[180223] Bargaining

Envelope theorem
Folk’s theorem
Variation of Rubinstein Bargaining problem

[180216] Repeated game and 1-shot deviation

In this notes, we study 1-shot deviation, which is the method to obtain subgame perfect equilibria (SPE) for infinite repeated games. Some related definitions and examples are as follows:

Repeated game (Stage game, history, payoff, strategy, NE, SPE, perfect/imperfect, public/private, Stochastic/dyanamic)
One-shot deviation and one-shot deviation principle
Automaton and continuation payoff

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[180209] Subgame perfect equilibria

In this notes, we study the solution concept Subgame perfect equilibria. We will start with the definitions and understand it by various basic examples.

The definitions we go over includes:

Pure/ Mixed reduced form game
Nash equilibria of an extensive form game
Subgame
Subgame perfect equilibria

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[180202] Extensive form game

In this notes, we study the basic notions in the extensive form game, highlight and exemplify the relation between the notion mixed strategy and behavior strategy.

This notes can not be completed without the discussions in the section meeting.

Before that, we remind the symbol $\mathbb{R}_+^n$ means the set $\{x: x\ge 0\}$ and, similarly, $\mathbb{R}_{++}^n$ means the set $\{x: x> 0\}$ . Here $x \ge y$ on n-dim Euclidean space means all coordinates of vector x is greater than or equal to that of vector y; $x > y$ means $x\ge y$ and $x\neq y$ . In particular, we have $\mathbb{R}_+=[0,\infty)$ .