Innovative Applications of OR
A dynamic principal-agent framework for modeling the performance of infrastructure

https://doi.org/10.1016/j.ejor.2016.03.027Get rights and content

Highlights

  • This paper presents a novel approach to modeling infrastructure development.

  • It monitors the dynamic and complex evolution of infrastructure systems.

  • It integrates the nature of decisions with technical, economic and operational aspects.

  • It evaluates, more realistically, the relationship between all players’ actions.

  • It better describes the player’s payoffs based on their strategies.

Abstract

This paper presents a novel approach to the problem of infrastructure development by integrating technical, economic and operational aspects, as well as the interactions between the entities who jointly carry out the project. The problem is defined within the context of a Public Private Partnership (PPP), where a public entity delegates the design, construction and maintenance of an infrastructure system to a private entity. Despite the benefits of this procurement method, the relationship between the two entities is inherently conflictive. Three main factors give rise to such conflict: the goals of the public and private party do not coincide, there is information asymmetry between them and their interaction unfolds in environments under uncertainty. The theory of contracts refers to this problem as a principal-agent problem; however, due to the complexity of the problem, it is necessary to recreate a dynamic interaction between the principal (i.e., the public entity) and the agent (i.e., the private entity) while including the monitoring of the infrastructure performance as an essential part of the interaction. The complex relationship between the sequential actions of players and the time-dependent behavior of a physical system is explored using a hybrid agent-based simulation model. The model is illustrated with several examples that show the versatility of the approach and its ability to accommodate the different decision strategies of the players (i.e., principal, agent) and the model of a physical infrastructure system.

Introduction

Since infrastructure systems are conceived to serve basic necessities of society, public institutions are responsible for their creation and persistence. However, the processes that entail its development are complex and sometimes public institutions are not prepared to manage them efficiently. This situation has paved the way for procurement methods where these complex tasks are delegated to specialized private third parties who are able to inject private capital investment and deal with complex technical aspects of design, construction and maintenance. Today, one of the most widely used category of this kind of delegation is the Public-Private Partnership (PPP) (Hoppe, Kusterer, Schmitz, 2013, Kwak, Chih, Ibbs, 2009, Levy, 2008, Yescombe, 2007).

The World Bank defines a PPP as a medium to long term arrangement where the public sector (e.g., a government agency) delegates some services or works to the private sector (e.g., a private firm), having agreed on objectives and conditions for the delivery. For clarity and consistency with other literature on the subject, we will refer to the government agency as the principal and treat it with female gender. The private firm will be referred to as the agent, with male gender. The services or works delegated to the agent are often either the enhancement of existing infrastructure or the design and construction of new infrastructure. Once this is completed, the public works are transferred temporarily to the agent—usually for a period ranging between 10 and 30 years—in which he assumes the responsibility of maintaining (i.e., performing maintenance works or updates to counteract deterioration) and operating the infrastructure (i.e., carrying out all the logistics necessary to provide the intended service) while receiving the rent produced by its operation. The agent also agrees to share risks with the principal. Those risks are related to design and construction costs, market demand, service and maintenance costs. It is common that in order to make the project economically attractive to the agent, the principal must provide subsidy: a payment schedule transferred to the agent during the infrastructure’s operation. In order to ensure that the mentioned ‘objectives and conditions’ of the arrangement are fulfilled, the principal will keep track of certain performance indicators of the infrastructure by executing inspections. At the end of this contracted period, the government takes back control of the infrastructure system.

The central thesis that we want to convey in this paper is that the history and the success—or failure—of an infrastructure project featuring delegation (such as a PPP) results from the interplay of all the following aspects:

  • 1.

    the economic game between the principal and the agent,

  • 2.

    the regulatory framework and contractual design that constraint their interaction,

  • 3.

    the performance of physical infrastructure, and

  • 4.

    the natural environment in which the infrastructure is embedded.

