4. • PLAYERS: Who is interacting
• STRATEGIES: What are their options
• PAYOFFS: What are their incentives
• INFORMATION: What do they know
• RATIONALITY: How do they think
5. • we’ll limit ourselves to two-person games
• finite number of strategies.
6.
7. • if each player has chosen a strategy, and no player can
benefit by changing strategies while the other players
keep theirs unchanged, then the current set of strategy
choices and the corresponding payoffs constitutes a
Nash equilibrium.
8. • If the agent (player) sticks to his strategy once and for all
• If the agent (player) randomize his choices according to
those possibilities
10. • Two members of a criminal gang are arrested and
imprisoned.
• Each prisoner is in solitary confinement with no means
of communicating with the other.
• The prosecutors lack sufficient evidence to convict the
pair on the principal charge, but they have enough to
convict both on a lesser charge.
• the prosecutors offer each prisoner a bargain.
11. Prisoner B
Prisoner A
Prisoner B stays silent
(cooperates)
Prisoner B betrays
(defects)
Prisoner A stays silent
(cooperates)
Each serves 1 year
Prisoner A: 3 years
Prisoner B: goes free
Prisoner A betrays
(defects)
Prisoner A: goes free
Prisoner B: 3 years
Each serves 2 years
12. • Betraying a partner offers a greater reward than
cooperating with them,
• All purely rational self-interested prisoners will betray the
other, meaning the only possible outcome for two purely
rational prisoners is for them to betray each other.
• The interesting part of this result is that pursuing
individual reward logically leads both of the prisoners to
betray when they would get a better reward if they both
kept silent.
• In reality, humans display a systemic bias towards
cooperative behavior in this and similar games despite
what is predicted by simple models of "rational" self-
13. • The payoff matrix for the duopoly game in pricing
strategies has the same structure as the prisoner’s
dilemma.
• The Nash equilibrium occurs when each fellow is
charging the
lowest possible price.
14. • If each firm charges a high price, then they both get large
profits.
• But if one firm is charging a high price, then it will pay
the other firm to cut its price a little to capture the other
fellows market
• Both firms cut their prices, they both end up making lower
profits.
• Whatever price the other fellow is charging, it will always
pay you to shave your price a little bit.
• The Nash equilibrium occurs when each fellow is
charging the lowest possible price.
