|Since the 1980s, there has been an increasing use of games theory
in the field of finance, including stock and forex trading . The
standard assumption of perfect competition was challenged. Analysis
with the assumption of strategic interactions which uses games theory
implicitly or explicitly becomes more popular. The use of games theory
in the field of finance brings many new insights and should definitely
be encouraged. But it also means that finance specialists need to be
familiar with a new field of knowledge. Furthermore, one should also
caution that games theory itself is a relatively new field and many of the
game theoretic solution concepts are still being researched, refined and
revised, and are not without controversy.
|I would like to give an example of a paper that relies on the use
of a controversial game theoretic concept. That controversial concept
is mixed strategy equilibrium, a fact well known among games
theorists . The paper I quoted below is Dezsi . This is of course
not denying the interesting and insightful results that the study had
generated. The paper models the strategic interactions between a stock
market manipulator and the National Securities Commission, the
regulatory authority. It is a complete information simultaneous game.
The manipulator chooses between manipulating the stock market for
private gains and not doing so . The National Securities Commission
chooses between investigation in the stock market to punish and deter
manipulation or not doing so. There is no pure strategy equilibrium.
There is a unique mixed strategy equilibrium in which both the
manipulator and the National Securities Commission randomizes.
While the results are interesting, further examination reveals certain
anomalies that are common to models involving the use of mixed
|The unique mixed strategy equilibrium is
|Note that when the gains from market manipulation (r) increases
and finally equals to the fine (a) imposed by the National Securities
Commission, and when the cost of investigation (c) incurred by
the National Securities increases and finally equals to the gains of
investigation a + com(1−α ) , the unique mixed strategy equilibrium has the manipulator playing manipulation with greater probability and
with certainty when r equals a and, the National Securities Commission
playing investigation with greater probability and with certainty when
c= a + com(1−α ) . The problem, however, is that when c equals to
a + com(1−α ) , we have c−a =α .com > 0 . That being the case, from
the payoff matrix, it is clear then the strategy Investigate is weakly
dominated by the strategy Not Investigate. As such, the equilibrium
result that strategy Investigate is played with probability one is
implausible. On the other hand, when r decreases and equals to 0 and
c decreases and equals to 0, the mixed strategy equilibrium becomes
p=0 and q=0. Yet, in this case, NI is weakly dominated by I and the
unique mixed strategy equilibrium is again implausible. Of course, such
anomalies of mixed strategy equilibrium are well known among games
theorist (Table 1).
|In sum, there is a lot to gain for researchers to be more familiar with
games theory and apply it to the field of finance.
- Aumann RJ (1985) What is game theory trying to accomplish? K. Arrow and S. Honkapohja (eds.), Frontiers of Economics, Basil Blackwell, Oxford.
- Benabou R, Roland, Laroque G (1992) Using privileged information to manipulate markets: insiders, gurus and credibility. The Quarterly Journal of Economics 107: 921-958.
- Dezsi D (2011) A game theory model of stock exchange market manipulation. International Conference of Scientific Paper AFASES 2011, Brasov.
- Vila JL (1989) Simple games of market manipulation. Economics Letters 29: 21-26.