Optimization Days 2024

HEC Montréal, Québec, Canada, 6 — 8 May 2024

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WA4 - Game Theory

May 8, 2024 10:30 AM – 12:10 PM

Location: Lise Birikundavyi - Lionel Rey (blue)

Chaired by Fouad El Ouardighi

4 Presentations

  • 10:30 AM - 10:55 AM

    Counterparty credit risk under netting agreements: A dynamic game Interpretation

    • Ahmadreza Tavasoli, presenter, HEC Montreal
    • Michèle Breton, GERAD, HEC Montréal

    We investigate counterparty credit risk and credit valuation adjustments in
    portfolios including derivatives with early-exercise opportunities, under a
    netting agreement. We show that credit risk and netting agreements have a
    significant impact on the way portfolios are managed (that is, on options'
    exercise strategies) and, therefore, on the value of the portfolio and on
    the price of counterparty risk. We derive the value of a netted portfolio as
    the solution of a zero-sum, finite horizon, discrete-time stochastic game.
    We show that this dynamic-game interpretation can be used to determine the
    value of the reglementary capital charges required of financial institutions
    to cover for counterparty credit risk and we propose a numerical valuation
    method. Numerical investigations show that currently used numerical
    approaches can grossly misestimate the value of credit valuation adjustments.

  • 10:55 AM - 11:20 AM

    Freight consolidation through carrier collaboration - A cooperative game

    • Fabio Mercurio, presenter, Eindhoven University of Technology
    • Loe Schlicher, Eindhoven University of Technology
    • Sonja Ursula Katharina Rohmer, HEC Montréal
    • Tom Van Woensel, Eindhoven University of Technology

    The rise in e-commerce, generally associated with smaller individual shipment sizes and short delivery timelines, has led to an increase in less-than-truckload shipping, requiring high levels of coordination between individual deliveries to keep costs low. Freight consolidation through carrier collaboration can help achieve higher shipping volumes without significantly increasing delivery times. However, a lack of trust and other barriers still prevent data and capacity sharing between carriers. Emerging technologies (e.g., Blockchain, IoT) help reduce these barriers, though often entail significant initial investments. Considering both the financial benefits of consolidation as well as the additional cost arising from collaboration, we explore under which circumstances carriers collaborate. For this purpose, we propose a cooperative game where multiple carriers deliver to the same final location and thus may decide to collaborate, sharing the costs of shipping and transferring, including fixed costs arising from potential investments. We show that a stable allocation of the joint costs is not always possible, which affects stability and thus may hinder collaboration. However, stability is guaranteed when fixed costs are very low, very high, or symmetric. Via numerical experiments we indicate that collaboration is very likely to be sustainable outside of these extreme cases, although exceptions may exist.

  • 11:20 AM - 11:45 AM

    Impact of Market Heterogeneity on Retailers' Competition for Quality of Services, Price and Location in a Duopoly

    • Saman Asvadi, presenter, PhD candidate, John Molson School of Business
    • Satyaveer Chauhan, Professor , John Molson School of Business

    In this paper, we investigate the impact of customer heterogeneity on the coordinated decisions regarding location, pricing, and service quality strategies for two retailers operating within a market. Specifically, we differentiate between two customer segments: Premium and Economy customers. Our analysis demonstrates that market heterogeneity significantly influences the optimal choices made by the two retailers. We highlight that the spatial distribution of these two customer classes within the market plays a crucial role in shaping the retailers' decisions concerning location, pricing, service levels, and ultimately, their profitability. Additionally, our study explores scenarios when the retailers make decisions concurrently or enter the market sequentially, revealing how these different approaches affect their decisions and profits. Through mathematical and numerical analyses, we establish the relationships between optimal decisions and various key parameters of the problem. These parameters include the utility derived from services for each customer class, travel costs, market demand dimensions, and the distribution of the two customer classes across the demand market. The outcomes of our research offer valuable insights for retailers and supply chain practitioners, guiding them in the selection of customer segments to serve in different scenarios, ultimately enabling them to maximize their profitability.

  • 11:45 AM - 12:10 PM

    Should forests be restored by producers or deforesters?

    • Fouad El Ouardighi, presenter, ESSEC Business School
    • Giorgio Gnecco, IMT - School for Advanced Studies
    • Eugene Khmelnitsky, Tel Aviv University
    • Marcello Sanguinetti, University of Genova

    A non-cooperative dynamic model is formulated where two countries are considered, one being involved in a production activity (i.e., the producer) and the other in a deforestation activity (i.e., the deforester). While deforestation directly reduces the environmental absorption efficiency of pollution, both activities generate polluting emissions that accumulate over time, which engenders a destructive impact on the environmental absorption efficiency. These harmful effects call for restoration efforts to curb an increase in the cost of negative externalities engendered by the pollution accumulation. Two scenarios are considered where the restoration efforts are incurred either by the deforester or the producer. Given the benchmark provided by the cooperative solution, we investigate i) whether the restoration efforts should be under the deforester's or the producer's control, and ii) how open-loop (or commitment-based) versus closed-loop (or contingent-based) Nash equilibrium strategies for either of these two scenarios affect the long run outcome. Based on extensive numerical analysis, we show that, with commitment-based strategies, the environmental absorption efficiency can be restored indifferently by the deforester or the producer. Also, compared with a cooperative solution, the possibility of the existence of multiple, history-dependent steady states persists with commitment-based strategies, regardless of whether the restoration efforts of the environmental absorption efficiency are undertaken by the deforester or by the producer. In contrast, in an closed-loop Nash equilibrium, though the players' overall utility is lower than the cooperative and commitment-based solutions, the long term environmental absorption efficiency is significantly improved if the producer controls the restoration effort. In addition, the history-dependency that may arise under commitment-based strategies is neutralized.

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