In practice, a systematic framework that integrates these aspects to inform all the decisions involved in the delegation does not exist. We want to propose a model for such framework with the aim of showing the mechanisms by which these four aspects influence the result of the interaction. Additionally, we present suggestions that could transform the model into a decision support system for government agencies.

Even though the term partnership suggests that principal and agent are united by a legal partnership, and have intrinsic motivation for cooperating to achieve the greater good, this is not necessarily the case. As Yescombe points out (Yescombe, 2007, p.3), ‘partnership’ in this context is mostly a political slogan. In the use of a PPP procurement method the following circumstances are likely to appear:

  • Information asymmetry: this is mainly caused because during the contractual relationship, the agent’s actions are generally unobservable to the principal. Then, the agent knows his own level of effort and, therefore, can predict the infrastructure performance much better than the principal. On the other hand, the principal does not know how much effort the agent has employed in maintenance interventions and he can only estimate the performance of the infrastructure by actively inspecting it.

  • Conflicting goals: this occurs because the objectives of both the agent and the principal lead to an adversarial relationship. Then, while the principal wants to reach a specific monetary balance and maximize some performance measure of the infrastructure, the agent simply wants to maximize his monetary balance.

  • Stochasticity: the physical infrastructure system is fundamentally a stochastic system. Thus, from the point of view of a player (principal or agent), the merit of an action to be deployed at the present time instant is uncertain.

The act of delegation when these three features exist creates a moral hazard. In economics, the term moral hazard describes the situation in which an individual with private information is willing to take greater risks because someone else bears with the consequences. In our particular problem, the agent is willing to take risks by not doing a proper maintenance because the principal won’t be aware of it and she is the one who will suffer from a low infrastructure performance.

The regulatory framework and the contractual design of the interaction is the main leverage point that the principal can use to control the moral hazard problem. In the literature dedicated to contracts in infrastructure projects we could identify two approaches. The first approach (Auriol, Picard, 2013, Medda, 2007) is deductive and quantitative. It is based on economics and game theory and uses closed form representations for the idealized interaction of fully rational economic agents. It deals with information constraints, risk preferences, utility functions and optimization problems. It is fundamentally prescriptive. It is able to produce precise quantitative specifications at the cost of reducing the complexity by imposing overly simplified assumptions on the problem so that it becomes mathematically tractable. This approach addresses the first component of our thesis (Section 1.1). The second approach (Meunier, Quinet, 2010, Yescombe, 2007) is inductive, and mostly qualitative. It is focused on the interface of finance, regulation and institutions. It is often sustained by experience, the extrapolation from past events and guided by subjective opinion. This approach is fundamentally descriptive. It makes reference to the minute details that involve the formation and persistence of a PPP. However, while being empirical and close to concrete examples, it often lacks the ability to produce a rigorous prescription of contract design. This approach addresses the second component of our thesis (Section 1.1).

Neither the first nor the second approach address the third and fourth components of our model (see Section 1.1) since they do not model the problem as a dynamic and path dependent interaction. Furthermore, they both overlook the fact that the physical system deteriorates over time, which would in turn elicit reactive actions from players. In summary, economic and management research on this topic has not studied the consequences of their principles in the context of a physical reality that influences players. Nevertheless, research on deterioration models for many kinds of civil infrastructure assets do exist (e.g., Frangopol, Kallen, Noortwijk, 2004, Kleiner, Rajani, 2001, Kumar, Cline, Gardoni, 2015, Sanchez-Silva, Klutke, Rosowsky, 2011). These models effectively make the connection between: the properties of physical objects that compose the infrastructure system, the operations exerted on them, the pressures and demands coming from their environment and the resultant change in physical condition measured with some performance index.

In this paper we propose a framework to designing contracts based on a reliable, reproducible quantitative model that acknowledges the intricate details of real economic and operational interactions and the inevitable deterioration of a physical infrastructure system under environmental pressures. For that purpose, we will develop an agent-based simulation model capable of tracing an interaction history between the principal, the agent, the natural environment and its effect on the infrastructure system. From such interaction we will calculate the utility for each player, which will rate the goodness of the delegation relationship that emerges out of certain player’s strategies and problem parameters.

