Fairness and fuzzy coalitions

In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies

This paper analyses two properties of the core in a two-period exchange economy under uncertainty: the veto power of arbitrary sized coalitions; and coalitional fairness of core allocations. We study these properties in relation to classical (static) and sequential (dynamic) core notions and apply our results to asset markets and asymmetric information models. We develop a formal setting where consumption sets have no lower bound and impose a series of general restrictions on the first period trades of each agent. All our results are applications of the same lemma about improvements to an allocation that is either non-core or non-coalitionally fair. Roughly speaking, the lemma states that if all the members of a coalition achieve a better allocation in some way (for instance, by blocking the status quo allocation or because they envy the net trade of other coalitions) then an alternative improvement can be obtained through a perturbation of the initial improvement.

Mechanism Design for Multi-Type Housing Markets with Acceptable Bundles

We extend the Top-Trading-Cycles (TTC) mechanism to select strict core allocations for housing markets with multiple types of items, where each agent may be endowed and allocated with multiple items of each type. In doing so, we advance the state of the art in mechanism design for housing markets along two dimensions: First, our setting is more general than multi-type housing markets (Moulin 1995; Sikdar, Adali, and Xia 2017) and the setting of Fujita et al. (2015). Further, we introduce housing markets with acceptable bundles (HMABs) as a more general setting where each agent may have arbitrary sets of acceptable bundles. Second, our extension of TTC is strict core selecting under the weaker restriction on preferences of CMI-trees, which we introduce as a new domain restriction on preferences that generalizes commonly-studied languages in previous works.

Matching as a Stochastic Process

Results of multi-party bargaining are usually described by concepts from cooperative game theory, in particular by the core. In one-on-one matching, core allocations are stable in the sense that no pair of unmatched or otherwise matched players can improve their incomes by forming a match. Because of incomplete information and bounded rationality, it is difficult to adopt a core allocation immediately. Theoretical investigations cope with the problem of whether core allocations can be adopted in a stochastic process with repeated re-matching. In this paper, we investigate sequences of matching with data from an experimental 2×2 labor market with wage negotiations. This market has seven possible matching structures (states) and is additionally characterized by the negotiated wages and profits. First, we describe the stochastic process of transitions from one state to another including the average transition times. Second, we identify different influences on the process parameters as, for example, the difference of incomes in a match. Third, allocations in the core should be completely durable or at least more durable than comparable out-of-core allocations, but they are not. Final bargaining results (induced by a time limit) appear as snapshots of a stochastic process without absorbing states and with only weak systematic influences.