I came from a small town in China. As I lived with my grandparents for a long time, I have heard about quite a few things in my hometown and the problem that held the strongest impression is the “gambling” problem. While it is called the “gambling problem”, it is actually people playing games such as majiang and poker while betting money on them. Discussion around this problem has become more and more severe over the years: many people think that this is a tradition for people to bet and the “gambling” part has become an leisure activity rather than an illegal activity. Others argued that gambling always causes great loss to some families and people will use immoral means to gain advantage for themselves when gambling which make the game not fair. I am doing this research as I want to find how much harm this activity has brought on people’s family and also how much of a tradition this is and I wish I dig deeply in the harm and happiness this activity brought to Chinese common men, or just the gambling problem in general.
This issue should receive increased attention from others as thousands of families are breaking apart while no one really consider this seriously: many people belief that gambling will not make people lose too much money as they thought no one will want to play a losing game. However the dark side of this is the “makers”(owners/ set-up person of gambling) will make people win some amount of money by manipulation of the game which seduce them into putting more money into the game and people will not be rational once they win too much: I have seen many cases where people become greedy and receive a huge lost. At the other hand,Chinese government, which is indeed very worried about this issue, has no way of resolving it without cooperation: the gambling sites can quickly be relocated and the makers will often use fake IDs when registering for companies. Therefore people should look into this issue and contribute in order to save those gambler’s from makers’ hands.
Lets take the game from two perspective: government and ordinary male that gambles. Government has three actions in total:
A: ban gamble
B: restrict gamble
C: Do nothing
And the gambler has three options:
D: Continue gambling
E: Gamble with reduced amount of money
F: Stop gamble
We assign the payoff as (x,y) = (payoff to gambler, payoff to government)
|F||(10, -15)||(15, -10)||(15,15)|
Reasoning for values:
For AD, it is the worse case scenario where gamblers don’t stop gambling which causes government to spent a lot of fund in arresting gamblers because of its policy and gamblers to be arrested in large amount because of government’s policy. There a -50 for gambler and -20 for government will be suitable.
For AE, government will have a much better time of catching the gamblers with reduced activities– their workload will reduce a lot. Similarly for gamblers their lost will decrease because people give up gambling. A (-30,-15) would be suitable.
For AF, although government don’t need to catch any gamblers, they will receive social pressure from the media as they put in funds into a program but have no success as the gamblers all quit gambling. Gamblers will still obtain a positive as they stop gambling. A value of (10, -15) will be fine.
For BD , government doesn’t not enforce a strong plan to catch gamblers while gamblers don’t reduce amount of gambling at all– this mean that the government can only catch limited amounts of gamblers while the gamblers doesn’t receive much lost. Therefore a value of (-5,-15) will be good.
For BE, it is a semi- win win situation: gamblers reduced their size while government receive a good reputation for effectively reducing the gambling( it is not true- a lot of gamblers quit themselves in this case.) On the gamblers side, the minimal effort by government on stopping gambling will serve as a warning and as they start to quit themselves it will likely reduce the amount of gambling by a significant amount, thus giving a value of (10,10).
For FA and FB, the gamblers stops gamble while the government lost reputation for investing into useless project. (10,-15) and (15,-10) according (FB has a better outcome for government and gamblers and government reduce their effort of trying to catch gamblers.)
For FC it is the harmonic scenario- people and government both do no actions and everything is good. Value will be (15,15)
Now we first find equilibrium by saddle point (A saddle point is a payoff that is simultaneously a row minimum and a column maximum. To locate saddle points, find the row minima and box the column maxima.)
Why is saddle point useful? Well saddle point is just a case where players chooses the strategy that maximizes her minimum payoff- just a way to play the game. If the points of ensuring minimum payoff is the same for two players, then this point will be called saddle point(s).)
Here is the picture when solving it:
CF is the saddle point of pure strategy Nash equilibrium, and it means that this is a point where both gamblers and government is content and happy to choose to.
Now considering the Nash mixed strategies, where each players play the other players game and find a point that can give them a maximal solution if others play their optimal strategy– they will obtain a value that gives them the highest expected value as long as their opponent plays rationally. In other words this is just putting yourself in other’s shoes.
Now, government will play gambler’s game and gambler will play governments game
y=7/17 but probability cant be negative– this is because there is a pure strategy solution so mixed strategy solution in theory should not exist.
