Linear Learning Models for Two-Party Negotiations

Three mathematical models of two-party bargaining are developed. Each of them is based on the Bush-Mosteller linear operator model of learning. The first model includes an assumption that the probability a negotiator is cooperative is subject to Bush-Mosteller learning. The second model is basically the same as the first, except learning is assumed to depend on the reward from the other and the type of stimulus (in the form of an offer) he presents. The third model assumes that the conditional probability the negotiator is cooperative given his last offer and that of the other party is subject to learning modification. The three models were tested by having nine experimental groups of fifty subjects each negotiate with a preprogrammed stooge. The data were used to estimate the models' parameters. Computer simulations of the bargaining based on the models and their estimated parameters were run. The results of the simulations were compared with the experimental data. The simulations based on first and third models successfully predict the probability a negotiator will cooperate and the trial of agreement in the experimental groups.