1. ECO290E: Game Theory Lecture 8 Games in Extensive-Form

2. Review of Midterm The definition of NE. Dominated strategy and NE. How to solve “Rock-Paper-Scissors” game.

3. Definition of NE A Nash equilibrium is a combination of strategies, denoted as s*, which satisfies the following condition: A Nash equilibrium is neither a strategy nor a combination or payoffs.

4. Dominated strategy and NE If iterated elimination of strictly dominated strategies eliminates all but one combination of strategies, denoted as s, then s becomes the unique NE of the game. If a combination of strategies s is a NE, then s survives iterated elimination of strictly dominated strategies.

5. Review of Lecture 6 There are two NE: (In, A) and (Out, PW) (Out, PW) relies on a non-credible threat. Monopolist Entrant Price WarAccommodat e In 1 Out 4 0 4 0

6. Lessons Dynamic games often have multiple Nash equilibria, and some of them do not seem plausible since they rely on non-credible threats. By solving games from the back to the forward, we can erase those implausible equilibria.  Backward Induction This idea will lead us to the refinement of NE, the subgame perfect Nash equilibrium.

7. Extensive Form Games The extensive-form representation of a game specifies the following 5 elements: The players in the game When each player has the move What each player can do at each of her opportunities to move What each player knows at ---. The payoff received by each player for each combination of moves that could be chosen by the players.

8. Normal-Form Representation Every dynamic game generates a single normal-form representation. A strategy for a player is a complete plan of actions specifying a feasible action for the player in every contingency. 1 2(L’,L’)(L’,R’)(R’,L’)(R’,R’) L3,1 1,2 R2,10,02,10,0