This paper is organized as follows. In Section 2, we present the traditional principal-agent framework and highlight its limitations. In Section 3 we propose an alternative interaction game that is the basis of the simulation model. In Section 4 a conceptual model of the interaction process is presented as a dynamic system, making explicit the dependence relationships. Then, the mathematical formulation of the model is described in detail in Section 5. The broad characteristics of the implementation in the form of a hybrid agent-based model are explained in Section 6. In Section 7 we present a set of numerical experiments and further analyses that highlight relevant aspects of the model. In Section 8 we discuss the validation of the model and provide suggestions for future work. We conclude in Section 9 by stressing the advantages of this approach and highlighting the importance of unifying methods of diverse disciplines in order to design and manage socio-technical systems.

Section snippets

Basic formulation

In game theory (Fudenberg, Tirole, 1991, Leyton-Brown, Shoham, 2008, Rasmusen, 2006), a principal-agent (PA) problem (Laffont & Martimort, 2009) is one in which an uninformed player (the principal) delegates a task to an informed player (the agent) in exchange for a wage. PA models in general are presented in two versions: adverse selection and moral hazard. In this paper, we will focus on the moral hazard problem (Dutta & Radner, 1994). An example of the application of this approach to the

Problem overview

The continuous sequential game describes the dynamic interaction between Principal, Agent and Nature; and it is used to evaluate the effect on the performance of an infrastructure system. Then, the principal (e.g., government agency) will carry out periodic inspections of the system condition to ensure that it is operating above a pre-specified performance level. She will also impose penalty fees to induce the agent to behave according to her interests. Therefore, the objective of the principal

System dynamics

Let’s now define more precisely the relationship between all different actors and the mechanism by which infrastructure evolves (Fig. 3). Then, we will frame the concepts of game theory presented so far, within the context of System Dynamics (SD) (Forrester, 1973, Forrester, 2013). SD is a mathematical methodology that simulates the behavior of a complex system by identifying its parts and the connections between those parts in the form of relationships of dependence. The system dynamics of our

Hybrid system dynamics

The combination of continuous and discrete behavior in a system is denoted with the term hybrid (Goebel, Sanfelice, & Teel, 2012). The theory of hybrid system dynamics have been used extensively to model mechanical and electrical systems (Goebel et al., 2012), but can be easily extended to other systems. A hybrid system can move throughout its state space both in a continuous and instantaneous manner. The continuous evolution of the system is given by a differential equation (or set of

Implementing the game

As the formulation for the game progressively grows in complexity, it becomes more difficult to fit its structure into the basic models provided by game theory. Then, in order to recreate the game as formulated in the previous section without incurring in further simplifications, we developed an hybrid simulation model that combines System Dynamics (SD) and Agent-Based Modeling (ABM).

Numerical experiments

We have covered in Section 5 the theoretical structure of the problem and in Section 6 the arrangement of its implementation as a hybrid AB-SD model. This section will present numerical experiments for a specific problem instance. We will characterize the following problem by specifying the parameters listed in Table 3 and the strategies that each player deploys.

Discussion

This section will address two important aspects of the approach we propose: a discussion about its validation and ways to improve our model.

Conclusions

Delegation plays a prominent role in the procurement of infrastructure systems. The delegation of tasks to a self-interested entity coupled with random changes in the environment creates a moral hazard problem. We showed that aggregate models have limitations in two main respects. First, they offer inappropriate account of how players’ actions produce outcomes by proposing a functional relationship that is not suitable to express concrete operations and response of physical objects. Second, we

Acknowledgments

This publication was funded by the Research Program 2012 from the Office of the Vice President for Research, Universidad de Los Andes (Bogotá, Colombia). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the Universidad de Los Andes (Bogotá, Colombia).

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