What is Strategic Information? A Workshop on Game Theory

London School of Economics and Political Science

Monday – Tuesday 15 – 16 April, 2024

Financial support from the London Mathematical Society is gratefully acknowledged.

Organisers: Galit Ashkenazi-Golan, Olivier Gossner, and Bernhard von Stengel

Speakers:

Gregorio Curello	Matteo Escudé	Michal Feldman	Tangren Feng	Françoise Forges
Mira Frick	Olivier Gossner	Penélope Hernández	Thomas Norman
Christina Pawlowitsch	Clemens Possnig	Ina Taneva	Bernhard von Stengel

Registration:

Room capacity is limited. Participants who are not speakers will need to register with an email to Emily Jackson (e.jackson2@lse.ac.uk) please with cc: to b.von-stengel@lse.ac.uk and G.Ashkenazi-Golan@lse.ac.uk

Location at LSE:

Schedule

Click on a speaker name for talk abstract

Presentation Details

Speaker	Title, Links	Abstract
Gregorio Curello University of Bonn, Germany	The Comparative Statics of Persuasion (joint with Ludvig Sinander)	In the canonical persuasion model, comparative statics has been an open question. We answer it, delineating which shifts of the sender's interim payoff lead her optimally to choose a more informative signal. Our first theorem identifies a coarse notion of 'increased convexity' that we show characterises those shifts of the sender's interim payoff that lead her optimally to choose no less informative signals. To strengthen this conclusion to 'more informative' requires further assumptions: our second theorem identifies the necessary and sufficient condition on the sender's interim payoff, which strictly generalises the 'S' shape commonly imposed in the literature. We identify conditions under which increased alignment of interests between sender and receiver lead to comparative statics, and study applications.
Matteo Escudé LUISS University, Rome	Transparent Allocations with Costly Falsification (joint with Piero Gottardi)	A principal wishes to accept an agent if and only if he is suitable, while the latter wants to be accepted regardless of suitability. Each of them possesses private information about the quality of the match. We study principal-optimal mechanisms when: (i) transfers are not feasible but (ii) misreporting is costly for the agent. We show that, if the principal has a narrow focus – in the sense that her possible types fully disagree on which agents are suitable – principal-optimal mechanisms never require her to reveal her private information. In contrast, if her focus is broad, revealing her preferences to the agent may be beneficial: transparent mechanisms might be strictly principal-optimal.
Michal Feldman Tel-Aviv University	Combinatorial Contracts (joint with Tomer Ezra, Paul Duetting, and Thomas Kesselheim)	Contract design captures situations where a principal delegates the execution of a costly task to an agent. To complete the task, the agent chooses an action from a set of costly actions. The principal can only observe the outcome, which is stochastically determined by the chosen action. The principal incentivizes the desired action through a contract, that specifies payments based on the observed outcome. In this talk, I will survey two papers on combinatorial contracts, which highlight different sources of complexity that arise in contract design. The first (FOCS'21) is where the agent can choose any subset of a given set of actions; the second (STOC'23) is where the principal motivates a team of agents. We provide (approximation) algorithms and hardness results for the optimal contract problem in these scenarios.
Tangren Feng Bocconi University, Milan	Getting Information from Enemies (joint with Qinggong Wu)	A decision maker (DM) faces a binary choice. The DM does not know which alternative is better, but a group of experts do. However, the experts would like the DM to make the wrong choice. Given the hostility, is it still possible for the DM to extract useful information from the experts using mechanism design? We answer 'Yes': There are mechanisms where truth-telling is a Bayesian or even ex post equilibrium, even though the information leak benefits DM and hurts the expert. On the other hand, if truth-telling is required to be an interim or ex post dominant strategy, then no mechanism extracts information in favor of the DM.
Françoise Forges University of Paris – Dauphine	Neologisms in Cheap Talk Games (joint with Stéphan Sémirat)	Pure perfect Bayesian equilibria in sender-receiver games with finitely many types for the sender are characterized as incentive compatible partitions of the sender's types. Refinements involve neologism-proof and undefeated partitions. In the case of ordered types, real-valued decisions, and well-behaved utility functions, we propose a family of iterative optimization processes, which can be interpreted as better response dynamics. We show that they all converge to a unique incentive compatible partition, which is undefeated and also the only one that could be neologism-proof.
