Adaptive Learning and Quasi Fictitious Play in “Do-It-Yourself Lottery” with Incomplete Information - Advances in Social Simulation - page 222

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

Takashi Yamada and Takao Terano

Department of Computational Intelligence and Systems Science,
Interdisciplinary Graduate School of Science and Engineering,
Tokyo Institute of Technology
4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa, 226-8502 Japan
[e-mail], [e-mail]

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 eco-
nomics approach. DIY-L is a multi-player and multi-strategy game with
a unique but skew-symmetric mixed strategy equilibrium. Here compu-
tational 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 ad-
vantage of the behaviors of quasi fictitious play agents when there are
plural quasi fictitious play agents.

1 Introduction

J.D. Barrow introduces a guessing game called “do-it-yourself lottery” (DIY-L)
where players choose and submit one positive integer and the one choosing the
smallest number that is not chosen by anyone else is the winner [1]. When one
rebuilds this lottery so that it has an upper limit and the number of players is
fixed, (s)he can express it as a game. More precisely, DIY-L is a multi-player,
multi-strategy and non-cooperative general-sum game with unique mixed strat-
egy equilibrium. Besides, since this is a guessing game, it is usually iterated
several times and players are expected to think how others will choose an inte-
ger not given foregone choices of others to win.
Multi-player and multi-strategy game situations are quite common in socio-
economic systems. But, they have not been studied as deeply as 2 2 ones because

multi-player games are considered more complex [3,11,13]. Or, one may have to

×