This paper presents a recursive reasoning formalism of Bayesian optimization (BO) to model the reasoning process in the interactions between boundedly rational, self-interested agents with unknown, complex, and costly-to-evaluate payoff functions in repeated games, which we call Recursive Reasoning-Based BO (R2-B2). Our R2-B2 algorithm is general in that it does not constrain the relationship among the payoff functions of different agents and can thus be applied to various types of games such as constant-sum, general-sum, and common-payoff games. We prove that by reasoning at level 2 or more and at one level higher than the other agents, our R2-B2 agent can achieve faster asymptotic convergence to no regret than that without utilizing recursive reasoning. We also propose a computationally cheaper variant of R2-B2 called R2-B2-Lite at the expense of a weaker convergence guarantee. The performance and generality of our R2-B2 algorithm are empirically demonstrated using synthetic games, adversarial machine learning, and multi-agent reinforcement learning.

The effort required to service maintenance requests on a software system increases as the software system ages and deteriorates. Thus, it may be economical to replace an aged software system with a freshly written one to contain the escalating cost of maintenance. We develop a normative model of software maintenance and replacement effort that enables us to study the optimal policies for software replacement. Based on both analytical and simulation solutions, we determine the timings of software rewriting and replacement, and hence the schedule of rewriting, as well as the size of the rewriting team as functions of the: user environment, effectiveness of rewriting, technology platform, development quality, software familiarity, and maintenance quality of the existing and the new software systems. Among other things, we show that a volatile user environment often leads to a delayed rewriting and an early replacement (i.e., a compressed development schedule). On the other hand, a greater familiarity with either the existing or the new software system allows for a less-compressed development schedule. In addition, we also show that potential savings from rewriting will be higher if the new software system is developed with a superior technology platform, if programmers' familiarity with the new software system is greater, and if the software system is rewritten with a higher initial quality.