated game is played more
than once
• Cooperative and non-cooperative games: In co-operative games the
players can communicate with each other and collude. Game in which
negotiation and enforcement of binding contracts are not possible.
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An equilibriumstrategy
• To determine an equilibrium situation, the players
should be rational utility maximizers.
• There are two types of equilibrium and appropriate
strategies that involves different payoffs.
• Dominant Strategy Equilibrium
• Nash Equilibrium Strategy
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Types of EquillibriumStrategies
1. Dominant strategy equilibrium
• A strategy that results in the highest payoff to a player
regardless of the opponent’s action.
• Secure strategy: A strategy that guarantees the highest
payoff given the worst possible scenario.
2. Nash equilibrium strategy
• A condition describing a set of strategies in which no
player can improve her payoff by unilaterally changing
her own strategy, given the other players’ strategies.

Dominant Strategy
Player A
Player B
Strategy Left Right
Up 10, 20 15, 8
Down -10 , 7 10, 10
Outcome of a game in which each firm is doing the best it
can regardless of what its competitors are doing.
Player A has a dominant strategy:Up
Player B has no dominant strategy

Nash EquilibriumStrategy
Player A
Player B
Strategy Left Right
Up 10, 20 15, 8
Down -10 , 7 10, 10
In this game, each firm is indifferent about which product it
produces—so long as it does not introduce the same product as
its competitor. The strategy set given by 10, 20 the payoff matrix
which is stable and constitutes a Nash equilibrium: Given the
strategy of its opponent, each firm is doing the best it can and
has no incentive to deviate.
A Nash equilibrium results when Player A’s plays “Up” and Player
B plays “Left”

One-Shot Games: PricingDecisions
Firm A
Firm B
Strategy Low price High price
Low price 0, 0 50, -10
High price -10 , 50 10, 10
 A Nash equilibrium results when both players charge “Low
price”
 Payoffs associated with the Nash equilibrium is inferior from
firms’ viewpoint compared to both “agreeing” to charge
“High price”: hence, a dilemma.

One-Shot Games: CooperativeDecisions
Firm A
Firm B
Strategy 120-Volt
Outlets
90-Volt Outlets
120-Volt Outlets $100, $100 $0, $0
90-Volt Outlets $0 , $0 $100, $100
 There are two Nash equilibrium outcomes associated with this game:
 Equilibrium strategy 1: Both players choose 120-volt outlets
 Equilibrium strategy 2: Both players choose 90-volt outlets
Ways to coordinate on one equilibrium:
1) permit player communication
2) government set standard

Infinitely Repeatedgame
• An infinitely repeated game is a game that is
played over and over again forever, and in which
players receive payoffs during each play of the
game.
• Disconnect between current decisions and future
payoffs suggest that payoffs must be appropriately
discounted.
• Trigger strategy: the strategy is contingent on the
past play of the game and some past action
‘triggers’ a different action by a player
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Collusion with TriggerStrategies
Firm A
Firm B
Low price 0, 0 50, -40
High price -40 , 50 10, 10
 The Nash equilibrium to the one-shot, each firm charge low prices
In pricing game: Low, Low and earn zero profits.
 When this game is repeatedly played, it is possible for firms to
collude without fear of being cheated on using trigger strategies.
 Trigger strategy: strategy that is contingent on the past play of a
game and in which some particular past action “triggers” a different
action by a player.

FactorsAffecting Collusionin Pricing Games
• Number of firms in the market: collusion is easier when
there are few firms
• Firm size: it is easier for a large firm to monitor a small
firm
• History of the market: firm’s understanding to collude
with rival
• Punishment mechanisms: pricing mechanism that
affect firm’s ability to punish rivals
10-

Finitely repeatedgames
• Finitely repeated games are games in which a one-shot
game is repeated a finite number of times.
• Variations of finitely repeated games, two classes of
game:
• do not know when the game will end;
• do not know when the game will end;
• know when the game will end.
10-

Games with an uncertain Final Period
Firm A
Firm B
Low price 0, 0 50, -40
High price -40 , 50 10, 10
An uncertain final period mirrors the analysis of infinitely repea
games. Use the same trigger strategy.
No incentive to cheat on the collusive outcome associated with
finitely repeated game with an unknown end point above, provi

Repeated Games with a Known Final Period
Firm A
Firm B
Low price 0, 0 50, -40
High price -40 , 50 10, 10
When this game is repeated some known finite number of
times
and the game has only one Nash equilibrium.
Firm can not collude because a point will come when both
players are certain there is no tomorrow. Then promise to
“Tcohoepoenralytee”qwuililbbreiumbroiskethnesingle-shot, simultaneous-move Na
equilibrium; in the game above, both firms charge low price.
10-

Conclusion
1. Strategic behaviour considers the interdependence between
firms, in terms of one firm’s decisions affecting another,
causing a response affecting the initial firm.
2. Game theory provides some very useful insights into how
firms, and other parties, behave in situations where
interdependence is important.
3. There are many parameters in game situations:
static/dynamic games, co-operative/non-cooperative games,
one-shot/repeated games, perfect/imperfect information, two
players/many players, discrete/continuous strategies, zero-
sum/non-zero-sum games.
4. Game theory has particularly useful applications in the areas
of the theory of the firm and competition theory.
10-23

Recap
• On Key Terms and Concepts
2-24

Key terms andDefinitions
• Game theory
• Cooperative/coordination games
• Dominant strategy
• Nash equilibrium
• Mixed strategies.
• Repeated game
• Sequential bargaining
• Simultaneous move game
• Trigger strategy
2-

Chapter 7 a market structure game theory part a

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