Ryo Kawasaki

Farsighted stable sets in Hotelling’s location games☆

We apply the farsighted stable set to two versions of Hotelling’s location games: one with a linear market and another with a circular market. It is shown that there always exists a farsighted stable set in both games, which consists of location profiles that yield equal payoff to all players. This stable set contains location profiles that reflect minimum differentiation as well as those profiles that reflect local monopoly. These results are in contrast to those obtained in the literature that use some variant of Nash equilibrium. While this stable set is unique when the number of players is two, uniqueness no longer holds for both models when the number of players is at least three.

Farsighted stability of the competitive allocations in an exchange economy with indivisible goods

The set of competitive allocations in an exchange economy with indivisible goods of Shapley and Scarf (1974) is an important solution concept in the literature. In this paper, we consider a farsighted version of the von Neumann and Morgenstern stable set by using the farsighted approach of Chwe (1994) and by modifying the domination relation defined by Wako (1999) to incorporate farsightedness. We show that there exists a unique farsighted stable set, which coincides with the set of competitive allocations.

Generalized average rules as stable Nash mechanisms to implement generalized median rules

We consider a problem in which a policy is chosen from a one-dimensional set over which voters have single-peaked preferences. While Moulin (Public Choice 35:437–455, 1980) and others subsequent works have focused on strategy-proof rules, Renault and Trannoy (Mimeo 2011) and Renault and Trannoy (J Pub Econ Theory 7:169–199, 2005) have shown that the average rule implements a generalized median rule in Nash equilibria and provide an interpretation of the parameters in Moulin’s rule. In this article, we first extend their result by showing that a wide range of voting rules which includes the average rule can implement Moulin’s rule in Nash equilibria. Moreover, we show additionally that within this class, generalized average rules are Cournot stable. That is, from any strategy profile, any best response path must converge to a Nash equilibrium.

Dynamics, stability, and foresight in the Shapley-Scarf housing market

While most of the literature starting with Shapley and Scarf (1974) have considered a static exchange economy with indivisibilities, this paper studies the dynamics of such an economy. We find that both the dynamics generated by competitive equilibrium and the one generated by weakly dominance relation, converge to a set of allocations we define as strictly stable, which we can show to exist. Moreover, we show that even when only pairwise exchanges between two traders are allowed, the strictly stable allocations are attained eventually if traders are sufficiently farsighted.

Maximin, minimax, and von Neumann–Morgenstern farsighted stable sets☆

In this note, we investigate the relationship between the classical concepts of maximin and minimax, which were originally defined in the context of zero-sum games in von Neumann and Morgenstern (1953), and the von Neumann–Morgenstern (vNM) farsighted stable set using the indirect domination defined in Chwe (1994). We show two main results for two-player games: an existence result and an almost-uniqueness result. Under a mild assumption, we show that any strategy profile that is Pareto efficient and strictly individually rational–that is, strictly above each player’s maximin value–is generically a singleton vNM farsighted stable set. Moreover, there does not exist a vNM farsighted stable set that includes a strategy profile that is strictly individually rational and yields a payoff greater than the minimax value for a player, but not Pareto efficient.

Farsightedly stable tariffs

This article analyzes the tariff negotiation game between two countries when the countries are sufficiently farsighted. It extends the research of Nakanishi (2000) and Oladi (2005) for the tariff retaliation game in which countries take into account subsequent retaliations that may occur after their own retaliation. We show that when countries are sufficiently farsighted, all farsighted stable sets of the tariff game of Nakanishi (2000) are singletons, which are Pareto efficient and strictly individually rational tariff combinations. These results hold regardless of whether coalitional deviations are allowed or not.