Agent-Based Modeling of Lottery Markets
Over the past decades we witnessed a series of studies
devoted to the economic analysis of the lottery markets (Morgan and Vasche,
1979; Morgan and Vasche, 1982; Mikesell, 1994; Mason et al. 1997; McConkey
et al., 1997; Ian, 1998; Purfield and Waldron, 1999). One of the most frequently
studied issue is the demand for lottery tickets. This issue is important
because the tax revenue raised from lottery business can crucially depend
on the lottery designs, such as the “rollover”, rainfall numbers, ...,etc,
and none of these designs can be effectively evaluated without information
on the determinants of lottery demand. Many of the studies used demographic
and socioeconomic data to estimate lottery demand. However, this standard
econometric approach mainly treated the demand decision as an individual
rational choice problem. Within this framework, how many tickets one would
buy is only determined by his own personal profile, and has nothing to do
with how other people would act.
However, the real situation is not that simple.
By the usual design, the lottery prizes is a positive function of aggregate
sales. The larger the sales, the larger the rizes. When agents are not expected
utility maximizers, and the purchasing decision is not so much dependent
on the sophisticated calculation of the winning odd, the giant prizes, in
particular, the huge jackpot, appearing occasionally, may excite a large
group of prospective agents. The gossip added to the jackpot by mass medium
will further compound the alert. As a result, more people may decide to get
in when they can no longer resist the temptation, which then makes the jackpot
even more glamorous, and convince more people to buy, and on and on. This
defines a self-reinforcing process as the one we experienced in the stock
market. Depending on the lottery designs, there are other things, such as
unlimited rollover widely accepted in many lottery markets, can fuel the
lottery boom. The self-reinforcing mechanism can work in the other direction
as well, and turn the market (and tax revenue) into a losing streak. This
may also help explain why lottery demand can sometimes be fluctuating and
unstable.
The essence of this discussion is that the
lottery market is more complicated than just the scaling-up aggregation of
individuals' independent decision. Rather, it is a market composing of many
highly interacting agents whose decisions are inevitably interdependent.
In modeling, a room for imitation, fashion and contagion should be allowed
for. More generally, agents' preference for lottery should be adaptive and
evolving rather than fixed. By the same token, one should model agents as
an adaptive agents who, based on their past experience, are continuously
updating their anticipation of the value of lottery tickets, and revising
their decisions accordingly. With this motivation, we propose an agent-based
computational modeling of the lottery market. Using genetic algorithms, we
are able to capture the decisions of lottery demand made by adaptive agents
in a highly interactive environment, and simulate the time series of the
aggregate sales of a lottery. The effect of the lottery design on tax revenue
can also be analyzed using this agent-based simulation. Empirical data
from Taiwan National Lottery will be used to examine the performance of our
agent-based model.
Shu-Heng Chen
National Chengchi University
AI-ECON Research Center
Department of Economics
http://aiecon.org
chchen@nccu.edu.tw
Bin-Tzong Chie
National chengchi University
AI-ECON Research Center
Department of Economics
http://aiecon.org
chie@aiecon.org