Joep van Sloun | Searcharxiv

arXiv2025

Rationalizable Behavior in the Hotelling Model with Waiting Costs

This paper revisits the Hotelling model with waiting costs Kohlberg (1983), focusing on two specific settings where pure Nash equilibria do not exist: the asymmetric model with two firms and the symmetric model with three firms. In the asymmetric two-firm model, we show that the weaker concept of point rationalizability has strong predictive power, as it selects exactly two locations for both firms. As the two firms become more similar in their efficiency in handling queues of consumers, the two point rationalizable locations converge towards the center of the line. In the symmetric three-firm model, the set of point rationalizable choices forms an interval. This interval is shrinking in the inefficiency levels of the firms in handling queues of consumers.

econ.TH↗

arXiv2025

Rationalizability and Monotonocity in Games with Incomplete Information

This paper examines games with strategic complements or substitutes and incomplete information, where players are uncertain about the opponents' parameters. We assume that the players' beliefs about the opponent's parameters are selected from some given set of beliefs. One extreme is the case where these sets only contain a single belief, representing a scenario where the players' actual beliefs about the parameters are commonly known among the players. Another extreme is the situation where these sets contain all possible beliefs, representing a scenario where the players have no information about the opponents' beliefs about parameters. But we also allow for intermediate cases, where these sets contain some, but not all, possible beliefs about the parameters. We introduce an assumption of weakly increasing differences that takes both the choice belief and parameter belief of a player into account. Under this assumption, we demonstrate that greater choice-parameter beliefs leads to greater optimal choices. Moreover, we show that the greatest and least point rationalizable choice of a player is increasing in their parameter, and these can be determined through an iterative procedure. In each round of the iterative procedure, the lowest surviving choice is optimal for the lowest choice-parameter belief, while the greatest surviving choice is optimal for the highest choice-parameter belief.

econ.TH↗