Game Theory and Applications

Date:

June 17 to 21. AFTERNOON: 15 to 18h

Instructor

I am Profesor agregado at Universitat de Barcelona. Dep of Economic, Financial and Actuarial Mathematics. Faculty of Economics and Business Administration.
PhD in Economics Universitat de Barcelona
Graduate in Economics Universitat de Barcelona (EUS program)

I am (or have been) also the responsible professor for various courses of Game Theory in master's programs in Economics, Research in Business, Actuarial and Financial Sciences, and Marketing.

C. RELEVANT MERITS
C.1. Publications (last only)
Papers:
1. Calleja P; Llerena F; Sudhölter P. 2023. Remarks on solidarity in bankruptcy problems when agents merge or split. Mathematical Social Sciences 125, pp.61-64.
2. Calleja, P; Llerena, F. 2022. Non-manipulability by clones in bankruptcy problems. Economics Letters 221-110921, pp.1-6.
3. Atai, A; Calleja P; Soteras S. 2021. Open shop scheduling games. European Journal of Operational Research 295-1, pp.12-21.
4. Calleja P; Llerena F; Sudhölter P. 2021. Axiomatizations of Dutta-Ray's egalitarian solution on the domain of convex games. Journal of Mathematical Economics 95-102477, pp.1-10.
6. Calleja P; Llerena F; Sudhölter P. 2020. Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency. Mathematics of Operations Research 45-3, pp.1056-1068.
7. Calleja P; Llerena F. 2020. Consistency, weak fairness and the Shapley value. Mathematical Social Sciences 105, pp.28-33.
8. Calleja P; Llerena F. 2019. Path monotonicity, consistency and axiomatizations of some weighted solutions. International Journal of Game Theory 48, pp.287-310.
9. Calleja P; Llerena F. 2017. Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results. Social Choice and Welfare 48, pp.197-220.
Books:
11. Alvarez Mozos M; Calleja Cortés P; Izquierdo Aznar JM; Martinez de Albeniz FJ; Nuñez Oliva M. 2021. Teoría de juegos. Editorial de prestigi - UOC. UNIVERSITAT OBERTA DE CATALUNYA.

C.2. Congress,

1. Calleja P; Llerena F. Non-manipulability by clones in bankruptcy problems. 23rd SAET (Society for the Advancement of Economic Theory) Conference. 2024, Santiago de Chile. Invited conference
2. Calleja P; Llerena F; Sudholter, P. On manipulability in financial systems. 22nd SAET Conference. 2023, Paris. Invited conference
3. Calleja P; Llerena F; Sudholter, P. On manipulability in financial systems. 33rd Stony Brook International Conference on Game Theory. 2022, Stony Brook. Presentation.
4. Calleja P; Llerena F. Proportional clearing mechanisms in financial systems: an axiomatic approach. 1st UB Game Theory Workshop. 2022, Barcelona. Invited conference.
5. Calleja P; Llerena, F; Sudhölter, P. Characterizing weighted prenucleoli without consistency. 29th EURO. 2018, Valencia. Invited conference.

C.3. Research projects.
1. PID2020-113110GB-I00. Distribución equitativa en problemas de reparto, coaliciones, redes y mercados. Ministerio de Ciencia, Innovación y Universidades. 2021-2024. IP: Marina Núñez, Carlos Rafels. Researcher.
2. AS017672. Networks in Societies: Information, Elections, and Financial Markets. Vicerectorat de recerca de la Universitat de Barcelona. 2022-2023. IP: Oriol Tejada. Researcher.
3. 2017SGR778, Teoria de Jocs i Mercats d'Assignació. Agència de Gestió d'Ajuts Universitaris i de Recerca (AGAUR). 2017-2021. IP: Marina Núñez. Researcher

C.4. Ttransfer merits

1. Collective exhibition at different Spanish universities: “Quan no n'hi ha prou per repartir. Pensar matemàticament” Founded as a transference Project by the MCIU (FCT-17-12121).

Language

English

Description

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. Although this is a new discipline in Economics, starting with “The Theory of Games and Economic Behavior” by von Neumann and Morgenstern (1944), it is developed on the basis of mathematical tools, especially (but not only) those focusing on optimization and operations research issues.

Course goals

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 main goal is to understand and apply the notions of Nash equilibrium, subgame perfect Nash equilibrium and Bayesian Nash equilibrium due to Nash, Selten and Harsanyi (the three receiving the Nobel prize in Economics in 1994).

The applications to market structure models and to other branches of economics and mathematics 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 as for example applying the Shapley value.

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.

Course contents

1. Static games with complete information.

Strategic dominance (rational decisions) and the prisoner’s dilemma. Concept and examples of Nash equilibrium. Existence. The tragedy of the commons. Social vs individual decison making. Applications to competition in markets: Cournot’s and Bertrand’s duopoly models.

2. Dynamic games with complete information

Representation of an extensive-form game: information sets and backward induction. Subgames; the perfect Nash equilibrium in subgames; examples. Applications to competition in markets: Stackelberg’s duopoly.

3. Static games with incomplete information

Introduction to games with incomplete information. Static Bayesian games: types, conjectures, payments and strategies. Bayesian Nash equilibrium. Applications: Cournot’s duopoly with incomplete information; auctions

4. Cooperative games

The core. The Shapley value. Operations research cooperative games on networks.

Prerequisites

Although no prior knowledge of any specific mathematical discipline is required, a familiarity with logical and mathematical reasoning is desirable.

Targeted at

All students. Specially those interested in applications of mathematics and operations research to economics.

Evaluation

The assessment of the course will basically consist of the activities set during practical sessions together with a problem set.

The activities developed in class is worth 30%, while the problem set is worth 40%.

The remaining 30% corresponds to a different activity requiring the students to look for a real life problem in which applying game theory ideas and techniques make sense.

We will devote some of the practical sessions to prepare this activity as well.

Software requirements

No software requirements. It is a course thought to deeply get into the decision making process when interaction appears, rather than on the computational issues regarding this decision making process.