Core and coalitional fairness: the case of information sharing rules

Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies

“…The study of c-fair allocations in mixed markets with asymmetric information is not new. For example, positive results in the presence of atoms are provided in Donnini, Graziano, and Pesce (2014) and Bhowmik (2015), among others. To best of our knowledge, the fairness of ex-ante core allocations has not been studied in relation to asset market economies.…”

“…Also, in the case where the initial endowment is spread over a continuum of small agents, atoms can arise if agents combine in non negligible large coalitions (see Gabszewicz and Shitovitz 1992). 5 Compare Evren and Hüsseinov (2008); related papers include Hervés-Beloso et al (2000) and Hervés-Beloso, Moreno-García, and Yannelis (2005), Pesce (2010), Bhowmik and Cao (2013), Bhowmik (2015), Bhowmik and Graziano (2015). 6 This idea was proposed by Varian (1974), (see also Schmeidler and Vind 1972) and, although on a slightly different basis, by Gabszewicz (1975) and was developed in Bhowmik (2015).…”

Coalitional extreme desirability in finitely additive economies with asymmetric information

“…The following assumption is referred to as nested condition in the literature for information sharing rules in individualistic economies, refer to [2,11,22]. It also appeared in a coalitional model of Basile et al [7], representing the intuitive idea that the state of information can never decrease if coalitions share their private information.…”

“…, we assume that the information F F of a coalition F is given by a rule that depends on the private information of each of its members. It is well known that the information of an agent can be different for different coalitions and it is captured by an information sharing rule, refer to [2,11,22]. Thus, the information of an agent t in F may be different from their initial private information.…”

“…We can now define F F to be the σ-algebra generated by common refinement of information partitions of members of F given by any information sharing rule. If the information sharing rule is nested (see, for example, Definition 5.3 in [2] or the assumption (P 2 ) in [11]) then [A.2] is trivially satisfied. For various information sharing rules satisfying the nested property, we refer to Table 1 in [11, p. 481].…”