A Third Way. What Happens When Competition Enters the Prisoner’s Dilemma?

By Dr. Alfonso de Miguel

Imagine two firms in a supply chain that depend on each other to keep goods moving efficiently. If both share information, coordinate schedules, and honor their commitments, the interaction creates value for both sides. But each side may also be tempted to pursue a short-term advantage by shifting costs, withholding information, or taking advantage of the other’s effort.

This kind of tension - between cooperation and exploitation, between what benefits the individual and what benefits the relationship as a whole - lies at the heart of many economic interactions. One of the most famous models used to think about such dilemmas is the Prisoner’s Dilemma. For decades, it has helped researchers think about how cooperation can emerge, survive, or collapse in social, economic, and biological systems.

Yet many real-world interactions involve more than a simple choice between cooperation and exploitation. People, firms, and institutions also compete for resources, influence, and rewards. This is the domain of Contest Theory, a branch of economics and game theory that studies situations in which success depends on how much individuals invest in competition. More formally, it looks at contests in which participants commit effort or resources, and their chances of success depend on those relative investments.

Our recent work brings these two perspectives together. We ask what happens when the classic Prisoner’s Dilemma is extended with a third possible behavior: not just cooperation and defection, but also fighting. Here, however, “fighting” should not be taken too literally. It does not necessarily mean physical confrontation. In our model, it refers to a stylized form of explicit, rule-based competition over resources. This distinction matters. Defection, in this context, is better understood as exploitative behavior: gaining at the expense of someone else. Fighting, by contrast, represents a contest in which both sides put something at stake and each has a chance of winning. That is very much in the spirit of Contest Theory and the mathematical formalism we use in the paper.

To explore this idea, we built an idealized model in which agents repeatedly interact with their neighbors and adapt their behavior over time. Each agent can adopt one of three strategies: cooperate (C), defect (D), or fight (F). Cooperators generate mutual gains when they interact with one another. Defectors exploit cooperators for their own benefit.

Fighters, meanwhile, engage in contests over resources. When a fighter interacts with another player, both sides invest part of their available resources, and the winner is decided probabilistically: investing more improves one’s chances, but it does not guarantee victory.

In that sense, the model distinguishes between two very different kinds of “non-cooperation.” One is exploitative: taking advantage of someone who cooperates. The other is competitive: entering a contest in which both sides commit resources under the same rules. That distinction, although simple, opens up a much richer picture of strategic behavior than the usual cooperation-versus-defection setting.

The model is also evolutionary. Agents do not keep the same strategy forever. As interactions repeat, they can compare how well they are doing with respect to their neighbors, and may then switch strategy with some probability. In that sense, better-performing strategies tend to spread, but not in a perfectly mechanical or fully rational way.

What we found is a surprisingly rich landscape of possible outcomes. The model displays up to five distinct long-run regimes. Some are familiar from the standard Prisoner’s Dilemma: one phase of full cooperation, and another in which cooperators and defectors coexist. But once competition is introduced, new possibilities appear. There is a regime in which cooperators and fighters coexist while defectors disappear, and another, narrower region in which all three strategies coexist. There is also a regime we call the dead economy, where cooperators disappear entirely. Since cooperation is the only mechanism in the model that actually creates new wealth through mutually beneficial interaction, its extinction leaves a system in which resources are only contested, redistributed, and depleted. In that case, long-run payoffs collapse.

One of the most interesting results is that competition does not simply destroy cooperation. Under some conditions, it can actually help delay the dominance of defectors. In the standard Prisoner’s Dilemma, once the temptation to defect becomes large enough, defectors tend to overwhelm cooperators. In our extended model, however, the presence of fighters can push that dominance to higher values of temptation, effectively enlarging the region in which cooperation remains viable. In other words, explicit contest-based competition can, somewhat counterintuitively, protect cooperation from purely exploitative behavior.

At the same time, more competition is not always better for competitors themselves. Fighters only survive if the investment in contests is above a critical threshold. But beyond

a certain point, investing even more becomes counterproductive: the fighter population first grows, reaches an optimum, and then declines again. This is one of the nonlinear effects revealed by the model, and it suggests that competition, too, can become excessive.

Of course, this is an abstract theoretical model, not a literal portrait of social life. But that is precisely its value. By stripping the problem down to a few essential mechanisms, the model helps us think more clearly about different ways in which cooperation, exploitation, and competition interact. Not all forms of non-cooperation are the same. Some destroy value by exploiting others; others redistribute opportunities through open contests; and under some conditions, those differences can reshape the collective outcome in surprising ways.