We show that whenever a decision maker reasons about an optimal decision he is able to find one, even with non-transitive preferences. The existence of a reasoning process allows him to strategically manipulate how he reasons. A reasoning strategy that is robust against (finite) deviations is captured by the notion of cognitive equilibrum. We show that a cognitive equilibrium exists under all complete preferences, and characterize outcomes that can be implemented within it. Cognitive equilibria employ complex cognitive strategies. Simple strategies suffice only under transitive preferences. Robustness of the model is evaluated in the language of von Neumann-Morgenstern stable sets.
While the maximin strategy has become the standard, and most agreed-upon solution for decision-making in adversarial settings, as discussed in game theory, computer science and other disciplines, its power arises from the use of mixed strategies, a.k.a. probabilistic algorithms. Nevertheless, in adversarial settings we face the risk of information leakage about the actual strategy instantiation. Hence, real robust algorithms should take information leakage into account. To address this fundamental issue, we introduce the study of adversarial leakage in games. We consider two models of leakage. In both of them the adversary is able to learn the value of b binary predicates about the strategy instantiation. In one of the models these predicates are selected after the decision-maker announces its probabilistic algorithm and in the other one they are decided in advance. We give tight results about the effects of adversarial leakage in general zero-sum games with binary payoffs as a function of the level of leakage captured by b in both models. We also compare the power of adversarial leakage in the two models and the robustness of the original maximin strategies of games to adversarial leakage. Finally, we study the computation of optimal strategies for adversarial leakage models. Together, our study introduces a new framework for robust decision-making, and provides rigorous fundamental understanding of its properties.
These papers don’t seem relevant to quining cooperation because they don’t focus on computation or quining. There’s no shortage of papers proposing new equilibrium concepts and new games to justify them with, our literature search also turned up many of them, my prior for their usefulness is low.
Other interesting papers I found by checking papers that cited Tennenholtz (2004):
Cognitive Equilibrium:
Adversarial Leakage in Games:
These papers don’t seem relevant to quining cooperation because they don’t focus on computation or quining. There’s no shortage of papers proposing new equilibrium concepts and new games to justify them with, our literature search also turned up many of them, my prior for their usefulness is low.
No, I didn’t mean to imply that these papers focus on quining.