Game theory
maqi0912
week8.pptxCh 6. Games
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Recap
In the past five weeks, we discussed graph theory (structure).
From this week, we are jumping into the second part of the textbook.
The central themes of social networks are:
Structure: : Graph theory
Connectedness of a social network (links)
Interdependence in the behaviors of the individuals who inhabit the network
Behavior: Game theory
Interconnectedness at the level of individual behavior
The outcome of a person’s decision depends not just on how they choose among several options, but also on the choices made by the people they are interacting wit
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What does it mean by “interconnectedness of behaviors”?
My choice depends on someone else’s choice
Let’s watch this video by
https://www.youtube.com/watch?v=M3oWYHYoBvk&t=3311s
2013 Yale Presidential Inauguration Symposia
In this video, one dean’s choice depended on the other dean’s choice of shooting or stepping forward.
If one dean shot and then missed, the other dean can keep on stepping forward for a better chance.
If one dean did not shoot, the other dean must guess what the other dean’s next course of action.
Too bad we can’t play this game in person!
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Prisoner's Dilemma
The game (p. 144 in your textbook)
If you confess, and your partner doesn’t, then you will be released, and your partner will be sent to prison for 10 years.
If you both confess, then you will both serve 4 years (guilty plea).
If neither of you confesses, then, you will be charged with resisting arrest (a less serious offense) and serve only 1 year each.
Your partner is being offered the same deal. Do you want to confess?
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We need three tables to get to F6.2
| Suspect 1’s payoff | ||
| S2- Not confess | S2- Confess | |
| S1 - Not confess | ||
| S1- Confess |
| Suspect 2’s payoff | ||
| S2- Not confess | S2- Confess | |
| S1 - Not confess | ||
| S1- Confess |
| Combined | ||
| S2- Not confess | S2- Confess | |
| S1 - Not confess | ||
| S1- Confess |
Figure 6.2 Prisoner’s Dilemma
The values on the left indicate payoffs for player 1 in the row.
The values on the right indicate payoffs for player 2 in the column
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Argyris, Young (AY) -
Basic ingredients of games
Players: Suspect 1 and Suspect 2
Strategies: Confess vs. Not confess
Payoffs: the outcome that depends on the strategies selected by player. -4
Assumptions: Rationality
Maximize one’s own payoff
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Ready for another game?
Student presentation vs. exam game (page 141)
| Your payoff | ||
| Your partner- Presentation | Your partner- Exam | |
| You - Presentation | ||
| You- Exam |
| Your partner’s payoff | ||
| Your partner- Presentation | Your partner- Exam | |
| You - Presentation | ||
| You- Exam |
| Combined | ||
| Your partner - Presentation | Your partner- Exam | |
| You - Presentation | ||
| You- Exam |
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Important concepts drawn from the two examples
Best responses: it is the best choice of one player, given a belief about what the other player will do
In the prisoner’s dilemma: To not confess
In the exam vs. presentation game: To study for the exam
Dominant strategy
A dominant strategy for Player 1 is a strategy that is a best response to every strategy of Player 2.
A strictly dominant strategy for Player 1 is a strategy that is a strict best response to every strategy of Player 2.
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A game in which only one player has a strictly dominant strategy
Marketing strategy game (147-148)
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Application of this prisoners’ dilemma
Arms race
https://www.youtube.com/watch?v=iYPifEyFadA
Use of performance-enhancing drugs
https://www.youtube.com/watch?v=f1CuVe7m7aU
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Nash Equilibrium
When neither player in a two-player game has a strictly dominant strategy
Three-client game (page 149)
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Defining Nash Equilibrium
Even when there are no dominant strategies, we should expect players to use strategies that are best responses to each other.
More precisely, suppose that Player 1 chooses a strategy S and Player 2 chooses a strategy T. We say that this pair of strategies (S,T) is a Nash equilibrium if S is a best response to T, and T is a best response to S.
Not derived from rationality but from an equilibrium concept.
the players choose strategies that are best responses to each other, then no player has an incentive to deviate to an alternative strategy — so the system is in a kind of equilibrium state, with no force pushing it toward a different outcome.
1994 Nobel Prize in Economics
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Multiple Equilibria: Coordination Games
Games that have more than one Nash equilibrium
Coordination Game (p. 151)
Social convention can help the players coordinate on the shared strategies.
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Unbalanced coordination game
The battle of the sexes (p. 153)
Stag Hunt Game (p. 153)
Shows the importance of communication!
Discussion Question of the week
This is NOT the right table for the battle of the sexes, but I posted it here and correct it during my live lecture, because the correct table is not supplied in the textbook. You must watch the live video of lecture in order to answer the discussion question correctly.
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