Suppose that there were three possible states of nature as represented in the table below:

a. What conditions would be required for the regret theory utility function to predict preference cycling when choosing between pairs of the three possible gambles? Graph an example of a function that would satisfy these conditions.
b. Is it possible for preference cycling to occur given the same choices under expected utility maximization with probability weights? Show why or why not.
c. Would it be possible for preference cycling to occur given the same choices under rank-dependent expected-utility maximization? Show why or why not.

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States of Nature Probability Gamble 1 Gamble 2 Gamble 3 1 .35 S1,000 $1,800 $2,500 S2,000 $1,800 $1,500 25 $3,000 $1,800 $1,500