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left. Let 

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be the winning set of player 1. The game models a ‘last man standing’ endurance contest, as in a college drinking game or religious conflicts: Player 1 wants to leave the game at some point, but he doesn’t want to be the first to leave. 

In Example 2.1 both players have eventual perfect monitoring. In Example 2.2 none of the players has eventual perfect monitoring. In Example 2.3 only player 1 has eventual perfect monitoring. 

2.1. Example. Let k be a positive integer. Assume that at stage n each player observes his own actions and the actions of his opponent at stages smaller than n − k . Then the value of the game is 0. An optimal strategy for player 2 is to play S as long as he is not informed that player 1 has played L. When player 2 knows that player 1 played L at some point, player 2 then plays L. 

Note that in the previous example, the number k need not be constant. It can depend on the stage number, and can differ between the players. As long as player 2 knows the actions of his opponent eventually, the game is determined and the value is 0. (The independence of the value on the information partitions in this example is not typical) 

2.2. Example. Assume that each player knows his own previous actions, but does not observe his opponent’s actions. Then the game is not determined. In fact, val Γ = 0 and val Γ = 1. 

2.3. Example. Assume that player 1 observes the past actions of player 2, but player 2 doesn’t observe the past actions of player 1. Then the game is not determined. In fact, val Γ = 1 / 2 and val Γ = 1. An optimal strategy for player 1 is: At stage 0 play L or S with probability 1 / 2, and, at stage 2 k for k ≥ 1, play the action of player 2 from stage 2 k − 1. 

