Adaptive Learning and Quasi Fictitious Play in “Do-It-Yourself Lottery” with Incomplete Information

Abstract

This study investigates a kind of guessing game, “do-it-yourself lottery” (DIY-L), with two types of players, adaptive learning and quasi fictitious play, by agent-based computational economics approach. DIY-L is a multi-player and multi-strategy game with a unique but skew-symmetric mixed strategy equilibrium. Here computational experiments are pursued to see what kind of game dynamics is observed and how each type of players behaves and learns in DIY-L by changing the game setup, learning parameters, and the number of each type of players. The main results are twofold: First a player who firstly and immediately learns to keep submitting the smallest integer becomes a winner in three-player games. Second, in four-player games, while the quasi fictitious play agent wisely wins when the other three players are all adaptive learners, one of the adaptive learners successfully makes advantage of the behaviors of quasi fictitious play agents when there are plural quasi fictitious play agents.