Credible group stability in many-to-many matching problems

It is known that in two-sided many-to-many matching problems, pairwise-stable matchings may not be immune to group deviations, unlike in many-to-one matching problems (Blair, 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise-responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.     

Endogenous party structure

This paper proposes a model of two-party representative democracy on a single-dimensional political space, in which voters choose their parties in order to influence the parties’ choices of representative. After two candidates are selected as the median of each party’s support group, Nature determines the candidates’ relative likability (valence). Based on the candidates’ political positions and relative likability, voters vote for the preferable candidate without being tied to their party’s choice. We show that (1) there exists a nontrivial equilibrium under natural conditions, and (2) the equilibrium party border and the ex ante probabilities of the two-party candidates winning are sensitive to the distribution of voters. In particular, we show that if a party has a more concentrated subgroup, then the party tends to alienate its centrally located voters, and the party’s probability of winning the final election is reduced. Even if voter distribution is symmetric, an extremist party (from either side) can emerge as voters become more politically divided.