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Lecturers: Eric Pacuit ( website), Olivier Roy ( website)
Venue: European Summer School for Logic, Language and Information
(ESSLLI 2010)
Meeting Times: 11.00 - 12.30 (Day 1, Day 2, Day 3, Day 4, Day 5)
Location: University of Copenhagen, Auditorium 21.1.21


Questions of collective agency and collective intentionality are not new in philosophy, but in recent years they have increasingly been investigated using logical methods. The work of Bacharach [2], Sugden [6] and Tuomela [7], in particular, elegantly combines philosophical relevancy with a strong inclination towards logical modeling of decision and action.

Logical and algebraic approaches are also more and more present in foundations of decision theory (cf. the work of Jeffrey [5] and Bradley [3]), epistemic game theory (Brandenburger [4] and van Benthem [8]), and, of course, dynamic epistemic logic [9,10]. These are three areas where questions of group agency and interaction also naturally arise. In these fields, however, group agency is rather studied from the perspective of individual decision makers, with the aim of understanding how the former stem from mutual expectations of the latter.

Little is known, however, about the relationship between these views on interaction and collective agency. On the one hand, decision- and game-theoretical approaches build on resolutely individualistic premises, and study the logic of individual belief and preferences in interactive decision making. On the other hand, the aforementioned philosophical theories take a more collectivist standpoint, focusing on how decision makers engage in “group”, “team” or “we-mode” of reasoning, which is often claimed to involve irreducibly collective attitudes.

This course will introduce these bodies of literature in order to clarify their relationship, both from a logical and a conceptual point of view. It will first cover recent development in the foundations of decision theory and epistemic foundations of equilibrium play in interaction. It will then move to the three philosophical theories of group agency mentioned above and, using logic as a common denominator, try to understand how they relate to decision- and game-theoretical approaches.


Below is a schedule for the course (which is subject to change) with links to the lecture slides and brief synopses.

Date Topic Slides
Day 1
Aug 16, 2010
Introduction, Motivation and Background
(brief synopsis)
Lecture 1
Day 2
Aug 17, 2010
Common Knowledge and Common Modes of Reasoning
(brief synopsis)
Lecture 2
Day 3
Aug 18, 2010
(Unreliable) Team Reasoning I
(brief synopsis)
Lecture 3
Day 4
Aug 19, 2010
(Unreliable) Team Reasoning II
(brief synopsis)
Lecture 4
Day 5
Aug 20, 2010
Correlations and Other Notions of Group Agency
(brief synopsis)
Lecture 5

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Day 1: Introduction, Motivation and Background

In this first lecture, we introduced and motivated the study of "teams" and, more generally, group modes of reasoning. We introduced some basic game theoretic notions (normal form game including some well-known games such as Hi-Lo and Prisoner's Dilemma) and the epistemic-doxastic models we will use during the week (type spaces and Bayesian models).

For more information, you can consult:
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Day 2: Common Knowledge and other Common Modes of Reasoning

This second lecture discussed various notions of group informational attitudes, such as common knowledge, distributed knowledge and common belief. We started by discussing the "standard" approach to common knowledge in the game theory literature (via so-called Aumann structures). The lecture focused on a number of important issues, such as levels of knowledge, the common knowledge of rationality assumption in game theory and the question where does common knowledge come from? (Lewis' answer: common modes of reasoning).

For more information, you can consult:
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Day 3: (Unreliable) Team Reasoning I

We started by finishing up our discussion of common knowledge and belief that we started yesterday. In particular we looked at Lewis' original analysis of common knowledge and compared it to the "standard" Aumann formalization. The next topic takes these ideas of Lewis even further by putting forward a notion of "team reasoning".

Most of today's lecture is about the theory of *Unreliable Team Interaction* mostly developed by Michael Bacharach in a paper from 1999 his posthumous book from 2006. According to this theory acting as a group involves two important switch in the mindset of the agents: *preference* and *agency transformation.* Preference transformation means that the individuals who identify with a given team adopt its preferences, aims and goals. Agency transformation means that they indeed act on these preferences, that they *team reason* in the following way: (1) compute which outcomes maximize the team preferences, 2) identify what is asked of them in order to reach this outcome and, (3) go and act accordingly. The notion of *unreliable team interaction* allows us to explore the consequences of this form of group identification in a general way. For more information, you can consult:
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Day 4: (Unreliable) Team Reasoning II

We saw today that team reasoning can account for coordination on the Pareto-Optimal profile in the Hi-Lo games, and for a certain amount of cooperation in the Prisoner's Dilemma. We will then see that preference transformation can be interpreted in terms of change in *framing*, and will use the notion of Bayesian equilibrium to stress the difference between acting individually with team preferences, and acting as a full-blown team member.

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Day 5: Correlations and Other Notions of Group Agency

Today we will consider a different way for agents to coordinate or entangle their action: so-called *correlations* in games. Correlations are very frequent phenomena, showing up for instance in the characterization of rationalizable strategies for more than 2 players, or in the infamous Newcomb's problem in decision theory. We will look at the notion of correlated strategies, where agents make their choices dependent on some *signals* from outside of the game. We will see that *correlated equilibrium* (Aumann, 1987) is a generalization of Nash equilibrium, and that it can account for some form of coordination. We will then move from these extrinsic to more *intrinsic* forms of correlations (Brandenburger and Friedenberg, 2007), where correlations in strategies do not come from outside signals but rather from *correlations in beliefs* or types. We will see the conditions under which correlated strategies can be explained by correlations in beliefs, but also that not all extrinsic correlations are explainable intrinsically. We will briefly consider the (open) question of correlated beliefs in qualitative structure, and explore the relation between correlated strategies and unreliable team interaction.

We concluded with some discussion of philosophical issues surrounding the teams and group agency.

For more information, you can consult: up_arrowBack to the schedule


The course aims at students interested in theories of interaction, either from a philosophical or from more applied point of view (e.g. multi-agent systems). It will be for the most part self-contained, thus does not require previous knowledge of the philosophical or game- and decision-theoretical material that we will cover, but asks for a reasonable level of mathematical maturity. Consult the following papers and books for more information:

  1. R.J. Aumann and J.H. Dreze (2008). Rational expectations in games. American Economic Review, 98 (1): 72–86.
  2. M. Bacharach (2006). Beyond Individual Choices: Teams and Frames in Game Theory. Princeton University Press, Princeton, 2006. Edited by N. Gold and R. Sugden.
  3. R. Bradley (2007). A unified bayesian decision theory. Theory and Decision, 63 (3): 233–263.
  4. A. Brandenburger (2007). The power of paradox: some recent developments in interactive epistemology. International Journal of Game Theory, 35: 465–492.
  5. R. Jeffrey (1965). The Logic of Decision, McGraw-Hill, New-York, 1965.
  6. R. Sugden (2003). The logic of team reasoning. Philosophical Explanations 6, pages 165–181, 2003.
  7. R. Tuomela (1995). The Importance of Us: A Philosophical Study of Basic Social Notions, Stanford University Press, Stanford.<\li>
  8. J. van Benthem (2007). Rational dynamic and epistemic logic in games. International Game Theory Review, 9 (1): 13–45.
  9. J. van Benthem (forthcoming). Logical dynamics of information and interaction. Cambridge University Press.
  10. H. van Ditmarsch, W. van de Hoek, and B. Kooi. Dynamic Epistemic Logic, volume 337 of Synthese Library Series, Springer.

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Additional Information

Relevant Conferences: