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We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences in a way that is socially optimal and/or stable. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model where agents’ preferences are binary, i.e., each agent classifies all pairs of the form ‘(activity, group size)’ into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents’ preferences satisfy certain natural constraints. [ABSTRACT FROM AUTHOR]

In combinatorial game theory, under normal play convention, all games are invertible, whereas only the empty game is invertible in misère play. For this reason, several restricted universes of games were studied, in which more games are invertible. Here, we study combinatorial games under misère play, in particular universes where no player would like to pass their turn. In these universes, we prove that having one extra condition makes all games become invertible. We then focus our attention on a specific quotient, called QZ, and show that all sums of universes whose quotient is QZ also have QZ as their quotient. [ABSTRACT FROM AUTHOR]

This paper considers the condition of perfect recall for the class of arbitrarily large discrete extensive form games. The known definitions of perfect recall are shown to be equivalent even beyond finite games. Further, a qualitatively new characterization in terms of choices is obtained. In particular, an extensive form game satisfies perfect recall if and only if the set of choices, viewed as sets of ultimate outcomes, fulfill the 'Trivial Intersection' property, that is, any two choices with nonempty intersection are ordered by set inclusion. [ABSTRACT FROM AUTHOR]

Experimental data for two types of bargaining games are used to study the role of strategic risk in the decision making process that takes place when subjects play a game only once. The bargaining games are the ultimatum game (UG) and the yes-or-no game (YNG). Strategic risk in a game stems from the effect on one player's payoff of the behavior of other players. In the UG this risk is high, while it is nearly absent in the YNG. In studying the decision making process of subjects we use the time elapsed before a choice is made (response time) as a proxy for amount of thought or introspection. We find that response times are on average larger in the UG than in the YNG, indicating a positive correlation between strategic risk and introspection. In both games the behavior of subjects with large response times is more dispersed than that of subjects with small response times. In the UG larger response time is associated with less generous and thus riskier behavior, while it is associated with more generous behavior in the YNG. [ABSTRACT FROM AUTHOR]