Aufgabe:
Consider two people who meet a narrow street, walking in opposite directions. They want to pass each other either by both walking on the left hand side or by both walking on the right hand side. This situation can be described as a game with two players. Each player can take one of two actions, to go left or to go right. That is, each player's strategy set contains two elements. If both players take the same action, they peacefully pass each other. If they take different actions, they bump into each other. Each player prefers the former to the latter consequence of their interaction.
Suppose that the people act simultaneously (simultaneous moves).
How many (pure) strategles does each of them have? -- Bitte auswählen \( --\vee \)
many possible strategy profiles are there in this game?. Bitte auswählen.\( \sim \)
Now, suppose the two people act one after the other (sequential moves).
How many (pure) strategies does the first mover have? - - Bitte auswählen ..v
How many (pure) strategles does the second mover have? - - Bitte auswählen -.v
How many subgame-perfect Nash equilibria does the sequential-move version of this game have? \( \quad \) Bitte auswählen .. \( \vee \)
You may wonder what makes a strategy "pure". A pure strategy, as opposed to a "(strictly) mixed" strategy is supposed to be played with certainty. A mixed strategy allows for randomization between several actions, e.g. playing two actions with equal probability. There are infinitely many mixed strategies, even if only two pure strategies are available.
Problem/Ansatz:
Hab irgendwie schon alles probiert, antwortmöglichkeiten sind immer 1-5. Habt ihr eine Idee?
