Nicolás Hernández-Santibáñez

arXiv2026

Multi-Principal Competition for an Exclusive Agent: characterization and approximation of Nash Equilibria

This paper introduces and studies a Principal-Agent competition model in which two risk-neutral Principals compete to hire a single Agent. The Agent chooses to work exclusively for one Principal, making the Agent's reservation utility endogenous, as it is determined by the competing offers. We characterize the Nash equilibria of the resulting game by relating them to the individual Principal-Agent contracting problems and analyzing the Agent's selection bias. We further introduce two numerical algorithms to approximate Nash equilibria by locating sign changes of the value functions of the Principals' individual problems. The first is a Newton-type method that exploits differentiability of the value functions, while the second is a bisection method that does not require differentiability. The proposed procedures are illustrated through several examples involving exponential, logarithmic, and constant relative risk aversion (CRRA) utility functions within the polynomial framework of Renner and Schmedders (2015). We also provide technical results regarding the regularity of the value function of a classical Principal-Agent problem, including differentiability under suitable conditions.

math.OC↗

arXiv2026

Investment and Operational Planning for electricity markets with massive entry of renewable energy

In wholesale electricity markets, electricity producers and the independent system operator (ISO) play a central role. The ISO is responsible for minimizing production costs while satisfying supply-demand balance and capacity constraints. In this paper, we study a continuous-time problem in which the ISO seeks to minimize the joint cost of operation and investment in an electricity network. The problem is formulated in terms of operational and investment control variables. We analyze the hierarchy between these controls and use the so-called Day-Ahead Problem to find an explicit form of the optimal operation. This allows us to reformulate the investment problem as a stochastic control problem with state constraints. We extend the results of state-constrained stochastic control to fit our setting. In particular, we use a version of the Pointing Inward Condition to fully characterize the value of the problem as the unique viscosity solution of a constrained HJB equation. We then assign a specific dynamic to the capacity-demand process and discuss how the assumptions for the HJB characterization result in a budget constraint for the planning. Finally, we run simulations for a three-node setting that resembles the Chilean market. We analyze short-, medium-, and long-term planning scenarios and discuss how to transition toward a system with high penetration of renewable energy.

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