The entries here combine two very different kinds of evidence. One kind is mathematical theorems, proved results about what is possible when self-interested players interact. The other is experiments that put real people into those situations and watch what they do. The gap between the two is the most interesting thing in the group.
What can be proved
The theorems give strategic reasoning its foundations. Von Neumann's Minimax Theorem shows that two-person zero-sum games have a stable solution. Nash's equilibrium and bargaining solution extend that to many players and to dividing a surplus. The Shapley Value gives a principled way to split joint gains by each member's contribution. The Folk Theorem shows that almost any cooperative outcome can be sustained when a relationship repeats indefinitely. Aumann's Agreement Theorem proves that rational people with shared priors cannot agree to disagree.
The auction results are the most practical. The Vickrey Auction shows that charging the winner the second-highest bid makes honest bidding the best strategy, and Revenue Equivalence shows very different formats raising the same expected revenue under standard conditions.
What people do
The experiments show people departing from the narrowly self-interested player of the theorems, and doing so consistently. In the Ultimatum Game, people reject unfair offers even though rejecting costs them money. In the Dictator Game, most people share when they need not. The Trust Game finds people sending money to strangers and strangers returning it. The Public Goods Game with Punishment and Third-Party Punishment show people paying to punish free riders, including ones who never harmed them, and cooperation surviving only where that punishment is possible.
A few entries record where people fall short of the theory in the other direction. The Winner's Curse catches the bidder who most overestimated what was on offer. The Nibble exploits the reluctance to reopen a deal already agreed, and Zero-Sum Framing produces conflict over a surplus that could have been shared.
Where it applies
Auction theory is among economics' most successful applications, used to design government sales of radio spectrum and recognised with the 2020 Nobel prize for Milgrom and Wilson. The Shapley value is used to allocate shared costs and, in machine learning, to attribute a model's output to its inputs. The experimental findings matter to anyone designing a workplace, a tax system or an online community, because they show that people will enforce fairness at their own expense if the structure lets them. Anyone who negotiates meets the nibble and the winner's curse sooner or later.
Where it is argued over
The experiments' generality is the main dispute. Henrich and colleagues ran the ultimatum game in fifteen small-scale societies and found offers and rejections varying widely with local economic life, so the laboratory results describe some populations better than others. Giving in the dictator game falls sharply when participants are also allowed to take, which suggests part of it reflects what the experiment seems to ask for. Aumann's theorem is proved, but its assumptions of shared priors and common knowledge rarely hold in real disagreements, which is itself informative.
Why it is worth knowing
The theorems say what is possible for rational players; the experiments say what real people do. Most practical strategy lives in the space between them: designing rules that work for the players people actually are. A reader who knows both halves avoids two mistakes, expecting pure self-interest from people who care about fairness, and expecting fairness from structures that give nobody a way to enforce it.
The entries behind this essay: Evidence in Games & Strategic Interaction. Every subject has its essays on the essays page.