How one gambles if one must: Effects of differing return rates on multistage betting decisions

In the multistage betting game (MBG), a decision maker (DM) is provided with some capital x which he is required to bet over m (m > 1) mutually exclusive and collectively exhaustive alternatives, each of which occurs with probability p_i (p_i > 0, i = 1,…, m; Σ_{i = 1}^mp_i = 1). If y_i is bet on alternative i (y_i ≥ 0, Σ_{i = 1}^my_i = x) and alternative i obtains, the DM's capital for the next stage is y_ir_i, (r_i > 0). The MBG lasts until either the DM loses his capital or N stages elapse, whichever comes first. Each of six subjects participated in six sessions consisting of several hundred 3-alternative MBG stages. A within-subject design assigned negative expected value (EV) bets to the first three sessions and positive EV bets to three more sessions. Significant effects were found due to return rate, capital size, homogeneous runs of either wins or losses, and individual differences. Four maximization of expected utility and two minimization of risk models were presented and tested. A modified logarithmic utility model is proposed, which provides the best fit to the data. The implications of the results and directions for further research are briefly discussed.