Finding all equilibria in games of strategic complements

I present a simple and fast algorithm that finds all the pure-strategy Nash equilibria in games with strategic complementarities. This is the first non-trivial algorithm for finding all pure-strategy Nash equilibria

A short and constructive proof of Tarski’s fixed-point theorem

I give short and constructive proofs of Tarski’s fixed-point theorem, and of Zhou’s extension of Tarski’s fixed-point theorem to set-valued maps

Correspondence Principle

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Extensive-form games and strategic complementarities

I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a nonempty, complete lattice—in particular, subgame-perfect Nash equilibria exist. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. My results are limited because extensive-form games of strategic complementarities turn out—surprisingly—to be a very restrictive class of games

Contracts vs. Salaries in Matching

Firms and workers may sign complex contracts that govern many aspects of their interactions. I show that when firms regard contracts as substitutes, bargaining over contracts can be understood as bargaining only over wages. Substitutes is the assumption commonly used to guarantee the existence of stable matchings of workers and firms

A weak correspondence principle for models with complementarities

I prove that, in models with complementarities, some non-monotone comparative statics must select unstable equilibria; and, under additional regularity conditions, that monotone comparative statics selects stable equilibria

The relevance of ontological commitments

In this introductory note, I describe my particular view of the notion of ontological commitments as honest and pragmatic working hypotheses that assume the existence (out there) of certain entities represented by the symbols in our theory. I argue that this is not naive, in the sense that it does not entail the belief that the hypotheses could ever be proved to be true (or false), but it is nevertheless justified by the success and predictive power of the theory that contains the concepts assumed to exist. I also claim that the ontological commitments one holds (even if tacitly so) have a great influence on what kind of science is produced, how it is used, and how it is understood. Not only I justify this claim, but I also propose a sketch of a possible falsification of it. As a natural conclusion, I defend the importance of identifying, clarifying and making explicit one's ontological commitments if fruitful scientific discussions are to be had. Finally, I compare my point of view with that of some philosophers and scientists who have put forward similar notions.Comment: Submitted for peer-revie