Consider a two-player game between Child’s Play and Kid’s Korner, each of which produces and sells wooden swing sets for children. Each player can set either a high or a low price for a standard two-swing, one-slide set. The game is given as below:
Kid’s korner |
|||
High price |
Low price |
||
Child’s play |
High price |
64, 64 |
20, 72 |
Low price |
72, 20 |
57, 57 |
a. Suppose the players meet and make price decisions only once.
What is the Nash equilibrium in pure strategy of the game? (10
pts)
b. Suppose this stage game is repeatedly
forever. Let each of the two firms use a grim trigger
strategy in which they both price high unless one of them
“defects”, in which case they price low for the rest of the game.
Find the range of values of the discount factor, for which this
strategy is able to sustain cooperation in every period between the
two firms. (10 pts)
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