“…We therefore must adapt all of the models so that they assign positive probability (likelihood) to all possible data points. In our recent work (e.g., Boylan and El-Gamal, 1993;McKelvey and Palfrey, 1992;ElGamal, McKelvey, and Palfrey, 1993a;El-Gamal and Palfrey, 1993), we have avoided the zero-likelihood problem by introducing an error structure which posits that subjects occasionally make errors The existence of such a value function uses the fact that the operator T, defined by satisfies monotonicity and discounting, and hence is a contraction mapping (Blackwell, 1965 where is the value to the nth player of using strategy ~' when all other players are using strategy p. It is straightforward (see McKelvey, 1990) If all players were perfectly rational, then all four stage games would end in the red players taking on the first round. If perfect rationality is not assumed, the problem becomes much more complicated (e.g., see Binmore, 1989;Reny, 1993;Rosenthal, 1982;Aumann, 1988;Kreps et al, 1982 corresponds to e jo = F-0/20), and then making our priors uniform over those supports.…”