# Olivier Gossner's research while affiliated with European School Of Economics and other places

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## Publications (72)

Background
Worldwide demand for SARS-CoV-2 RT-PCR testing is still high as testing remains central to follow the disease spread and vaccine efficacy. Group testing has been proposed as a solution to expand testing capabilities but sensitivity concerns may limit its impact on the management of the pandemic. Digital PCR (RT-dPCR) has been shown to be...

We study the impact of manipulating the attention of a decision‐maker who learns sequentially about a number of items before making a choice. Under natural assumptions on the decision‐maker's strategy, directing attention toward one item increases its likelihood of being chosen regardless of its value. This result applies when the decision‐maker ca...

Background: Worldwide demand for SARS-CoV-2 RT-PCR testing is increasing as more countries are impacted by COVID-19 and as testing remains central to contain the spread of the disease, both in countries where the disease is emerging and in countries that are past the first wave but exposed to re-emergence. Group testing has been proposed as a solut...

We show how group testing can be used in three applications to multiply the efficiency of tests against COVID-19: estimating virus prevalence, releasing group to the work force, and testing for individual infectious status. For an infection level around 2%, group testing could potentially allow to save 94% of tests in the first application, 95% in...

In decision problems under incomplete information, actions (identified to payoff vectors indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information, using concepts and tools from convex analysis. We define the value function as the support function of the set of ava...

In decision problems under incomplete information, payoff vectors (indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information using convex analysis. We then derive global estimates of the value of information of any information structure from local properties of the...

We study the impact of manipulating the attention of a decision-maker who learns sequentially about a number of items before making a choice. Under natural assumptions on the decision-maker’s strategy, directing attention toward one item increases its likelihood of being chosen regardless of its value. This result applies when the decisionmaker can...

In a choice model, we characterize the loss induced by misperceptions of payoff-relevant parameters across a distribution of decision problems. When the agent cannot avoid misperceptions but has some control over the distribution of errors, we show that strategies that minimize loss from misperception exhibit systematic biases, akin to some documen...

In a choice model, we characterize the loss induced by misperceptions of payoff-relevant parameters across a distribution of decision problems. When the agent cannot avoid misperceptions but has some control over the distribution of errors, we show that strategies that minimize loss from misperception exhibit systematic biases, akin to some documen...

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially ignorant of the payoff associated with each alternative, and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option, once payoffs are learned, the optimal choice rule from sets of alterna...

Consider agents who are heterogeneous in their preferences and wealth levels. These agents may acquire information prior to choosing an investment that has a property of no-arbitrage, and each piece of information bears a corresponding cost. We associate a numeric index to each information purchase (information-cost pair). This index describes the...

This paper studies the interaction of automata of size m. We characterise statistical properties satisfied by random plays generated by a correlated pair of automata with m states each. We show that in some respect the pair of automata can be identified with a more complex automaton of size comparable to mlogm\documentclass[12pt]{minimal} \usepacka...

We study perception biases arising under second-best perception strategies. An agent correctly observes a parameter that is payoff-relevant in many decision problems that she encounters in her environment but is unable to retain all the information until her decision. A designer of the decision process chooses a perception strategy that determines...

A decision maker (DM) makes choices from di erent sets of alternatives. The DM is initially fully ignorant of the payo associated to each alternative, and learns these payo s only after a large number of choices have been made. We show that, in the presence of an outside option once payo s are learned, the optimal choice rule from sets of alternati...

We introduce tests for finite-sample linear regressions with heteroskedastic errors. The tests are exact, i.e., they have guaranteed type I error probabilities when bounds are known on the range of the dependent variable, without any assumptions about the noise structure. We provide upper bounds on probability of type II errors, and apply the tests...

Stakes affect aggregate performance in a wide variety of settings. At the individual level, we define the critical ability as an agent's ability to adapt performance to the importance of the situation. We identify individual critical abilities of professional tennis players, relying on point-level data from twelve years of the US Open tournament. W...

Glossary Definition of the Subject Introduction Games with Observable Actions Games with Non‐observable Actions Acknowledgments Bibliography

We introduce several exact nonparametric tests for finite sample multivariate linear regressions, and compare their powers. This fills an important gap in the literature where the only known nonparametric tests are either asymptotic, or assume one covariate only.