Mira Frick Yale University	Multidimensional Screening with Rich Consumer Data (joint with Ryota Iijima and Yuhta Ishii)	We study multi-good sales by a seller who has access to rich data about a buyer's valuations for the goods. Optimal mechanisms in such multidimensional screening problems are known to in general be complicated and not resemble mechanisms observed in practice. Thus, we instead analyze the optimal convergence rate of the seller's revenue to the first-best revenue as the amount of data grows large. Our main result provides a rationale for a simple and widely used class of mechanisms – (pure) bundling – by showing that these mechanisms allow the seller to achieve the optimal convergence rate. In contrast, we find that another simple class of mechanisms – separate sales – yields a suboptimal convergence rate to the first-best and thus is outperformed by bundling whenever the seller has sufficiently precise information about consumers.
Olivier Gossner LSE and Ecole Polytechnique	SCAMP (joint with Rafael Veiel)	We study (interim correlated) rationalizability in games with incomplete information. For each given game with incomplete information, we show that all hierarchies of iterative deletion of dominated strategies can be captured through an automaton, the strategic automaton. We then prove that a finitely parameterized class of information structures, SCAMP, is sufficient to generate every outcome distribution induced by general common prior information structures. In this parameterized family, a profile of signals is identified to a path over the automaton, and the probability distribution of signal profiles defines a Markov chain.
Penélope Hernández University of Valencia	Strategic Communication inside Platforms (joint with Julián Chitiva)	Two main factors have helped the development of the advertising industry. First, Machine Learning algorithms help platforms such as Google and Facebook to know users better for more targeted advertising campaigns. Second, people share an interest in coordinating their actions, which is helped by communication among them. To study these phenomena we propose a three-stage game between a platform and its users. We assume users have private information about their types. A key assumption here is that although this information is private among users (each user knows his type but does not know the others' types) it is known by the platform thanks to its algorithms. In the first stage, the platform plays a Bayesian Persuasion game with its users. The main goal of the platform is to privately persuade its users, depending on their types, to bias their Bayesian belief of the state of the world. In the second stage, after the platform has privately communicated with the users, we describe a Cheap-Talk communication game among the users. In this stage, users forward the message received from the platform to a subset of other users; that subset is each user's only choice – they cannot reveal their type, but users who receive the message can update their belief about the other's type in a Bayesian way. In the last stage, users take an action that determines their utility. The utility function of each user considers that each user wants to take an action as close as possible to their favorite action, and which other users want to coordinate among them. We characterize the (unique) equilibrium action in the n-player game with private information by solving the last stage. Then, we compute the signalling equilibria of the cheap-talk game. Finally, we compute the optimal action of the platform under different assumptions for its utility function, such as maximizing revenue or the social welfare of its users.
Thomas Norman University of Oxford	Sunspots and Bayes Correlated Equilibrium	Sunspot equilibria allow the non-standard features of extrinsic price uncertainty and coordination of agents' choices in general equilibrium, but with no apparent mechanism governing their occurrence. We show in this paper that such a mechanism can be provided by making one of the agents a "market-maker", who sets prices and clears the market of any excess demand or supply. In a game where the market-maker chooses prices prior to trading, his optimal price choice is equivalent to his optimal choice of Bayes correlated equilibrium demands, yielding equivalence with an information design problem. The set of sender-preferred Bayes correlated equilibria of this game is shown to coincide with the set of sunspot equilibria of the underlying economy, with non-trivial sunspots arising outside the convex hull of Nash equilibria.
