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relatively sophisticated but not perfectly rational behaviors ironically prevent
from winning the game; The QFP agents are likely to submit the smallest inte-
ger with the largest expected payoff. One AL player then learns that choosing
2, not 1, is more appropriate. As a result, unlike in three-player DIY-L with two
(or more) QFP players, the way of thinking of AL players, but only for one of
them, can make advantage of the cleverer thinking and behavior of QFP players
in the end.
4 Concluding Remarks
This study investigates Barrow's “do-it-yourself lottery” with two types of play-
ers by agent-based computational approach. In a game with incomplete infor-
mation, players cannot know the past plays of others but they can imagine how
others behave from their own plays and the game results. Here we incorporate
adaptive learning and quasi fictitious play into DYI-L and implement compu-
tational experiments by changing the game setup and the learning parameters.
Our preliminary results show that sophistication works well only when other
players are all adaptive in four-player games. In other words, adaptive player(s)
can win the game as quasi fictitious play agents increase. On the other hand,
three-player games are something like “on a first-come-first-served basis.”
Acknowledgment.
We thank two anonymous referees for useful comments
and suggestions. Financial support from Japan Society for the Promotion of
Science (JSPS) Grant-in-Aid for Young Scientists (B) (24710163), from Canon
Europe Foundation under a 2013 Research Fellowship Program (Yamada), and
from JSPS and ANR under the Joint Research Project, Japan - France CHO-
RUS Program, “Behavioural and cognitive foundations for agent-based models
(becoa)” (Terano) is gratefully acknowledged.
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