Repeated Games: This first section considers repeated games in which players meet to make a certain decision or set of decisions again and again.  The nature of the repetition in the game and the information players have about it is crucially important.  If the game is repeated a finite number of times and the stopping point is known to all players then, in many cases, not much changes in the analysis.  If, on the other hand, the game is repeated an infinite number of times or, equivalently, with an unknown stopping point, then a number of new possibilities emerge.  

 

It is critical that students understand that the definition of strategy in this new scenario is different.  A strategy no longer involves simply picking from a set of possible pure strategy options or randomizing among those options.  In a repeated game, a strategy must specify what action a player will take in each iteration of the game, including how those actions change based on earlier actions and reactions from all players.  This can get very complicated and so it is best to focus on specific examples such as the trigger strategy or tit-for-tat as described in the text.

 

The consideration of repeated games does provide the opportunity to ‘solve’ games, such as the Prisoner’s Dilemma, that might have been viewed as too simplistic in the static case.  Students are usually relieved to learn that game theory provides a clear explanation for how cooperation might occur even in a noncooperative game.