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)
"Éthique lacanienne et théorie des jeux"
En partant du dilemme des prisonniers, dont Lacan fait l’objet d’un article dès 1945 et dont il reprendra l’analyse par la suite, en particulier dans les Écrits (1966), nous considérerons ce que l’éthique de la psychanalyse doit à la théorie des jeux. Peut-être aussi, et de façon plus risquée de ma part, ce que cette éthique aurait pu en prélever et qui fût d’importance égale à sa réflexion sur le temps logique et sur l’assertion de certitude anticipée. L’œuvre de Harsanyi est en plein développement dans les années 50-60 ; le nom d’Harsanyi n’apparaît pas dans « L’éthique de la psychanalyse ». Toutefois son auteur a déjà rencontré le travail de Von Neumann et de Morgenstern. Mon propos est donc de tenter d’esquisser les affinités de la recherche lacanienne en matière d’éthique avec les recherches éthiques et politiques (le plus souvent anglosaxonnes) inséparables de la théorie des jeux.

Alma Frischoff (MIT, Linguistics and Philosophy)
"A General Account of Exhaustification with an Iterated Rationality Model"
Scalar Implicatures (SIs), such as the inference from ‘some’ to ‘some but not all’ have been extensively studied in recent decades, both theoretically and experimentally. In recent work, Fox and Katzir (2021) provide two arguments supporting a grammatical approach to SIs over a family of pragmatic, game-theoretic models referred to as Iterated Rationality Models (IRMs), based on conjunctive readings of disjunctive (CRD) sentences. First, they argue that IRMs are unable to derive CRDs with more than two disjuncts. Second, they argue that IRMs are extremely sensitive to prior probabilities in the case of CRDs, and conclude that SI computation is modular. The goal of this work is to explore what it would take to make IRMs compatible with the arguments in the literature. Our main conclusions are: (a) that the ‘naive speaker’ in IRMs needs to be rethought, adopting a notion of weighted message scores (WMS); and (b) that the IRM itself needs to be conceptualized as an exhaustivity operator rather than a pragmatic process, to deal with modularity issues. These are nontrivial departures from familiar views on IRMs, but they are warranted by the empirical arguments. This sharpens a challenge for current semantic/pragmatic theories: choosing between competing exhaustivity mechanisms.

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 and 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.

Olivier Gossner (CNRS, École Polytechnique, and London School of Economics)
"A Measurable Approach to Information Equivalence"
Following Harsanyi (1967/68), an information environment in a Bayesian game can be represented by a probability space equipped with players’ information σ-fields and a measurable map to the state of nature. Since these primitives are probabilistic and measurable, it is natural to ask which aspects of an information environment are intrinsically measurable, and which aspects enter only because one introduces a topology for technical convenience.

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 Characterization of Common Priors"
We show that the equivalence of common priors and absence of agreeable bets of the famous no-betting theorem can be generalized 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 behavioral condition limiting acceptable bets.

Marilynn Johnson (University of San Diego, Philosophy)
"Veiling with Multiple Audiences: Cooperative Communication in Speech and Fashion"
In his 2007 book The Stuff of Thought and later papers in 2008, 2010, and 2011 Steven Pinker considers the work of philosopher of language Paul Grice and proposes a number of instances of perceived non-cooperation as problem cases for Grice’s Cooperative Principle. Pinker proposes a game-theoretic framework to understand some cases of what he calls “veiled speech” that, according to his argument, cannot be accounted for by Grice. I will begin by explaining what Pinker gets wrong about Grice’s Cooperative Principle, which is well equipped to explain the types of cases Pinker proposes as problematic, drawing on my previous work (Johnson 2016). We can understand some forms of so-called “veiled speech” as instances of a speaker cooperating with multiple audiences, which Grice discusses. When a speaker produces an utterance she may do so with two (or more) different hearers in mind, and aim to optimize with these both. Finally, I will connect this discussion with recent work in philosophy of fashion (Johnson 2022; Simmenauer and Ramponi Forthcoming) to consider how we might apply these ideas of cooperation with multiple audiences to the choices we make when adorning the body. Depending on whose gaze we are under there may be different costs and benefits to the messages sent with our clothing, and we as rational bodies moving in the world make choices such as wearing ambiguous clothing (Simmenauer and Ramponi Forthcoming), removing clothing, completely changing, and sometimes literally veiling to optimize these payoffs.

Roni Katzir (Tel Aviv University, Computational Linguistics Lab)
"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? We examine how far a public information provider, such as a media outlet, platform, or institutional mediator, can shape the way a group collectively understands the world when individuals already possess private information. Our analysis identifies fundamental constraints on the set of shared beliefs that can arise from public signals, showing that not every collective perception is achievable, even with carefully designed communication. Informational structure alone can impose subtle and sometimes surprising limits on how beliefs can be shifted, and these limits may prevent smooth or gradual changes in public opinion. We also develop a framework for comparing different information providers in terms of their ability to influence strategic outcomes, emphasizing the role of shared understanding and higher order beliefs in shaping collective behavior. Overall, the results clarify both the power and the inherent limits of public information in influencing joint perception in strategic environments.

Jérémy Ledent (University Paris Cité, Institut de Recherche en Informatique Fondamentale)
"Distributed Knowledge in Simplicial Models"
Based on joint work with Éric Goubault and Sergio Rajsbaum
The usual semantics of multi-agent epistemic logic is based on Kripke models, which represent agents' knowledge in terms of possible worlds connected by indistinguishability relations. In this talk, I will present an alternative semantics based on simplicial complexes, a geometric structure from the field of combinatorial topology. Conceptually, this represents a shift in perspective: the fundamental object of interest is no longer the possible worlds, but the agents' points of view about the world. This reveals a geometric structure that is already implicit in the usual Kripke framework. After a brief introduction to simplicial complexes, I will focus on the notion of distributed knowledge: that is, the knowledge that a group of agents would acquire, if they were able to perfectly share their local information. As it turns out, distributed knowledge (as well as its infinite iteration, common distributed knowledge), admits a natural geometric interpretation in terms of higher-dimensional connectivity of the simplicial complex. I illustrate the approach with examples from distributed computing, in particular the majority consensus task. https://www.arxiv.org/abs/2602.06945

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.

Aran Nayebi (Carnegie Mellon, Machine Learning, NeuroAgents lab)
"Intrinsic Barriers and Practical Pathways for Human-AI Alignment: An Agreement-Based Complexity Analysis"
We formalize AI alignment as a multi-objective optimization problem called (M, N, ε, δ)-agreement, in which a set of N agents (including humans) must reach approximate ε-agreement across M candidate objectives, with probability at least 1-δ. Analyzing communication complexity, we prove an information-theoretic lower bound showing that once either M or N is large enough, no amount of computational power or rationality can avoid intrinsic alignment overheads. This establishes rigorous limits to alignment itself, not merely to particular methods, clarifying a “No-Free-Lunch” principle: encoding “all human values” is inherently intractable and must be managed through consensus-driven reduction or prioritization of objectives. Complementing this impossibility result, we construct explicit algorithms as achievability certificates for alignment under both unbounded and bounded rationality with noisy communication. Even in these best-case regimes, our bounded-agent and sampling analysis shows that with large task spaces (D) and finite samples, reward hacking is globally inevitable: rare high-loss states are systematically under-covered, implying scalable oversight must target safety-critical slices rather than uniform coverage. Together, these results identify fundamental complexity barriers—tasks (M), agents (N), and state-space size (D)—and offer principles for more scalable human-AI collaboration.

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 and Daniel Toneian
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 neighbors 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.

Orr Well (University of Tel Aviv, Computational Linguistics Lab)
"Ineffability Follows from a Question-Based Approach to Focus"
Based on joint work with Moshe Bar-Lev and Roni Katzir
Focus, typically realized through pitch accent, is known to play an important role in establishing congruence between a question and its answer. The felicity of a question- answer pair often depends on where focus is placed: (1) What does John eat in PARIS?
a. John eats CREPES in Paris.
b. # John eats crepes in PARIS.
However, Schwarzschild (1993, 1997, 2004) observes that certain seemingly harmless question-answer pairs are infelicitous, regardless of focus placement: (2) What does John only eat in PARIS?
a. # John only eats CREPES in Paris.
b. # John only eats crepes in PARIS.
(2.a) carries the unwanted inference that John eats nothing but crepes in Paris, while (2.b) triggers the improper presupposition that John eats crepes somewhere. Previous approaches to the ineffability of (2) attempt to reduce the problem to formal constraints on the structure of the answer when considered in isolation. We show that such constraints are not only stipulative, but also fail to predict that the answer can be ameliorated by modifying the preceding question or other contextual factors. We argue instead that focus ineffability arises from an interaction between semantic content and the pragmatics of question answering. Specifically, ineffability follows under the assumption that focus introduces an implicit question into discourse. In cases like (2), either the implicit question does not coherently relate to the explicit background question, or the answer itself does not appropriately address it, regardless of how focus is assigned or how only’s quantificational domain is determined. Overall, the work highlights the central role that questions and answers play in the dynamics of discourse.