Alfredo Valencia Toledo

@unsaac.edu.pe

Departamento Académico de Matemáticas y Estadística
Universidad Nacional de San Antonio Abad del Cusco

Alfredo Valencia Toledo


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https://researchid.co/avalencia

RESEARCH INTERESTS

Game theory. Operations Research. Statistics. Applied Mathematics. Microeconomics.
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Scopus Publications

Scopus Publications

  • A coalitional extension of the ordinal Shapley-Shubik value
    Alfredo Valencia-Toledo, Juan Vidal-Puga
    Annals of Operations Research, 2026
    In cooperative game theory it is known that two-person bargaining problems have no relevant ordinal solution. For three-player bargaining problems, Shapley and Shubik propose an ordinal rule. However, this rule does not take into account the worth of proper subcoalitions of size 2. In this paper, we fill this gap by proposing a generalization of the Shapley-Shubik rule for non transferable utility games. The resulting solutions, when applied to transferable utility games, always belong to the core, which makes it a relevant alternative to other core-selectors such as the nucleolus. We also apply the new solution to a practical case related to mining and natural resources management.
  • Compensating local communities for mining transport: A game theoretical analysis
    Alfredo Valencia-Toledo, Juan Vidal-Puga
    Mathematical Social Sciences, 2025
    We propose a freight transportation problem to distribute the benefit provided by a corridor to compensate the communities on the route. Such distribution aims to avoid conflicts generated by the maintenance of the corridor or the ore transportation that causes external costs to communities that can block the route, forcing more expensive alternatives. We propose a cooperative game theory solution based on stability and fairness principles. In particular, we present some reasonable properties to characterize a family of core assignment rules for determining compensation to the local communities in the corridor. We illustrate the method with a case study using data from Peru.
  • Unearthing Influential Factors Shaping the Mining Industry’s Development in Peruvian Regions (Apurimac-Cusco): An Exploratory Factor Analysis Perspective
    Alfredo Valencia-Toledo
    Mining Metallurgy and Exploration, 2024
  • Developing models to assess the social impact of mining: An exploratory study trough necessary conditions analysis (NCA)
    Andrea Rey-Martí, Alfredo Valencia-Toledo, Nuria Chaparro-Banegas, Alicia Mas-Tur, Norat Roig-Tierno
    Resources Policy, 2023
    The mining sector has been in the spotlight for many years because of its negative impact on society and the environment. The focus on sustainable development at the international and national levels has led to increased criticism of mining, creating issues on numerous occasions. However, the progress of many developing countries depends on the mining sector, which can provide economic benefits to local communities. This paper aims to identify the benefits that the mining sector should provide to local communities to offset its negative effects on the environment. The paper explores not only the negative environmental effects of mining but also its positive side. Using necessary condition analysis (NCA), social action, physical infrastructures, basic services, health, and education are studied from an economic development perspective to identify the necessary levels of these factors in order to achieve the environmental satisfaction of local communities. The results indicate that education, health, and basic services have a crucial impact on the local community's environmental satisfaction. This finding suggests that local communities perceive the effect of the mining sector as positive when it provides education, health, and basic services to the surrounding area.
  • A sequential bargaining protocol for land rental arrangements
    Alfredo Valencia-Toledo, Juan Vidal-Puga
    Review of Economic Design, 2020
    We consider land rental between a single tenant and several lessors. The tenant should negotiate sequentially with each lessor for the available land. In each stage, we apply the Nash bargaining solution, as a short-cut to solving non-cooperative bargaining games. Our results imply that, when all land is necessary, a uniform price per unit is more favorable for the tenant than a lessor-dependent price. Furthermore, a lessor is better off with a lessor-dependent price only when negotiating first. For the tenant, lessors’ merging is relevant with lessor-dependent price but not with uniform price.
  • Reassignment-proof rules for land rental problems
    Alfredo Valencia-Toledo, Juan Vidal-Puga
    International Journal of Game Theory, 2020
    We consider land rental problems where there are several communities that can act as lessors and a single tenant who does not necessary need all the available land. A rule should determine which communities become lessors, how much land they rent and at which price. We present a complete characterization of the family of rules that satisfy reassignment-proofness by merging and spliting, apart from land monotonicity. We also define two parametric subfamilies. The first one is characterized by adding a property of weighted standard for two-person. The second one is characterized by adding consistency and continuity.
  • Hart and Mas-Colell consistency in PERT problems
    Gustavo Bergantiños, Alfredo Valencia-Toledo, Juan Vidal-Puga
    Discrete Applied Mathematics, 2018
    The Program Evaluation Review Technique (PERT) is a tool used to schedule and coordinate activities in a complex project. In assigning the cost of a potential delay, we characterize the Shapley rule as the only rule that satisfies Hart and Mas-Colell consistency and other desirable properties.
  • Duality in land rental problems
    Alfredo Valencia-Toledo, Juan Vidal-Puga
    Operations Research Letters, 2018
    Land rental problems describe situations where one tenant demands land from several lessors. The way lessors rent their land can be seen as equivalent to a bankruptcy problem. We extend the idea of self-duality in bankruptcy problems to land rental problems. We provide a complete characterization of the family of rules that satisfy self-duality. Moreover, self-duality is enough to assure the proportional land share among lessors. Adding other reasonable properties, we pick up a single rule.