We study equilibria in static entry games with single-dimensional private information. Our framework embeds many models commonly used in applied work, allowing for firm heterogeneity and selective entry. We introduce the notion of strength, which summarizes a firm's ability to endure competition. In environments of applied interest, an equilibrium in which entry strategies are ordered according to the firms' strengths always exists. We call this equilibrium herculean. We derive simple and testable sufficient conditions guaranteeing equilibrium uniqueness and, consequently, a unique counterfactual prediction.
We study order statistics (OS) from independent non identically distributed (INID) samples for two large classes of statistical distributions: Exponentiated Distributions (ED) and Proportional Hazard Rate Models (PHRM). We show that for the analytical solution for the CDF (PDF) of OSs in ED and PHRM: i) each OS's CDF (PDF) depends on all shape parameters; ii) the CDF (PDF) of each OS is a weighted average of CDF (PDF) within the same family and with shape parameters equal to a partial sum of the original shape parameters; and iii) the weights are integers and sum up to 1. These properties allows for a clear analytical solution and allows a simple parameter estimation in these classes of distributions.
We use data from marriage records in Murcia, Spain, in the eighteenth century to study the role of women in social mobility in the pre-modern era. Our measure of social standing is identification as a don or doña, an honorific denoting high, though not necessarily noble, status. We show that this measure, which is acquired over the lifecycle, shows gendered transmission patterns. In particular, same-sex transmission is stronger than opposite-sex, for both sons and daughters. The relative transmission from fathers versus mothers varies over the lifecycle, and grandparents may affect the status of their grandchildren.
We introduce experimental persuasion between Sender and Receiver. Sender chooses an experiment to perform from a feasible set of experiments. Receiver observes the realization of this experiment and chooses an action. We characterize optimal persuasion in this baseline regime and in an alternative regime in which Sender can commit to garble the outcome of the experiment. Our model includes Bayesian persuasion as the special case in which every experiment is feasible; however, our analysis does not require concaviﬁcation. Since we focus on experiments rather than beliefs, we can accommodate general preferences including costly experiments and non-Bayesian inference.
We study market entry decisions when firms have private information about their profitability. We generalize current models by allowing general forms of market competition and heterogeneous firms that self-select when entering the market. Post-entry profits depend on market structure, and on the identities and the private information of the entering firms. We introduce a notion of the firm’s strength and show that an equilibrium where players’ strategies are ranked by strength, or herculean equilibrium, always exists. Moreover, when profits are elastic enough with respect to the firm’s private information, the herculean equilibrium is the unique equilibrium of the game.
We study equilibrium uniqueness in entry games with private information. Our framework embeds models commonly used in applied work, allowing rich forms of firm heterogeneity and selective entry. We introduce the notion of strength, which summarizes a firm’s ability to endure competition. In environments of applied interest, an equilibrium in which entry strategies are ranked according to strength, called herculean equilibrium, always exists. Thus, when the entry game has a unique equilibrium, it must be herculean. We derive simple sufficient conditions guaranteeing equilibrium uniqueness and, consequently, robust counterfactual analyses.