A common real-life problem is to fairly allocate a number of indivisible objects and a fixed amount of money among a group of agents. Fairness requires that each agent weakly prefers his consumption bundle to any other agent's bundle. In this context, fairness is incompatible with budget-balance...

We show that the characterization result of the weak core correspondence in simple games in Takamiya et al. (2018) still holds true even when the set of alternatives contains uncountably infinite elements

We provide a new proof of the non-emptiness of approximate cores of games with many players of a finite number of types. Earlier papers in the literature proceed by showing that, for games with many players, equal-treatment cores of their "balanced cover games", which are non-empty, can be...

This chapter surveys a sizable and growing literature on coalition formation. We refer to theories in which one or more groups of agents (“coalitions”) deliberately get together to jointly determine within-group actions, while interacting noncooperatively across groups. The chapter describes...

In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up-which are aggregated by a voting rule into a dichotomous...

This paper defines the concept of feedback Kant-Nash equilibrium for a discrete-time model of resource exploitation by infinitely-lived Kantian and Nashian players, where we define Kantian agents as those who act in accordance with the categorical imperative. We revisit a well-known dynamic...

In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up-which are aggregated by a voting rule into a dichotomous...

We introduce the prediction value (PV) as a measure of players' informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player i's prediction value equals the difference between the conditional...

We consider a committee that consists of n members with one person one vote approving a proposal if the number of affirmative votes from the members reaches threshold k. Which threshold k between 1 and n is "good" for the committee? We suppose that if a new threshold k' proposed by some...

The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in the input and the output. The corresponding games are...