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ECON 3801, Extensive-form games

This lecture continues the discussion on “Extensive Form Games”, starting using an example of repeatedly played prisoner’s dilemma game.

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Consider the prisoner’s dilemma, assuming that both players knows each other are rational…
Assume there two Different strategies: Cooperate and Traitor -> it is clear the cooperation will break down when repeatedly played, if anyone breaks the cooperation.

Consider a extensive form of Prisoner’s dilemma played two times, after each time the result is revealed:
We can think player 1 moves first and Player 2 moves without knowing the result, thus marked by dashing lines…

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Subgame and Subgame perfection

Subgame is the remaining game from a node selected from the full game tree, as long as it does not break the information section. For example, the twice-played prisoner’s dilemma have 5 subgames.

Subgame perfect equilibrium is the nash equilibrium in every subgame, which is the nash equilibrium of the full game. However, not all nash is a subgame perfect equilibrium.

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The trust game

The trust game is in fact a kind of Investment game, that one can choose from giving back and keep the investment from another player. Perfect rational people will not give back or invest in the game - which is the subgame perfection.

However, in reality the trust game works, and the value of investment and give back have been extensively studied and revealed difference across cultures.

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The rights and freedom of choice

Consider the anecdote talked by professor in class about being robbed in night. Did he exercised his “freedom of choice” by choosing from his life and his watch, or does everyone have a right to go back home without losing anything which made his choice forces?

What does it mean if someone exercises power over another one? Notice the difference between incentive and power. How to distinguish between the oppressor and the ones being oppressed?

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Next Class: Bad Equilibirum

cascades in the society.