Classic Strategic Form Games


Zero Sum: Matching Pennies - Tom and Bill each have a roll of pennies.  They simultaneously put a penny out on the table.  If the pennies match (Head - Head or Tail - Tail) then Bill gets both.  If they do not match then Tom gets both.  What one player wins, the other player loses. No matter what strategy is chosen, the value of the game is zero.

Bill H 1, -1 -1, 1
T -1, 1 1, -1

Prisoner's Dilemma - Kalvin and Cline have been arrested for a crime.  If they both confess (C) then they each go to jail for two years. If they both deny (D) the crime then they each get one year.  However, if Cline confesses and implicates his friend Kalvin, then Cline goes free and Kalvin gets three years in jail. From the standpoint of the combined value of the game for both players, the best strategic plan is for both of them to deny.  Will they do this? 

Cline C 2, 2 0, 3
D 3, 0 1, 1

Battle of the Sexes - Barney prefers to be with Betty to doing anything alone.  Same for Betty.  Barney would prefer to be at the Opera with Betty, but she would prefer to be at the movies with Barney.  This game is interesting because of the symmetry and because there are two equilibrium outcomes.

Opera Movie
Barney Opera 2, 1 0, 0
Movie 0, 0 1, 2

Hawk-Dove/Chicken - If both Sharon and Arafat adhere to hawkish positions then neither gains anything.  If they are both Doves then each gains 2.  The person playing Hawk against an opponent playing Dove earns 3. This is a very simple version of a game first developed by biologists. In either of the two equilibria there are both hawks and doves.

Sharon H 0, 0 3, 1
D 1, 3 2.5, 2.5

Coordination - If Bob and Sue follow the same training plan then they both get healthy.  But if they adhere to different plans then neither gains anything.  Either training plan will work, as long as they both do it.

Sue A 1, 1 0, 0
B 0, 0 1, 1

Pareto Coordination - If all of the members of the choir sing in the key of A then they sound great. If they sing in B-flat then they don't sound quite as good.  If they sing in different keys then they shouldn't sing at all. In this version of the coordination game they players are better off if they coordinate, but coordinating on a particular strategy makes them best off.

Tenors A 2, 2 0, 0
B 0, 0 1, 1

In the game of the pulchritudinous Pigs, Dirk and Sydney share a pen.  Dirk is  very domineering and Sydney is very submissive.  There is a button on one wall of the pen.  When it is pushed food is dispensed at the trough on the opposing wall.  If Sydney pushes the button then Dirk gobbles up all of the food and Sydney gets none. If Dirk pushes the button then Sydney gets to eat during the time it takes for Dirk to run over to the trough.  If neither pushes the button then they go hungry.

Push Don't
Dirk Push 4, 2 2, 3
Don't 6, -1 0, 0