Pixabay

Pixabay

One of the great workhorses in game theory is the prisoner’s dilemma. This thought experiment involves two players—Alice and Bob—who have committed a crime and are arrested. They are then separated so they cannot communicate, and each is offered a deal to snitch on the other.

But the rewards from snitching are complex. If one player snitches but the other does not, the snitcher goes free while the other spends six months in jail. If both snitch, both get three months. But if both cooperate and stay silent, they each get only one month in jail.

What is the best strategy for a player? Should he or she stay silent and cooperate, or defect and snitch?

Economists, evolutionary biologists, and game theorists have long studied the different strategies in detail. They know that in a one-off game, the best strategy is to defect and snitch, because it guarantees that this player doesn’t get the maximum sentence.

But if the game is repeated, the players can use their experience to develop new strategies: to exact revenge, for example, or to learn to cooperate. Indeed, the so-called iterated prisoner’s dilemma shows how cooperative behavior must have evolved for social creatures. That solved what was once a significant problem for evolutionary biologists.

Another as-yet-unsolved question is how exploitation must have evolved in society: how individuals end up using another to increase their own payoff.

One obvious answer is that powerful individuals can exploit the less powerful by virtue of their strength. But this suggests that exploitative behavior cannot occur between individual who are otherwise equal. And yet the sheer scale and ubiquity of exploitation suggests that exactly this must occur. How?

Today, we get an answer thanks to the work of Yuma Fujimotoa and Kunihiko Kaneko at the University of Tokyo in Japan. These guys use the iterated prisoner’s dilemma to show how one player can exploit the other to get a better payoff. They also show why the exploited player goes along with the exploitation to create a stable strategy.

First, some background. Back in 2012, game theorists discovered a strategy in the iterated prisoner’s dilemma that guaranteed one player a better outcome than the other. The specific circumstances in which this could happen were when Alice learned from previous games while Bob did not and played the same strategy. When that happens, the first player can exploit the second to guarantee a better outcome over time.

That was something of a bombshell for game theorists, who had long assumed that a symmetric outcome was inevitable. Indeed, many real-world tactics are based on this thinking, not least of which are high-stakes political strategies like mutually assured destruction, on which the future of the entire planet depends. The discovery that one player can secretly manipulate the other sent shock waves through the community.

Eventually, game theorists reassured themselves with the idea that in the real world, both sides always learn from previous experiences, so no one can become a victim in this way.

Now Fujimotoa and Kaneko show that this is wrong. They have studied an iterated prisoner’s dilemma game in which both players learn from previous experience and adapt their strategy accordingly. Their breakthrough result is that even in these circumstances, it is possible for one player to exploit the other to get a better payoff.

“We numerically and analytically demonstrate that an exploitative relationship can be achieved despite symmetric strategy dynamics and symmetric rule of games,” they say.

And curiously, this is a stable strategy. “This exploitative relationship is stable, even though the exploited player, who receives a lower payoff than the exploiting player, has optimized their own strategy,” they say.

The obvious question is how such a scenario can arise. And the answer is that it depends on the initial conditions of the game. Fujimotoa and Kaneko show that when Alice learns Bob’s strategy, she can exploit his behavior to secure a better outcome for herself.

But she can ensure Bob’s cooperation by ensuring that this strategy also secures a better outcome for him. For example, in certain circumstances Alice can ensure that Bob will have a better outcome than the one associated with both players defecting.

Because of this, Bob has an incentive to accept the exploitation, even though Alice does even better. “Thus, the exploitative relationship is stabilized by both the players,” say the researchers.

Of course, there are other possible outcomes as well, such as the exploitative behavior see-sawing between the players. Indeed, the outcomes can be complex and depend sensitively on the initial conditions.

But the key result is that exploitation itself can be a stable strategy because it secures a better outcome for both players.

That’s fascinating work that shows how exploitation can arise even when both players are seemingly equal and the conditions and rules are symmetric.

It looks as if exploitation is an inevitable property of systems in which scenarios like the prisoner’s dilemma play out. In other words, it is a basic property of human society. “This study provides a new perspective on the origin of exploitation in society,” say Fujimotoa and Kaneko.

But that doesn’t mean it is a situation we must accept. The next question this kind of work must answer is how exploitation can be avoided or what strategy exploited individuals must use to change their lot. There is clearly a lot more work to be done by game theorists.

Ref: arxiv.org/abs/1905.06602 : Emergence of Exploitation as Symmetry Breaking in Iterated Prisoner’s Dilemma

Advertisement