Week 6

• subgame perfect equilibrium is found using backward induction
• subgame perfect equilibrium involves solving each subgame from the final subgames and working up to the first decision
• perfect recall involves players remembering past moves and states
• common knowledge involves the situation, rules and payoffs being known to all the players
• common knowledge and perfect recall are assumed for sequentially played game theory
• a sequentially played game can be shown in normal form representation
• in a sequentially played game, everyone knows everyone's potential payoffs, and everyone knows everyone knows
• each terminal (end) node of a game tree show the payoffs
• a branch out of a node of a game tree show the actions available to the player
• at each node of a game tree, one player makes a choice
• a game tree completely describes the game and situation
• a game tree provides a complete description of a sequentially played game
• sequentially played games create an extensive form
• some Normal form Nash equilibria may be not justifiable, as the actual situation that would cause the outcome will not happen (often because the game has ended)
• the Normal form Nash Equilibrium of extensive form games can be used to find a Nash Equilibrium path through the extensive form game tree
• the Nash Equilibrium of extensive form games can be found by using the normal form of the game
• A strategy profile involves all the best choices in all possible subgames