What math can teach us about standing up to bullies
Game theory study shows that being uncooperative gives weaker parties the upper hand

Date:
June 27, 2023
Source:
Dartmouth College
Summary:
New research from Dartmouth takes a fresh look at game theory
to show that being uncooperative can help people on the weaker
side of a power dynamic achieve a more equal outcome -- and even
inflict some loss on their abusive counterpart. The findings
can be applied to help equalize the balance of power in labor
negotiations, international relations and everyday interactions,
as well as integrate cooperation into interconnected AI systems
such as driverless cars.


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FULL STORY ==========================================================================
In a time of income inequality and ruthless politics, people with
outsized power or an unrelenting willingness to browbeat others often
seem to come out ahead.

New research from Dartmouth, however, shows that being uncooperative
can help people on the weaker side of the power dynamic achieve a more
equal outcome - - and even inflict some loss on their abusive counterpart.

The findings provide a tool based in game theory -- the field of
mathematics focused on optimizing competitive strategies -- that could be applied to help equalize the balance of power in labor negotiations or international relations and could even be used to integrate cooperation
into interconnected artificial intelligence systems such as driverless
cars.

Published in the latest issue of the journalPNAS Nexus,the study takes
a fresh look at what are known in game theory as "zero-determinant
strategies" developed by renowned scientists William Press, now at
the University of Texas at Austin, and the late Freeman Dyson at the
Institute for Advanced Study in Princeton, New Jersey.

Zero-determinant strategies dictate that "extortionists" control
situations to their advantage by becoming less and less cooperative --
though just cooperative enough to keep the other party engaged -- and by
never being the first to concede when there's a stalemate. Theoretically,
they will always outperform their opponent by demanding and receiving
a larger share of what's at stake.

But the Dartmouth paper uses mathematical models of interactions to
uncover an "Achilles heel" to these seemingly uncrackable scenarios,
said senior author Feng Fu, an associate professor of mathematics. Fu
and first author Xingru Chen, who received her Ph.D. in mathematics from Dartmouth in 2021, discovered an "unbending strategy" in which resistance
to being steamrolled not only causes an extortionist to ultimately lose
more than their opponent but can result in a more equal outcome as the overbearing party compromises in a scramble to get the best payoff.

"Unbending players who choose not to be extorted can resist by refusing
to fully cooperate. They also give up part of their own payoff, but
the extortioner loses even more," said Chen, who is now an assistant
professor at the Beijing University of Posts and Telecommunications.

"Our work shows that when an extortioner is faced with an unbending
player, their best response is to offer a fair split, thereby guaranteeing
an equal payoff for both parties," she said. "In other words, fairness
and cooperation can be cultivated and enforced by unbending players."
These scenarios frequently play out in the real world, Fu said. Labor
relations provide a poignant model. A large corporation can strong-arm suppliers and producers such as farmworkers to accept lower prices
for their effort by threatening to replace them and cut them off from
a lucrative market. But a strike or protest can turn the balance of
power back toward the workers' favor and result in more fairness and cooperation, such as when a labor union wins some concessions from
an employer.

While the power dynamic in these scenarios is never equal, Fu said,
his and Chen's work shows that unbending players can reap benefits by
defecting from time to time and sabotaging what extortioners are truly
after -- the highest payoff for themselves.

"The practical insight from our work is for weaker parties to be unbending
and resist being the first to compromise, thereby transforming the
interaction into an ultimatum game in which extortioners are incentivized
to be fairer and more cooperative to avoid 'lose-lose' situations,"
Fu said.

"Consider the dynamics of power between dominant entities such as
Donald Trump and the lack of unbending from the Republican Party, or,
on the other hand, the military and political resistance to Russia's
invasion of Ukraine that has helped counteract incredible asymmetry," he
said. "These results can be applied to real-world situations, from social equity and fair pay to developing systems that promote cooperation among
AI agents, such as autonomous driving." Chen and Fu's paper expands
the theoretical understanding of zero-determinant interactions while
also outlining how the outsized power of extortioners can be checked,
said mathematician Christian Hilbe, leader of the Dynamics of Social
Behavior research group at the Max Planck Institute for Evolutionary
Biology in Germany "Among the technical contributions, they stress
that even extortioners can be outperformed in some games. I don't think
that has been fully appreciated by the community before," said Hilbe,
who was not involved in the study but is familiar with it. "Among the conceptual insights, I like the idea of unbending strategies, behaviors
that encourage an extortionate player to eventually settle at a fairer outcome." Behavioral research involving human participants has shown
that extortioners may constitute a significant portion of our everyday interactions, said Hilbe, who published a 2016 paper in the journal
PLOS ONE reporting just that. He also co-authored a 2014 study in Nature Communications that found people playing against a computerized opponent strongly resisted when the computer engaged in threatening conduct,
even when it reduced their own payout.

"The empirical evidence to date suggests that people do engage in these extortionate behaviors, especially in asymmetric situations, and that
the extorted party often tries to resist it, which is then costly to
both parties," Hilbe said.

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========================================================================== Story Source: Materials provided by Dartmouth_College. Original written
by Morgan Kelly.

Note: Content may be edited for style and length.


========================================================================== Journal Reference:
1. Xingru Chen, Feng Fu. Outlearning extortioners: unbending
strategies can
foster reciprocal fairness and cooperation. PNAS Nexus, 2023; 2
(6) DOI: 10.1093/pnasnexus/pgad176 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2023/06/230627123108.htm

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