Operation research Topic: Game Theory

1. Introduction to Game
Theory
Group members
α Kashif Ayaz
α Haroon khan
α Abdul Basit 1

2. • OR professionals aim to provide a rational basis for decision making by
seeking to understand and structure complex situations and to use this
understanding to predict system behavior and improve system
performance.
• using analytical and numerical techniques to develop and manipulate
mathematical and computer models of organizational systems composed of
people, machines, and procedures.
Why OR?
What is OR?
Optimization:
• Maximizing. (payoffs, supply, productivity)
• Minimizing. (cost, waste)
Till now we Studied Independent decision making
(no competitor)
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3. Developedin1950sbymathematiciansJohn von
Neumann and economist Oskar Morgenstern
Designedtoevaluatesituationswhere
individualsandorganizationscanhave
conflictingobjectives
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4.  A game is a generic term, involving conflict situations of
particular sort.
 Game Theory is a set of tools and techniques for
decisions under uncertainty involving two or more
intelligent opponents in which each opponent aspires
to optimize his own decision at the expense of the
other opponents. In game theory, an opponent is
referred to as player.
 Each player has a number of choices, finite or infinite,
called strategies.
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5. Key Elements of a game
Four elements to describe a game:
 Players: Who is interacting?
 Strategies: What are their options?
 Payoffs: What are their incentives?
 Information: What do they know?
 Rationality: How do they think?
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6.  Classification of Games
• Two-Person Game – A game with 2 number of players.
• Zero-Sum Game – A game in which sum of amounts won by all
winners is equal to sum of amounts lost by all losers.
• Non-Zero Sum Game – A game in which the sum of gains and
losses are not equal.
• Pure-Strategy Game – A game in which the best strategy for
each player is to play one strategy throughout the game.
• Mixed-Strategy Game – A game in which each player employs
different strategies at different times in the game.
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7.  Pure strategy (example)
(MaxiMin and MiniMax)
 Market have two firms:
 Firm X and Y
 strategies
 Reduce prices
 Advertisement
 Change packing
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8.  Pure strategy (example)
Maximin=5
Minimax=5
5 is saddle point
Optimum strategy of X is X1
Optimum strategy of Y is Y1
Value of game = 5
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Payoff matrix showing profit of firm X
Y1 Y2 Y3 Maximin
X1 3 7 2 2
X2 4 3 8 3
X3 5 8 9 5
Minimax 5 8 9

9. Solutions of the Games
 To predict what will be the
solution/outcome of the game we
need some tools:
 Nash equilibrium
 dominated
 dominant
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10. The decisions of the players are a Nash
Equilibrium if no individual prefers a different
choice.
In other words, each player is choosing the
best strategy, given the strategies chosen by the
other players.
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11. a strategy that gives higher payoffs no
matter what the opponent does.
One firm’s best strategy may not depend on
thechoice madeby theotherparticipantsin
thegame
Leadsto Nash equilibriumbecausethe player
willusethedominant strategy and theother
willrespondwithits best alternative
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12. An alternative that yields a lower payoff than some
other strategies
a strategy is dominated if it is always better to play
some other strategy, regardless of what opponents
may do
It simplifies the game because they are options
available to players which may be safely discarded
as a result of being strictly inferiorto other options.
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13.  Prisoners Dilemma
 Two individuals have been arrested for possession of
guns. The police suspects that they have committed 10
bank robberies;
 if nobody confesses the police, they will be jailed for 2
years.
 if only one confesses, she’ll go free and her partner will be
jailed for 40 years.
 if they both confess, they get 16 years
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14.  Matrix Representation of Prisoners
Dilemma
Bonnie
Confess
Do not
Confess
Clyde
Confess 16,16 0,40
Do not
Confess
40,0 2,2
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15. We want to predict the outcome of the
game
Bonnie
Confess
Do not
Confess
Clyde
Confess 16,16 0,40
Do not
Confess
40,0 2,2
Suppose that Clyde decides to confess. What is the best decision
for Bonnie?
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16. We want to predict the outcome of the
game
Bonnie
Confess
Do not
Confess
Clyde
Confess 16,16 0,40
Do not
Confess
40,0 2,2
Suppose that Clyde decides to remain silent. What is the best
decision for Bonnie?
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17. We want to predict the outcome of the
game
Bonnie
Confess
Do not
Confess
Clyde
Confess 16,16 0,40
Do not
Confess
40,0 2,2
Suppose that Bonnie decides to confess. What is the best decision
for Clyde?
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18. We want to predict the outcome of the
game
Bonnie
Confess
Do not
Confess
Clyde
Confess 16,16 0,40
Do not
Confess
40,0 2,2
Suppose that Bonnie decides to remain silent. What is the best
decision for Clyde?
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19.  Solution of the game
Bonnie
Confess
Do not
Confess
Clyde
Confess 16,16 0,40
Do not
Confess
40,0 2,2
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20.  Conclusion:
 Players, payoff, strategies.
 Taking decision (production)
 Competing situations
 Maximizing payoffs regard competitors
 Take advantages of competitor strategies
 Make decision on basis of participant strategies
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21. Any question??????
THANK YOU!!!!!
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