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There are two games A and B prevailing in the market. For both games, the utility derived from the game depends on the proportion

 

There are two games A and B prevailing in the market. For both games, the utility derived from the game depends on the proportion of players playing that game. The utility functions derived from game A and B are as follow respectively: u_A = 5p_A u_B=p_B where p_X is the proportion of players playing game X. Assume that a player would only choose one game from A and B. If currently there is no one playing game A. Would a player choose to play game A or game B? What will be the outcome if they all make a similar decision? a. Game B and everyone chooses game B. b. Game A and B with the same probability, and the ratio of the number of players playing game A to that playing game B will keep at 1:1. c. Game A and B with probability 1:5, and the ratio of the number of players playing game A to that playing game B will reach 1:5. d. Game A, and Everyone chooses game A.

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