Learning in “Do-It-Yourself Lottery” with Full Information: A Computational Study

We study the kind of dynamics players using a belief-based learning model lead to in Barrow’s “do-it-yourself lottery” by an agent-based computational economics approach. The lottery is that players choose a positive integer that is expected to be the smallest, but no one else chooses. For this purpose, we consider a simple game form in which every player knows all players’ submissions at the time of their decision making. We use computer simulations to change the game setup and the parameters of the learning model. Our main findings are twofold: First, the distributions of the submitted and winning integers are different from those in equilibrium in many cases. Second, the game patterns are contingent upon the two parameters in the learning model and the game setup itself: While a lower-sensitivity parameter value often leads to a somewhat randomized behavior, in the case of a higher-sensitivity parameter, the collective behavior is either a single pattern or plural ones.