This paper presents a dynamic model of endogenous coalition formation in cooperative games with transferable utility. The players are boundedly rational. At e a c h time step, a player decides which of the existing coalitions to join, and demands a payo . These decisions are determined by a best{reply rule, given the coalition structure and allocation in the previous period. Further, the players experiment with myopically suboptimal strategies whenever there are potential gains from trade. We establish an isomorphism between the set of absorbing states of the process and the set of core allocations, and show that the process converges to one of these states with probability one whenever the core is non{empty. These results do not require superadditivity of the characteristic function, and they carry over to the case of coalitional values depending on the coalition structure.

In the modern literature on game theory there are several versions of what is known as Zermelo's theorem. It is shown that most of these modern statements of Zermelo's theorem bear only a partial relationship to what Zermelo really did. We also give a short survey and discussion of the closely related but almost unknown work by König and Kálmar. Their papers extend and considerably generalize Zermelo's approach. A translation of Zermelo's paper is included in the appendix.

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This paper discusses whether self-learning price-setting algorithms can coordinate their pricing behavior to achieve a collusive outcome that maximizes the joint profits of the firms using them. Although legal scholars have generally assumed that algorithmic collusion is not only possible but also exceptionally easy, computer scientists examining cooperation between algorithms as well as economists investigating collusion in experimental oligopolies have countered that coordinated, tacitly collusive behavior is not as rapid, easy, or even inevitable as often suggested. Research in experimental economics has shown that the exchange of information is vital to collusion when more than two firms operate within a given market. Communication between algorithms is also a topic in research on artificial intelligence, in which some scholars have recently indicated that algorithms can learn to communicate, albeit in somewhat limited ways. Taken together, algorithmic collusion currently seems far more difficult to achieve than legal scholars have often assumed and is thus not a particularly relevant competitive concern at present. Moreover, there are several legal problems associated with algorithmic collusion, including questions of liability, of auditing and monitoring algorithms, and of enforcing competition law.

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