Solving we get
y=-⅕ p is negative– again there will not be a mixed strategy.
The important thing to grab here is if people play rationally and consider purely their economics benefits, they should always play CF– no mixed strategy will be allowed. Thinking about it this is with simple reasoning– the CF is a point where both players receive a possible value. So why don’t choose a value that benefits both of the players? Also another thing to note is that 15 is the highest value for two players. So they are definitely contend with this value– another way of explaining this solution. (However there is limitation and it will be discussed later. )
Another very common technique of solving a non zero sum game is Pareto optimal strategy. ( Pareto strategy is just a fancy name of picking as high as possible from both of the players– the key point is that no other outcome that makes every player at least as well off and at least one player strictly better off.)
A common way to give pareto outcomes is just draw out a diagram and find the points on the line that lies out the most on the right- top corner. If we draw the graph out for the matrix we see:
The solution found implied a few things. BE suggest one of the two best case scenarios as it was best for government to implement some regulation while gamblers reduce the amount of money they put in gambling– it would be easier for them to eradicate gambling when people put less money since people’s original wish of gaining wealth from gambling will reduce, giving government an easier time eradicating it. CF suggest another best case scenario, yet unlikely– government will not ignore the gambling problem and gamblers will not give up gambling for no reason.
So how can the players carry out their solutions?
Government in the BE scenario could set high class officials to visit more isolated villages and really find the key impulse of gambling, whether it was desire to gain wealth, lack of entertainment or officials receiving bribe to allow the gambling to continue. After this government could implement solution– e.g. if desire to gain wealth is the key cause, government can easily stop this by educating people about the nature of gambling ( always losing money in a long run)
Now for the gamblers part the situation becomes more complex: let’s consider the values assigned to the matrix. Is that accurate? Well before answering this question, lets do a google form:
This google form should provide you with some basic information that shows the matrix is not always correct. Indeed gambling is very harmful to a healthy life and people should not do it and the values should be negative. But let’s say you enter gambling accidentally and you are in enormous debt. You have two choices: tell your family about this and try to work to pay the debt or keep gambling to pay off the debt. Unfortunately, the human nature will tend to choose the second choice: here is a link that explains mathematically why that happens.
Also there is a video on youtube that explains this:(mathematically, this one is quite hard to understand but still provide some insights)
Therefore the matrix values maybe amazing wrong and the solution will not hold– once someone enters the gambling world and accumulate debt, the matrix value could change to this in their mind:
|F||(-10000, -15)||(-10000, -10)||(-10000,15)|
(The government’s action does not even affect their choice as the gambler’s fallacy basically controls them.)
Therefore, there is not really any strategy that gamblers can do realistically to carry out the solution (likely controlled by that fallacy) except not entering gambling, but that itself is a contradiction. So the game is very limited to only when the gamblers are independent thinkers, not someone who is controlled under influence of gambler’s fallacy, which I believe will be quite a hard thing to do.
The finding of this research is basically “do not enter gambling”. If you enter gambling and need to carry out game theory to find what is the way out, you should always choose to give up gambling– a hard thing to do. Similarly government, assuming the gamblers are good game theorist and not under influence of the gamblers’ fallacy should not carry out any actions, which is not really realistic as the gamblers become unwise once they starts to gamble. The observation, indeed, is very depressing.
Now here is the important question: how can us, common people that are not gamblers or government officials, solve this problem( or in general solve the problem of people messing up their life by gambling). Well here are a few solutions that enable you to address this problem:
1st: if you see you friend/ family member requesting a large amount of family suddenly, ask them what happens instead of lending them money. This way a lot of tragedies could be stopped at an early stage where debt has not accumulates.
2nd: Although this might sound a little bit unnecessary, do not overuse the word “bet”. Nowadays people use the word “bet” way too much and this might influence the children as they might gradually equate bet with gambling: in fact in many cases I have seen the gamblers said they have been involving in small bets in their childhood. So please don’t overuse “bet”
3rd: Report any suspicious makers( that do not own a qualification or such). That will stop a lot of tragedies as many of those makers offer better rates than legal gambling sites- that will make people go there more often but they will also have a higher chance of manipulating the game and tricking the gamblers. So by reporting them you can ensure at least makers will not intentionally make people lose money.
A document could be download here if you feel like sharing this with your friends and family:
An amazing ted- talk link is here to explain why people are addicted to gambling: