PD:Teoria de Jocs i Aplicacions Econòmiques

Teaching plan for the course unit

Català

Castellano

English

General information

Course unit name: Game Theory and Applications in Economics

Course unit code: 361868

Academic year: 2025-2026

Coordinator: Mikel Alvarez Mozos

Department: Department of Economic, Financial and Actuarial Mathematics

Credits: 6

Single program: S

Estimated learning time

Total number of hours 150

Face-to-face and/or online activities

	- Lecture with practical component	Face-to-face		30
	- Problem-solving class	Face-to-face		30

Supervised project	40
(Continuous assessment activities to be handed in.)

Independent learning

Recommendations

Students must have completed all of the compulsory subjects taken up to this point in the degree. This subject contributes to the students’ general understanding of some aspects of advanced microeconomics.

Competences / Learning outcomes to be gained during study

-	Capacity for learning and responsibility (capacity for analysis and synthesis, to adopt global perspectives and to apply the knowledge acquired/capacity to take decisions and adapt to new situations).

-	To take decisions. This competence involves the following: - To be able to identify the essential aspects of a problem, that is, the agents, the available actions, the information that the agents have, the results and the consequences of the various potential actions. To be able to identify areas of uncertainty, make hypotheses and deduce results. To maintain a critical approach to the results. - To be able to think strategically and accept hypotheses about the behaviour of others, to analyse balances and to know the search techniques and the hypotheses on which these balances are based. - To make effective financial and business decisions: a) to gain knowledge of the basic concepts of economics and business in order to analyse decisions; b) to use suitable quantitative and qualitative tools; c) to identify, frame and resolve problems of varying degrees of complexity.
-	Capacity to understand problems, extract the essential information and produce the appropriate mathematical formulations for their analysis and resolution.
-	Capacity to identify, formulate and solve decision-making problems in organizational settings, using operations research models and integrating the results of statistical analyses where necessary.
-	To develop a critical ability to analyse economic theories and models. This competence involves the following: - To critically analyse and assess the economic behaviour of individuals and the way they make decisions. - To analyse the aggregate behaviour in an economy and its implications. - To empirically compare the suitability of theoretical models for a specific economic area.
-	Understanding of the applications of mathematics in other branches of science and technology.
-	Capacity to conceive, model, analyse, validate and interpret real-life situations and problems, adapting theoretical models to the specific requirements of different areas of application.

Learning objectives

Referring to knowledge

Game theory refers to the study of multi-person decision problems, both those that involve explicit agreement between agents or players (cooperative games), and those that are resolved through individual decisions without the possibility of establishing binding agreements between agents (non-cooperative games). The objective of the course is to acquire basic notions of game theory and of the economic applications derived from it and that motivate it.

In non-cooperative game theory, the central concepts are strategy and equilibrium. These are specifically applied both to static games, with or without complete information, and to dynamic games with complete information. The applications to market structure models and to other branches of economic theory (e.g., negotiation models) are important for motivating and justifying the concepts used.

The core concept of cooperative game theory is analysis of the benefits of forming coalitions. Specifically, this course focuses on transferable utility cooperative games in which the goal is to study the formation of these coalitions while at the same time analysing the criteria for the distribution of the surpluses that they give rise to. Voting models are also studied.

Referring to abilities, skills

With regard to non-cooperative game theory, students should be able to:

— Formulate simple situations as non-cooperative games, identifying the players, the strategies available and the possible outcomes.

— Apply the concept of the Nash equilibrium to deduce the predictable behaviour of economic agents.

— Interpret equilibriums obtained in the context of the problem and develop the capacity for critical thinking.

— Analyse the specific features of static Bayesian games with incomplete information and of dynamic games, distinguish these features in static games with complete information, and apply the appropriate solution procedures in each case.

— Analyse market structure models from the perspective of games and, in particular, price or quantity competition in an oligopolistic context.

— Interpret auctions as a non-cooperative game and analyse the strategic behaviour of the agents involved.

With regard to cooperative game theory, students should be able to:

— Formulate simple situations as cooperative games, identifying the players and the possible outcomes of every coalition.

— Recognize acceptable distributions from a coalitional perspective.

— Apply surplus or cost distribution criteria and propose and debate the properties of different types of distribution models.

— Analyse a voting situation and recognize the relative power of each of the agents involved.