Christina Pawlowitsch University of Paris-Panthéon-Assas	Meaning in Costly-Signaling Games	Costly-signaling theory is a well-established paradigm in economics and theoretical biology. In this talk, using a parametrized family of discrete games with two states of nature (high and low), two signals (presence and absence of a costly signal), and two reactions to signals (accept and do not accept), I address the question What "meaning" is in this games? What meaning the presence, respectively, the absence of the costly comes to carry in the various co-existing equilibria of this game, and how this changes, as a function of the prior probability on the states of nature and the cost of the signal. Special attention is given to cases so far neglected in the literature: mixed-strategy, partially revealing/partially "pooling" equilibria, which are interpreted as a form of "indirect speech"; and the co-existence of "all-signal-accept" and "nobody-signal-accept" equilibria in case of a high prior on the high type, which is explored as the basis of "countersignaling" and, related to that, a phenomenon of "indirect discrimination" when a costly-signaling mechanism interacts with discrimination based on observable characteristics. Illustrations from the study of language are given.
Clemens Possnig University of Waterloo, Canada	Reinforcement Learning and Collusion	This paper presents an analytical characterization of the long run policies learned by algorithms that interact repeatedly. These algorithms update policies which are maps from observed states to actions. I show that the long run policies correspond to equilibria that are stable points of a tractable differential equation. As a running example, I consider a repeated Cournot game of quantity competition, for which learning the stage game Nash equilibrium serves as non-collusive benchmark. I give necessary and sufficient conditions for this Nash equilibrium not to be learned. These conditions are requirements on the state variables algorithms use to determine their actions, and on the stage game. When algorithms determine actions based only on the past period's price, the Nash equilibrium can be learned. However, agents may condition their actions on richer types of information beyond the past period's price. In that case, I give sufficient conditions such that the policies converge with positive probability to a collusive equilibrium, while never converging to the Nash equilibrium.
Ina Taneva University of Edinburgh	Information, Higher-Order Reasoning and Contingent Thinking (joint with Brian Rogers)	The assumption of rationality and higher-order reasoning about rationality underpins many models of strategic behavior. We investigate the degree to which this assumption holds in a simple incomplete information game and how that depends on the particular informational environment of the game. The project aims to provide a simple framework for identifying higher-order rationality in incomplete information games and test the implications of different types of information structures on the players' displayed orders of rationality. We have run a lab experiment and collected data from 115 participants across three treatments, holding the basic game fixed and varying the information structure, where information structures across treatments are ranked in terms of contingent thinking difficulty. We are able to obtain within-subject comparisons of the degree to which more difficult information structures impact the levels of rationality of players.
Bernhard von Stengel LSE	Information Gain and Computational Complexity	The concept of Extensive-Form Correlated Equilibrium (EFCE, von Stengel and Forges, MOR 2008) applies to extensive games with perfect recall. Similar to a standard correlated equilibrium (CE) for the strategic form of the game, a mediator draws a strategy profile from a known joint distribution at the start of the game. The mediator privately reveals to each player the moves in that profile as a recommended action, but not at the beginning, only when the player reaches the information set with that move. This is analogous to the "locality" of behaviour strategies as used in a Nash equilibrium. Unlike in an Agent-Form CE, where every information set has a separate agent, players in an EFCE remain in control of their own future. An EFCE can be computed in polynomial time, which is a long-standing open question for CE. This raises the question of how to associate a recommended action with an information set. (Recent work on regret-based learning an EFCE partly addresses this question.) Without giving an answer, I want to challenge how we represent information in games in general. Information sets in extensive games (and similarly, information structures) represent information as what is unknown about the "state of the world". Should information not be modeled better as something active, as something the player learns? A big (complicated) information set means lack of knowledge, and a small (singleton) information means perfect information. This is not how people act and think: lack of knowledge, being naive, should have a simple representation, and only with further information the world should become richer.