each player has a dominant strategy, and when each plays it, the resulting payoffs are smaller than if each had played a dominated strategy • Consider another example.. 910[r]
(1)Games and Strategic Behavior
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Learning Objectives
1 List the three basic elements of a game
Recognize and discuss the effects of dominant strategies and dominated strategies
2 Identify and explain the prisoner's dilemma and how it applies to real-world situations
3 Explain games in which the timing of players' choices matter
(3)Strategies and Payoffs
• Actions have payoffs that depend on:
– The actions
– When they are taken – The actions of others
• Some markets are characterized by interdependence
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Game Theory
• Basic elements of a game:
– The players
– Their available strategies, actions, or decisions – The payoff to each player for each possible action
• A dominant strategy is one that yields a higher
payoff no matter what the other player does
– A dominated strategy is any other strategy available
(5)Singapore and Thai – Scenario 1 • Players: Singapore Airlines and Thai Airways
supplying service between Singapore and Bangkok
– No other carriers
• Strategies: Increase advertising by $1,000 or not • Assumption: all payoffs are know to all parties
• A payoff matrix is a table that describes the
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Payoff Matrix
• Payoff is symmetric
• Dominant strategy is raise advertising spending
– Both companies are worse off
Thai Airways Options Singapore
Airlines Options Raise Spending No Raise Raise Spending Singapore: $5,500
Thai: $5,500
Singapore: $8,000
Thai: $2,000
No Raise Singapore: $2,000
Thai: $8,000
Singapore: $6,000
(7)Equilibrium in a Game
• A Nash equilibrium is any combination of
strategies in which each player’s strategy is her or his best choice, given the other player’s
strategies
– Equilibrium occurs when each player follows his
dominant strategy, if it exists
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• Same situation
– Different payoffs; non-symmetric
– Thai raises spending
• Singapore anticipates Thai action; does not raise
Lower-Left cell is a Nash equilibrium
Thai Airways Options
Singapore Airlines Options
Raise Spending No Raise
Raise
Spending
Singapore: $3,000
Thai: $4,000
Singapore: $8,000
Thai: $3,000
No Raise Singapore: $4,000
Thai: $5,000
Singapore: $5,000
(9)Prisoner’s Dilemma
• The advertising example illustrates an important class of games called the prisoner’s dilemma
• The prisoner’s dilemma is a game in which
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– Two prisoners are held in separate cells for a serious
crime they did commit
– The prosecutor lacks sufficient evidence
Kakuzu's Options Hidan's
Options Confess Don't Confess
Confess Hidan: 5 years
Kakuzu: 5 years
Hidan: 0 years
Kakuzu: 20 years Don't Confess Hidan: 20 years
Kakuzu: 0 years
Hidan: 1 year
Kakuzu: 1 year
Dominant strategy