# An Introduction to Game Theory with Engineering Applications

*Dario Bauso’s Game Theory with Engineering Applications was published by SIAM in 2016. The text describes the foundations of game theory and is intended for both undergraduate and graduate students, industry researchers, and even social scientists, biologists, and physicists. More specifically, it explores the physical intuition of game theory, analyzes design techniques, and addresses emerging cooperation and competition trends in complex distributed systems.*

*The following excerpt introduces the book and is adapted from the Preface. It has been abridged and edited for clarity.*

In the field of systems and control, a key research direction involves *engineering systems*: highly distributed collective systems with humans in the loop. In this context, *highly distributed* indicates that decisions, information, and objectives are distributed throughout the system, and *humans in the loop* implies that the players have bounded rationality and limited computation capabilities. Societal and cultural habits may also influence decisions.

I chose to write* Game Theory with Engineering Applications *because the use of *game theory* within the realm of engineering systems contributes to the design of incentives that obtain socially desirable behaviors from the players. In *demand-side management*, for example, an increase in electricity price may induce a change in prosumer consumption patterns. In *opinion dynamics*, marketing campaigns can influence the market share if we assume that the customers are susceptible players with the same opinions as their neighbors. And in *pedestrian flow*, informing pedestrians of congestion at different locations might redistribute traffic more effectively.

**Figure 1.**Noncooperative game between two players. The horizontal axis represents the action set for player 1 and the vertical axis represents the action set for player 2. The plot illustrates the level curves for both player 1 (solid) and player 2 (dashed). The optimum for player 1 is \(P\) and the optimum for player 2 is \(Q\). If they play simultaneously, the best outcome that they can obtain is \(R\) (the Nash equilibrium). But if player 1 is the leader and player 2 is the follower, they converge to \(S\) (the Stackelberg equilibrium). Figure courtesy of

*Game Theory with Engineering Applications*and reprinted with permission from Springer Science+Business Media.

Evolutionary notions demonstrate that equilibria are relevant only if the players can converge to such solutions in a dynamic setting, essentially transforming the game into a kind of dynamic feedback system. But game theory models are *more *than just dynamic feedback systems; each player learns the environment, which in turn learns the player, and so forth. This coupled learning style introduces a higher level of difficulty to the feedback structure.

Much of the book focuses on *games with a large number of players*. In such scenarios, each player uses an aggregate description of the environment that is based on a distribution function for actions or states — which is the main concept in a *mean field game*. If a game consists of a mapping from congestion levels to payoffs, the evolution model is thus a dynamic model that operates in the opposite direction; it maps flows of payoffs to flows of congestion levels. Here, systems and control theory provide a set of sophisticated stabilizability tools for the design of self-organizing and resilient systems that are characterized by cooperation and competition.

### Goals of the Book

*Game Theory with Engineering Applications* aims to integrate game theory with systems and control theory under the unconventional framework of engineering systems. Part I addresses the foundations of the theory of noncooperative and cooperative games—both static and dynamic—while also highlighting new trends in cooperative differential games, learning, approachability (games with vector payoffs), and mean field games (games with many homogeneous players).

Part II seeks to illustrate stylized models of engineered and societal situations. These models deliver fundamental insights into several areas, including individual strategic behaviors, scalability and stability of collective behavior, and the influence of heterogeneity and local interactions. The text also discusses uncertainty and model misspecification, with an emphasis on grand engineering challenges like *resilience *and *big data*.

### Structure of the Book

Part I of *Game Theory with Engineering Applications *comprises 12 chapters. Chapters 1 through 4 review the foundations of noncooperative games, chapters 5 and 6 deal with cooperative games, chapter 7 surveys evolutionary games, chapter 8 analyzes the replicator dynamics and succinctly overviews learning in games, chapter 9 handles differential games, and chapter 10 tackles stochastic games. Chapter 11 then pinpoints basic ideas and trends in games with vector payoffs, such as *approachability *and *attainability*, and chapter 12 provides a synopsis of mean field games.

Part II builds upon some of my previous journal articles and contains the remaining content, from chapters 13 to 21. In particular, chapters 14 and 15 both fall under the umbrella of power systems and respectively analyze demand-side management and the synchronization of power generators. Within the realm of socio-physical systems, chapter 13 discusses consensus in multi-agent systems and chapters 16 through 18 illustrate opinion dynamics, bargaining, and pedestrian flow applications. In the context of production/distribution systems, chapters 19 to 21 address supply chains, populations of producers, and cyber-physical systems.

### Audience and Coursework

The primary audience for this text comprises students, practitioners, and researchers in different areas of engineering, including industrial, aeronautical, manufacturing, civil, mechanical, and electrical engineering. The topic may also interest scholars in fields like computer science, economics, physics, and biology. Young researchers may especially benefit from reading Part II, and the comprehensive reference list at the end enables further study. The book thus provides a short pathway that allows undergraduate students to become emerging researchers.

In addition,* Game Theory with Engineering Applications* is also suitable as a textbook. For instance, Part I covers information that is appropriate for a first-year graduate class; in fact, it assembles materials from three 2013 graduate courses at the University of Trento, University of Oxford, and Imperial College London. Its tutorial style illustrates the major points in a manner that helps readers quickly grasp the key components of each concept.

Furthermore, an appendix section that covers mathematical review, optimization, Lyapunov stability, the basics of probability theory, and stochastic stability theory contributes to the text’s suitability in an undergraduate course. Part II even incorporates a number of simulation algorithms and numerical examples in MATLAB that may improve younger students’ coding skills.

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