Game theory

Zero-sum (or constant-sum) games: completely conflicting interests ie • penalty kick

Completely aligned interests • Examples: social conventions - wanting to dress the same 

Mixed-motive game (mix between conflict and cooperation) -examples: working on a group project.

 Sequential moves - Each player takes turns making a move  • How will my (rational) opponent react to my choice? 

 Simultaneous moves- Both players play at the same time• What is my opponent choosing right now? • The opponent is also thinking what you are choosing! 

 Both sequential and simultaneous moves.

Imperfect information: some players do not know some of the previous moves of other players

 Perfect information: when a player moves, he knows all the previous moves of all players (including his own and nature’s)

• Incomplete information: some players do not know something about the game (payoffs, available actions) before the game starts.

 • Examples: private-value auctions, poker • 

We call private information “player’s type”.

 • Complete information: everyone knows the strategy sets and utilities of everyone else

Asymmetric information: some players know more than others • Information can be asymmetric because it is imperfect (some player observes the choice of a third player or nature) • Or because it is incomplete (player knows his type, but others do not) • Player who has information can signal it. Players who do not have information can screen to learn this information.

 • Strategic uncertainty: not knowing what others will choose or have chosen • Theoretically, strategic uncertainty exists if there are multiple equilibria or players are choosing mixed strategies. • In practice, strategic uncertainty can exist in any simultaneous-choice game