Teaching blocks

1. Static games with complete information

1.1. Introduction: elements of a game and forms of representation

1.2. Two-player games with a finite number of strategies: bimatrix games

1.3. Strategic dominance: the prisoner’s dilemma

1.4. Concept and examples of Nash equilibrium

1.5. Zero-sum games

1.6. Games with three or more players

1.7. Games with n players: the tragedy of commons

1.8. Games with infinite strategies. The existence of the Nash equilibrium

1.9. Equilibrium in mixed strategies in bimatrix games

1.10. Market games: Cournot’s and Bertrand’s duopoly models

2. Dynamic games with complete information

2.1. Representation of an extensive-form game: information sets

2.2. The concept of strategy and strategic representation of a dynamic game

2.3. Subgames. The perfect Nash equilibrium in subgames. Examples

2.4. Dynamic games with complete, perfect information: backward induction

2.5. Market games: Stackelberg’s duopoly

2.6. The iterated prisoner’s dilemma

3. Static games with incomplete information

3.1. Introduction to games with incomplete information

3.2. Decision trees with random moves

3.3. Static Bayesian games: types, conjectures, payments and strategies

3.4. Bayesian Nash equilibrium

3.5. Examples: a prisoner’s dilemma with incomplete information; a simplified auction

3.6. Applications: Cournot’s duopoly with incomplete information; auctions

4. Cooperative games

4.1. Introduction. The characteristic function

4.2. Efficient distributions

4.3. Coalitional rationality: the core

4.4. A single-point solution: the Shapley value

4.5. Application to cost distribution problems: single-source connection games

4.6. Voting games and power indices

Teaching methods and general organization

The learning objectives are achieved through a combination of theory lectures with a practical component and a series of practical activities to be completed throughout the course. Groups large enough are split for problem-solving practical sessions (one two-hour session every two weeks): two lecturers teach the subgroups at the same time in parallel classrooms.

In class, the analysis of different examples requires students to understand the basic concepts of game theory. The general concepts and procedures are then applied to more complex examples originating in today’s economic reality. Therefore, the completion of practical activities plays an important role in the accomplishment of these objectives. The calendar of activities and deadlines for submission are posted on the Virtual Campus. A model solution is provided after each activity has been submitted.

Official assessment of learning outcomes

Continuous assessment

Continuous assessment consists of two face-to-face written tests and a series of activities and exercises. The first test assesses students on the contents taught in block 1 of the course and is worth 30% of the final grade. The second test assesses students on the contents taught in blocks 2, 3 and 4 of the course and is worth 50% of the final grade. The remaining 20% corresponds to the activities set during practical sessions. The calendar of activities is posted on the Virtual Campus.

To pass the course in the continuous assessment procedure, students must obtain a weighted overall mark of at least 5 out of 10 for the tests and activities. In addition, they must obtain marks of at least 3 out of 10 for both tests 1 and 2.

If students sit the final exam for continuous assessment, it is understood that they have chosen to follow continuous assessment. Students who do not sit the final exam for continuous assessment are entered for single assessment.

Repeat assessment

Repeat assessment is organized according to the criteria approved by the Academic Council. Students sit a single examination on the theoretical and practical aspects of the course on the official date.

Examination-based assessment

Single assessment consists of an examination on the theoretical and practical content of the course, held on the official single assessment date.

Repeat assessment

Repeat assessment is organized according to the criteria approved by the Academic Council. Students sit a single examination on the theoretical and practical aspects of the course on the official date.

Assessment of competences

The competences acquired through this course are essentially related to the capacity for decision-making. Game theory is basically the study of decision making in conflict and cooperation environments; therefore, all the assessed activities for the course are focused on the analysis of these situations and their elements (for more details, refer to the list of competences).

Reading and study resources

Check availability in Cercabib

Book

PÉREZ, Joaquin.; JIMENO, José. L.; CERDÀ, Emilio. (2013) : Teoría de juegos. Madrid: Garceta.

Book providing formal definitions of the concepts covered during the course, in a clear and concise manner. Includes model exercises and solutions. Chapters 1–5.

Catàleg UB

GARDNER, Roy. (1996) : Juegos para empresarios y economistas. Barcelona: Antoni Bosch,

Textbook on game theory applied to economic models. Chapters 1–7 and 11.

Catàleg UB

GIBBONS, Robert. (1993) : Un primer curso de teoría de juegos. Barcelona: Antoni Bosch,

Book on game theory, specific focus on economic models. Chapters 1–3.

Catàleg UB
Versió en línia (1993)

OSBORNE, Martín. J. (2004) : An introduction to game theory. Oxford University Press,

General reading on the most important topics of game theory. Ample information for the course content, and designed for students in the final year of the degree. Chapters 1–9.

Catáleg UB

RAFELS, Carles. [et al.] (1999) : Jocs cooperatius i aplicacions econòmiques. Barcelona: Edicions UB,

In-depth study of cooperative game models. Chapters 1–3 and 5.

Catàleg UB

BINMORE, Ken. (2011) : La teoría de juegos: una breve introducción. 2ª ed. Madrid: Alianza Editorial,

General reading on game theory.

Catàleg UB

SANCHEZ-CUENCA, Ignacio. : (2009) : Teoría de juegos. 2ªa ed. Madrid: CIS,

Brief clear manual with applications to sociology and political science.

Catàleg UB

DIXIT, Avinash.K. ; NALEBUFF, Barry .J. (2010) : El arte de la estrategia. Barcelona: Antoni Bosch,

General reading on the principal aspects of game theory.

Catàleg UB

WATSON, Joel. (2008) : Strategy: an introduction to game theory.. 2ª ed. New York : W.W. Norton & Company,

Catàleg UB

Mikel Álvarez Mozos, Pedro Calleja Cortés, Josep Maria Izquierdo Aznar, Francisco Javier Martínez De Albéniz Salas, Marina Núñez Oliva. Teoría de juegos. 2022. Editorial UOC

Versió en línia (2022)