Abstracts 2026

Half a Century of "Agreeing to Disagree"

Galit Ashkenazi-Golan (London School of Economics, Mathematics)
"The Role of Information in Adaptive Dynamics in Games"
We give a high-level introduction to adaptive dynamics, with emphasis on the role of information. From information about the game, to information about the opponent and information about the adaptive process the opponent is using.

Jean-Pierre Cléro (University of Rouen, Philosophy)
"Lacan: The Riddle of the 3 Prisonners and the Logic of Time"

Alia Gizatullina (University of St. Gallen, Economics)
"Agreement, Truth, and Shared Delusion in LLMs"
Abstract: We discuss when common agreement among large language models should be interpreted as evidence of common truth versus a symptom of common delusion driven by correlated priors from shared training data. Using a simple Bayesian perspective with misspecified, correlated “common priors” and stylized debate/aggregation protocols, we outline mechanisms that make consensus more or less informative about correctness and discuss empirical analysis for detecting agreement on a systematic error.

Yannai A. Gonczarowski (Harvard University, Economics & Computer Science)
"Common Knowledge, Regained"
For common knowledge to arise in dynamic settings, all players must simultaneously come to know it has arisen. Consequently, common knowledge cannot arise in many realistic settings with timing frictions. This counterintuitive observation of Halpern and Moses (1990) was discussed by Arrow et al. (1987) and Aumann (1989), was called a paradox by Morris (2014), and has evaded satisfactory resolution for four decades. We resolve this paradox by proposing a new definition for common knowledge, which coincides with the traditional one in static settings but is more permissive in dynamic settings. Under our definition, common knowledge can arise without simultaneity, particularly in canonical examples of the Haplern-Moses paradox. We demonstrate its usefulness by deriving for it an agreement theorem à la Aumann (1976), showing it arises in the setting of Geanakoplos and Polemarchakis (1982) with timing frictions added, and applying it to characterize equilibrium behavior in a dynamic coordination game.

Olga Gorelkina (UM6P, Africa Business School, Moroccan Center for Game Theory)
"Collusion via Information Sharing"
This paper studies collusion via certified sharing of information in the context of mechanism design with transfers. The model of collusion builds on Aumann’s (1976) description of knowledge. A cartel can agree on a contract to collude if it is common knowledge within the cartel that the contract is incentive compatible and individually rational. Subsequently, robustness of mechanisms to collusion via information sharing is defined as the impossibility of an agreement to collude. Robust mechanisms are characterized in three settings with variable degrees of agents' liability to the cartel. Finally, I introduce a novel collusion-robust auction mechanism that achieves the second-best revenue.

Ani Guerdjikova (University of Grenoble Alpes, Economics)
"How Do You Know What I Mean? Implication and Translation"
When agents entertain distinct perceptions of the word, communication between them will be imprecise. In particular, under differential awareness, an event as described by one agent may find no exact analog in another agent’s subjective understanding. Within this context, it is natural to consider a syntactic model where the agent’s understanding of the world is embodied by a language (i.e., a set of interconnected descriptions of the world). Communication between agents can therefore be understood as a process of translating statements from one language to another. This paper asks how such a translation might arise and how it might be identified by an observer. We show that even if translation between languages is consistent, i.e., preserves logical implications, it need not imply the existence of a joint state-space that embeds the individual models of the two agents. We expose why this failure occurs and provide an axiom that ensures the existence of a joint state spaces which embeds the individual state-spaces.

Ziv Hellman (Bar-Ilan University, Economics)
"Charges and Bets: a General Characterisation of Common Priors"
We show that the equivalence of common priors and absence of agreeable bets of the famous no-betting theorem can be generalised to any infinite space (not only compact spaces) if we expand the set of priors to include probability charges as priors. Going beyond the strict prior/no common prior dichotomy, we further uncover a fine-grained decomposition of the class of type spaces into a continuum of subclasses in each of which an epistemic condition approximating common priors is equivalent to a behavioural condition limiting acceptable bets.

Roni Katzir (Tel Aviv University, Linguistics)
"Focus and Questions"
Focus dependencies, including question-answer congruence (QF), free focus (FF), and association with focus (AF), are often treated in terms of various grammatical mechanisms that rely on (a) focus-semantic values along a second semantic dimension, and (b) an anaphoric operator, ~, that is sensitive to these values and can communicate them to various processes. I argue against this view and in favor of a unification through a pragmatic condition: an utterance is felicitous only if it is a good answer to a good (explicit or accommodated) question, with relevance understood relative to a question-induced partition of the context set.

David Lagziel (Ben-Gurion University of the Negev, Economics)
"Comparison of Oracles"
To what extent can an information provider influence the public's joint perception?

Yoram Moses (Technion - Israel Institute of Technology)
"What is Common About Common Knowledge?"
The talk will survey how Aumann's Agreeing to Disagree paper affected work on knowledge in distributed systems, and will argue that infinite nesting is not the essential aspect of common knowledge.

Christina Pawlowitsch (Université Paris-Panthéon-Assas, Laboratoire d'Économie Mathématique et de Microéconomie Appliquée)
"Delta-Epsilon Common Knowledge"
Based on joint work with
Stefan Schrott (University of Vienna, Mathematics) and
Daniel Toneian (University of Vienna, Mathematics)
I report on recent work, joint with Stefan Schrott and Daniel Toneian, proposing a novel notion of approximate common knowledge of an event, which, in continuation of work by Nielsen (1984), is formulated in the language of σ-algebras and applicable for general (and not just countable) probability spaces. The proposed concept, (δ, ε)-common knowledge of an event, relies on two elementary “nearby” set-theoretic notions: (1) an event B being δ-nearly contained in a σ-algebra, and (2) an event B being ε-nearly a subset of another event A. For (δ, ε)-common knowledge of an event, we establish: (1) equivalence of the σ-algebra-based definition and both a hierarchical and an alternating hierarchical definition (generalizing Aumann’s argument showing the equivalence of the partition-based definition and the informal alternating hierarchical definition of common knowledge), and (2) a generalization of Aumann’s Agreement Theorem, showing that when two individuals have (δ, ε)-common knowledge of their posteriors of an event—or more generally, of a random variable taking values in the unit interval—then the distance between these posteriors is bounded as a function of δ and ε. Furthermore, we extend Nielsen’s notion of common knowledge of a random variable to a notion of (δ, ε)-common knowledge of a random variable, formulated in terms of conditional variances. In this setting, we establish: (1) equivalence of the σ-algebra-based definition and both a hierarchical and an alternating hierarchical definition of (δ, ε)-common knowledge of a random variable, as well as (2) an agreement theorem for (δ, ε)-common knowledge of a random variable, showing that if the posteriors of a random variable X are (δ, ε)-common knowledge on an event B, then the L2-distance between the posteriors on B is bounded as a function of δ and ε.

Steven Pinker (Harvard University, Psychology)
"Common Knowledge and Rational Discourse Among Mortal Humans"
I explore two psychological questions inspired by the Agreement Theorem. One is the mental representation of common knowledge: how can a finite brain represent an infinite iteration of nested “He knows that she knows…” propositions? I present the results of studies suggesting that people represent common knowledge by a simple intuition that some fact is public, salient, or “out there,” together with a sense that this is sufficient to spin out an unlimited number of nested propositions if they ever needed to. The other is that the surprise that “agreeing to disagree,” which most people take to be the epitome of reasonable, civil discourse, is in fact irrational for deliberating agents with a shared understanding of the world. I examine the ideals of rational argumentation assumed by the theorem, particularly shared priors, common knowledge of posteriors, and mutual updating as a random walk, and contrast them with typical argumentation by less-than-rational humans.

Miklós Pintér (Corvinus University, Economics)
"Consistency of Beliefs: An Overview"
We provide a concise overview of the literature, beginning with Aumann (1976) on the consistency of beliefs and the characterization of a common prior, and progressing to the most recent results in this area. The presentation is organized along two complementary dimensions. The first emphasizes the underlying economic and conceptual intuitions behind the results, while the second addresses the corresponding technical framework and methodological contributions.

Herakles Polemarchakis (University of Warwick, Economics)
"On the Road to Agreement"
A Bayesian dialogue is a sequential exchange of beliefs. It is the prototype of a rational dialogue. At each stage, one of two interlocutors states his beliefs formed after the revision prompted by the beliefs stated by the other at the previous stage. The dialogue terminates when nothing is left to be said. The only property of a rational dialogue is eventual agreement. A third party, with access only to the transcript of a dialogue, cannot distinguish a Bayesian dialogue from an arbitrary sequence of alternating utterances. One can consider common knowledge and agreement as equilibrium conditions and the dialog that leads to common knowledge as the adjustment path. It follows that, across fundamentals, rationality is a refutable claim at equilibrium, while, along the adjustment path, it is not. Which bears an analogy with competitive markets. While Walrasian tâtonnement that leads to equilibrium, if it does, is arbitrary, equilibrium prices and quantities are not arbitrary. They may even identify fundamentals.

Klaus Ritzberger (Royal Holloway, University of London) and
Jörgen Weibull (Stockholm School of Economics)
"Solid Outcomes in Sender-Receiver Games"
We provide a game-theoretic analysis of sender-receiver games in order to shed further light on the emergence and stability of communication and language. We consider several game-theoretic approaches to this fundamental but complex issue. In particular, we use the notion of "game blocks and solid outcomes" (Ritzberger and Weibull 2025) and “tenable strategy blocks and settled equilibria” (Myerson and Weibull 2015), as well as point- and set-valued notions of evolutionary stability. In addition, we develop a novel approach to group selection that requires evolutionary stability at the individual level within groups.

Elias Tsakas (Maastricht University, Economics)
"Local Epistemic Conditions in Large Games"
The epistemic program has focused on providing foundations for game theoretic solutions concepts. This is typically done by means of conditions, like for instance common prior, common belief of rationality, etc. And while in small games such conditions seem innocent, in games with a large number of players they are more difficult to justify. Instead, it is more appealing to impose such conditions only locally in the context of an underlying network structure, e.g., it is much more reasonable to assume that players believe that their neighbours are rational, as opposed to believing in the rationality of other players who are located in very remote parts of the network. This gives rise to the following question: can we still justify the predictions of "global" solution concepts by means of "local" epistemic conditions? In this talk I will review some of my work from the early 2010's, as well as more recent work by other authors on this question.

Rafael Veiel (UT Austin, Economics)
"Three Views on Common Knowledge of Rationality"
We will look at the different structures of information that are obtained when assuming common knowledge of rationality in a game: This endows information with 1) an algebraic structure (players information is canonically given by a additive noise), 2) a geometric structure when that noise is small and players play a global game, and finally 3) a topological structure which ensures rationalizable outcomes to be close when information is perturbed. We will survey all three.