- the collection of best response correspondences.
- a mixed strategy for player .
- the probability that player plays .
- a behavioral strategy for player . The distinction with a mixed strategy will be clear in context.
- belief of player .
- belief of player on opponent’s strategy .
- denotes a decision tree
- terminal nodes in the decision tree
- denotes a decision node on the tree
- an information partition on the decision tree
- information set in for player
- generic element of information set.
- a set of actions available for information set
- an action partition
- a family of probabilities based on the partitions
In a game tree, a dashed line or an ellipse encompassing more than one vertex denotes a non-singleton information set
- horizon. total number of games for multistage games
- generic time step
- history up to (excluding) time step .
- the expected payoff of player from the information set onward by playing
- a strategy that is identical to except at . At we use the action instead.
- generic stage game
- a finitely repeated game wherein stage game is played consecutive times with as the common discount factor.
- an infinitely repeated game wherein stage game is played an infinite number of times with as the common discount factor.
- in the context of an infinitely repeated game, it denotes the set of all histories of length .
- Set of Type spaces of all players.
- Type space of player
- Player is type
- profile of player types.
- the belief of player with respect to the uncertainty over the other players’ types.
- a system of beliefs of an extensive form game.
- public alternative
- monetary gain or loss given a certain type.
- a decision rule on the public alternative.
- the monetary equivalent of public alternative for player of type .
- the set of outcomes in a mechanism design problem
- the best response actions of player given that player has chosen and where belief assigns positive probability only to types in the set in a signaling game.