The problem starts at time t0. At each time step, the participant can choose to opt out and claim a loser's reward Rl. At each time step, the participant has a probability p to win a winner's reward Rw, the participant is aware of p. Rewards decrease after each time step, at the same rate, and Rw > Rl always. After tn the 'game' is over and the participant claims Rl - the participant is aware of time tn.
For example at t0 Rw = 100, Rl = 50, p = 0.05, reward decay rate is 1 each turn and the tn = 30. First participant wins at t10 and claims a reward of (100 - 10 * 1) = 90. Second participant opts out at t20 and claims a reward of (50 - 20 * 1) = 30. Third participant loses at t30 and claims (50 - 30 * 1) = 20.
I'm interested in assessing the risk behavior of the second participant. I'm thinking that the second participant considers the remaining number of turns, probability p to win each turn, and average amount that the participant would win, and weights it against the current loser's reward at time t20. But I'm not sure this is the right way to consider the risk involved.
I've read the early works by Kahneman and Tversky but this seems a bit more complex, I would appreciate any hints on where to find solutions in literature as well.