Ivars Peterson's MathTrek

April 26, 1999

# A Viral Dilemma

You might think that selfishness is a characteristically human vice. A new study, however, reveals that even viruses would rather suffer than share.

In effect, the virus is caught up in a version of the prisoner's dilemma, a widely studied game in which acting for individual advantage clashes with acting for the collective benefit.

Game theorists devised the prisoner's dilemma about 50 years ago. The players are two prisoners, arrested for a joint crime, who are being interrogated in separate rooms. The following options are available to each prisoner.

• If one of them confesses and the other does not, the confessor gets a reward and his partner gets a heavy sentence.

• If both confess, each gets a light sentence.

• If neither confesses, both have a very good chance of going free.

Each prisoner is better off confessing, no matter what he or she believes the other prisoner will do. If both confess, however, both are worse off than if neither had confessed. The result is that individuals rationally pursuing their own best interest end up with an outcome that is unfortunate for both of them.

Game theorists, social scientists, economists, and others have expended a great deal of effort studying the prisoner's dilemma because it seems to lie at the core of many social phenomena. Two stores engaged in a price war, for example, face just that sort of decision. If one store doesn't cut prices, the other can drop prices to attract customers. If it does cut prices, the other must keep pace to retain its customers. If both stores reason this way and reduce prices, both make lower profits than if neither had cut prices. Arms races between nations can pose a similar dilemma.

Biologists Paul E. Turner of the University of Valencia in Spain and Lin Chao of the University of California, San Diego have now demonstrated that a bacteria-infecting virus--the RNA phage 6--also engages in the prisoner's dilemma. The researchers describe their investigations of these primitive players in the April 1 Nature.

"A virus is a natural-born cheat that makes its living by exploiting the vital functions of a host cell," Martin A. Nowak of the Institute for Advanced Study in Princeton, N.J., and Karl Sigmund of the University of Vienna in Austria note in the same issue of Nature. "Small wonder, then, that viruses also exploit each other."

When several variants of the same virus infect a cell, they compete with one another for resources to manufacture more copies, each of its own strain. Turner and Chao worked with 6 and its mutant clone H2 in a bacterial culture. The phage 6 manufactures larger quantities of the intracellular products needed for replication than its mutant cousin H2. At the same time, the mutant has a higher "fitness" (ability to produce offspring) when it is rare.

Experiments involving different population mixtures showed that phages grown in situations where multiple infection of bacterial cells is highly probable initially increased in fitness, then evolved toward lowered fitness.

The selfish H2 virus sequesters as much as possible of the available resources, lowering the capacity of the cooperative 6 virus to reproduce and generate products for replication that both can share. In evolutionary terms, the selfish strain's denial of access by a competitor to cell resources is apparently worth a loss of fitness--a decline in its own ability to produce as many offspring as it would if the situation were less competitive.

"Our data show that fitness trade-offs consistent with the prisoner's dilemma and other game theoretic models readily evolve in biological systems as simple as viruses," the researchers conclude. "Furthermore, the prisoner's dilemma provides a clear case for game theory to challenge the idea that natural selection should always lead to a fitness increase."

References:

Brams, S.J. 1994. Theory of Moves . Cambridge, England: Cambridge University Press.

Davis, M.D. 1997. Game Theory: A Nontechnical Introduction. Mineola, N.Y.: Dover.

Mero, L. 1998. Moral Calculations: Game Theory, Logic, and Human Frailty. New York: Copernicus.

Nowak, M.A., and K. Sigmund. 1999. Phage-lift for game theory. Nature 398(April 1):367.

Straffin, P.D. 1993. Game Theory and Strategy. Washington, D.C.: Mathematical Association of America.

Taylor, Alan D. 1995. Mathematics and Politics: Strategy, Voting, Power and Proof. New York: Springer-Verlag.

Turner, P.E., and L. Chao. 1999. Prisoner's dilemma in an RNA virus. Nature 398(April 1):441.

A collection of Web links related to the prisoner's dilemma can be found at http://www.constitution.org/pd/pd.htm.