PD:Teoria de Jocs per a l'Empresa

Teaching plan for the course unit

Català

English

General information

Course unit name: Game Theory for Businesses

Course unit code: 363712

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

Independent learning

Recommendations

Students must have completed all of the compulsory subjects taken up to this point in the degree. On the other hand, this subject helps students understand competitive and cooperative multiagent decision-making.

Competences / Learning outcomes to be gained during study

-	To be able to make financial and business decisions, taking into account the current economic situation. (More specifically: — Capacity to identify the essential elements of a decision-making problem: agents, available actions, information available to the agents, uncertainty factors, as well as the results and consequences of the different potential actions. — Capacity to identify areas of uncertainty, make hypotheses and deduce results. — Capacity to think strategically and accept hypotheses about the behaviour of others, to analyse balances and to know research techniques and the hypotheses on which these balances are based. — Capacity to make effective economic and business decisions: knowledge of the basic concepts of economics and business used to analyse decisions; use of suitable quantitative and qualitative tools; identification, definition and resolution of problems of varying degrees of complexity.)
-	To use basic quantitative methods and instruments to obtain and analyse company information and its socioeconomic environment, in accordance with the characteristics of the available information.
-	CE10. Ability to take planning and organizational decisions in an international business context.
-	CE6. Ability to appraise processes and decision-making in the development of international operations.

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 impart basic notions of game theory and to introduce 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 negotiation, contract or competition models and to other branches of information theory 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 with the purpose of becoming familiar with power indices.

Referring to abilities, skills

With regard to non-cooperative game theory, students will 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 equilibria 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 industrial organisation and competition models from the perspective of games.
— Interpret auctions as a non-cooperative game and analyse the strategic behaviour of the agents involved.

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

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

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 is 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 to be completed outside class and submitted to the teaching staff. 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. Students must also submit three distance learning activities, worth the remaining 20% of the final grade.

To pass the course via the continuous assessment option, 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 a student sits the final exam for continuous assessment, it is understood that s/he has 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 organised 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 organised 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 contexts of conflict and cooperation, therefore all assessment activities of the course are oriented to the student’s learning to analyse these situations and their elements.

Reading and study resources

Check availability in Cercabib

Book

BINMORE, Ken G. La Teoría de juegos : una breve introducción. Madrid : Alianza, cop. 2011

General reading on game theory.

Catàleg UB

DIXIT, Avinash K. ; NALEBUF, B.J. El Arte de la estrategia : la teoría de juegos, guía del éxito en sus negocios y en su vida diaria. Barcelona : Antoni Bosch, 2010

General reading on the principal aspects of game theory.

Catàleg UB

GARDNER, Roy. Juegos para empresarios y economistas. Barcelona: Antoni Bosch, 2009

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

Catàleg UB

GIBBONS, Robert. Un primer curso de teoría de juegos. Barcelona: Antoni Bosch, 2003

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

Catàleg UB

OSBORNE, Martín J. An introduction to game theory. New York: Oxford University Press, 2009

General reading on the most important topics of game theory. It exceeds the contents studied in this course and is useful for last-year students. Chapters 1-9.

Catàleg UB

PÉREZ NAVARRO, Joaquín. Teoría de juegos. Madrid: Garceta, 2013

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

RAFELS i PALLAROLA, Carles. (coord.) Jocs cooperatius i aplicacions econòmiques. Barcelona : Edicions Universitat de Barcelona, 1999

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

Catàleg UB

SÁNCHEZ-CUENCA RODRIGUEZ, Ignacio. Teoría de juegos. 2a. ed. Madrid: Centro de Investigaciones Sociológicas, 2009.

Brief clear manual with applications to sociology and political science.

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

Catàleg UB

Web page

GAME THEORY.NET : A resource for educators and students of game theory [en línia]. Educators, Students, Professionals and Geeks. Nashville, Tennessee, Estados Unidos . [Consulta: 19 juny 2017]. Disponible a: http://www.gametheory.net/

Notes, exercises, terminological dictionary, press articles, etc.