Team:HZAU-China/eco/2

     Before presenting the four types of possible GMO markets, we have some assumptions to make, some of which are to simplify questions.

     First, assume that the value of a GMO contains solely of one factor, the safety condition. Namely, we assume that the consumers only worry about the safety conditions of GMOs, so as long as the GMO is safe, it has value.

     Second, we omit the difference of GMO companies and GMO sellers and GMO developers, and call them by ``GMO seller''.

     Third, we assume that both the GMO sellers and the GMO consumers follow sequential rationality [23], namely, they all expect maximum payoff in every one of their choice.

     Fourth, we assume that the information is complete, which means that, both the sellers and the consumers know the type, strategies and payoffs of each other.

     Fifth, we assume that consumers are perfectly rational (to know more about the word rationality, see [24] or [25]), so their belief of the GMO safety condition could be said to reflect the intrinsic safety condition of said GMO.

     We can draw the outline of these four types of markets under the above assumptions.

     \begin{figure}[!htb] \small \centering \includegraphics{jueceshu.jpg} \caption{The decision process} \label{fig:aa} \end{figure}

     Suppose that there are roughly two kinds of GMOs, one that is intrinsically safe whose value is $A$, another that is intrinsically not so safe and may be hazardous whose value is $B$, and $A>B$. Since any consumer will want to buy the safe products and not the unsafe, so any seller of GMO will try to make the product as safe-looking as possible; and since the consumers cannot tell which category the product belongs to by simply looking at it in the market, the seller of the unsafe product will be able to pull off as the safe, and therefore the safe and unsafe products all share the same level of price $P$, but pretending to be safe will generate a certain cost of $W$, and $A>P>B$. The probability of consumer $x$ believing that GMO $y$ being safe is $p_{safe}$, the probability of consumer $x$ believing GMO $y$ to be unsafe is $p_{unsafe}$ ($x$ and $y$ being random). If we further assume that the consumers are perfectly rational, then their belief could be said to reflect the virtual safety condition of GMO.

     And a decision tree could be drawn:

     According to Shiyu Xie, the market equilibrium of a game under complete but imperfect information can be divided into four types by market efficiency: total failure, total success, near failure, partial success [22]. The four types of market are determined by the parameters $A$, $B$, $C$, $p_{safe}$, and $p_{unsafe}$.

2.1 Partial Success

     Suppose that the consumer believes that the probability of unsafe GMO occurring in the market $p_{unsafe}$ is small. Suppose, however, that the pretending cost of the unsafe product $C$ is also very small comparing with the selling price $P$. This is to say that the unsafe products can easily sneak into the market without much additional cost while the consumers trust and are optimistic about the GMO market.

     The consumer’s payoff $\pi$ if he decides to buy a certain GMO will then be $p_{safe}(A-P)+p_{unsafe}(B-P)$. since $A>P>B$ and here we suppose that $p_{unsafe}$ is small, then $\pi>0$. If the consumer decides not to buy, then his payoff will be that $\pi=0$. So as long as the GMO is sold, he will choose to buy it.

     Now back trace to the GMO seller’s decision. Because the above track of decision routes can be deducted by the GMO sellers, they will know that their products can be sold if they choose to sell it. So, will they? If its product is safe, the payoff for selling it will be $P$, $P>0$, which is the payoff if it chooses not sell, and its rational choice will be to sell. If its product is not safe, then the payoff of selling will be $P-C$, which is still greater than $0$ since $C$ is assumed to be small, so it will still choose to sell it.

     In this situation, the GMO sellers will sell their products regardless of their virtual safety condition, and the consumers will buy whatever that is presented to them by these sellers.

     In a GMO market like this, the conducts of the sellers do not reflect the safety condition of the GMO they sell, however, since the unsafe GMOs are not very prevailing (small $p_{unsafe}$), the buyers and sellers both can have a positive payoff in most times, though the consumers can sometimes stumble upon the unsafe GMO.