"For some well-known games, such as the Traveler's Dilemma or the Centipede Game, traditional game-theoretic solution concepts--and most notably Nash equilibrium--predict outcomes that are not consistent with empirical observations. In this paper, we introduce a new solution concept, iterated regret minimization, which exhibits the same qualitative behavior as that observed in experiments in many games of interest, including Traveler's Dilemma, the Centipede Game, Nash bargaining, and Bertrand competition. As the name suggests, iterated regret minimization involves the iterated deletion of strategies that do not minimize regret."

--- Quite astonishingly, no mention at all of low-regret learning!

"We introduce a novel mechanism to eliminate endgame effects in repeated prisoner’s dilemma experiments. In the main phase of a supergame our mechanism generates more persistent cooperation than finite horizon or random continuation rules. Moreover, we find evidence for cooperation-enhancing “active/reactive” strategies which concentrate in the initial phase of a supergame as subjects gain experience."

"Many real-life social dilemmas contain third parties who cannot make decisions in the dilemma, but are affected by its outcome (receive externalities) nonetheless. Dilemmas with identical payoffs for decision-making actors may greatly vary in their externalities for third parties. If actors value the welfare of thirds, externalities will affect actors’ decisions. ... two studies that employ four one-shot, 2-person prisoner’s dilemmas (PDs) that differ only in their externalities. The PDs respectively include a third party that (i) is indifferent, (ii) prefers defection, (iii) prefers cooperation. Our results show that while aggregate behavior is not affected by externalities, individual behavior is. Compared to a PD without externalities, prosocial individuals cooperate more when a third benefits from cooperation, but do not defect more when a third benefits from defection. The opposite pattern is found for competitive individuals."

Similar dynamics apply to religions, too, of course.

"problem of learning in repeated general-sum matrix games when a learning algorithm can observe the actions but not the payoffs of its associates. ... non-stationarity of the environment caused by learning associates in these games, most state-of-the-art algorithms perform poorly ... due to an inability to make profitable compromises.=,,, agent must effectively balance competing objectives, including bounding losses, playing optimally with respect to current beliefs, and taking calculated, but profitable, risks. ... we present ... M-Qubed, a reinforcement learning algorithm ... balancing best-response, cautious, and optimistic learning biases... learns to make profitable compromises across a wide-range of repeated matrix games played with many kinds of learners... average payoffs meet or exceed its maximin value in the limit.., in two-player games... average payoffs approach the value of the Nash bargaining solution... robust behavior in round-robin and evolutionary tournaments..."

Preprint, subsequently published Games and economic Behavior 30 (2000): 44--63

"We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. ... the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. ... obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary."

"This paper analyzes communication with a language that is vague in the sense that
identical messages do not always result in identical interpretations. It is shown that
strategic agents frequently add to this vagueness by being intentionally vague, i.e. they
deliberately choose less precise messages than they have to among the ones available
to them in equilibrium. Having to communicate with a vague language can be welfare
enhancing because it mitigates conflict. In equilibria that satisfy a dynamic stability
condition intentional vagueness increases with the degree of conflict between sender
and receiver."

Truly excellent book on mathematical models of herding, information contagion, etc. under rational choice, by a friend of family.

"We prove game-theoretic generalizations of some well known zero-one laws. Our proofs make the martingales behind the laws explicit."

Only papers, not books.

"we need to look beyond Bayesian decision theory for an answer to the general problem of making rational decisions under uncertainty....assuming that the decision-maker is not able to decide mathematically undecideable propositions."

Please stop making revealed preferences arguments when peoples' choices interact. _Thank_ you.