We introduce entropy techniques to study the classical reputation model in which a long-run player faces a series of short-run players. The long-run player's actions are possibly imperfectly observed. We derive explicit lower and upper bounds on the equi-librium payoffs to the long-run player.

We introduce entropy techniques to study the classical reputation model in which a long-run player faces a series of short-run players. The long-run player’s actions are possibly imperfectly observed. We derive explicit lower and upper bounds on the equilibrium payoffs to the long-run player.

We show that if an agent reasons according to standard inference rules, the axioms of truth and introspection extend from the set of non-epistemic propositions to the whole set of propositions. This implies that the usual axiomatization of the partitional possibility correspondence, which describes an agent who processes information rationally, is...

Consider any investor who fears ruin facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure is more informative than information structure if whenever he rejects at some price, he also rejects at...

In games with incomplete information, more information to a player implies a broader strategy set for this player in the normal form game, hence more knowledge implies more ability. We prove that, conversely, given two normal form games G and G' such that players in a subset J of the set of players possess more strategies in G' than in G, there exi...

We introduce and study a unified reasoning process which allows to represent the beliefs of both a fully rational agent and of an unaware one. This reasoning process provides natural properties to introspection and unawareness. The corresponding model for the rational or boundedly rational agents is both easy to describe and to work with, and the a...

We study the relationship between a player's lowest equilibrium payoff in a repeated game with imperfect monitoring and this player's minmax payoff in the corresponding one-shot game. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under an identifiability assumption, we further show that, if the...

We show how to derive nonparametric estimates from results for Bernoulli distributions, provided the means are the only parameters of interest. The only information is that the support of each random variable is contained in a known bounded set. Examples include presenting minimax risk properties of the sample mean and a minimax regret estimate for...

We study the impact of unobservable stochastic replacements for the long-run player in the classical reputation model with a long-run player and a series of short-run players. We provide explicit lower bounds on the Nash equilibrium payoffs of a long-run player, both ex-ante and following any positive probability history. Under general conditions o...

We study the potential evolutionary appeal of rationality in a model in which different populations differ with respect to their experimentation over rules of behavior. We show that more risky experimentation in the sense of mean preserving spread dominates less risky experimentation. Experimentation over the set of (strictly) rational rules is sho...

This papers studies an optimization problem under entropy constraints arising from repeated games with signals. We provide general properties of solutions and a full characterization of optimal solutions for 2 × 2 sets of actions. As an application we compute the minmax values of some repeated games with signals. oui

An observer of a process believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(xt|x1,…,xt−1) and Q(xt|x1,…,xt−1) for t=1,…,n by a function of the relative entropy between the marginals of P and Q on the n first realizations. We apply this bound to the cost of learning in sequential decisio...

In Bayesian environments with private information, as described by the types of Harsanyi, how can types of agents be (statistically) disassociated from each other and how are such disassociations reflected in the agents’ knowledge structure? Conditions studied are (i) subjective independence (the opponents’ types are independent conditional on one’...

We characterize the maximum payoff that a team can guarantee against another in a class of repeated games with im- perfect monitoring. Our result relies on the optimal trade-off for the team between optimization of stage-payoffs and generation of signals for future correlation.

We study whether rational information processing is testable. Our main result shows that, under positive conditions, negative introspection holds if and only if it holds for primitive propositions. In particular, it is sufficient to test negative introspection on primitive propositions.

We prove that efficiency can be asymptotically achieved in the two-player's prisoner's dilemma under private monitoring. While we impose some restrictions on the monitoring structure, we do not require that the monitoring be either almost-perfect or conditionally independent.

We study a repeated game with asymmetric information about a dynamic state of nature. In the course of the game, the better-informed player can communicate some or all of his information to the other. Our model covers costly and/or bounded communication. We characterize the set of equilibrium payoffs and contrast these with the communication eq...

Let (xn)n be a process with values in a finite set X and law P, and let yn f(xn) be a function of the process. At stage n, the conditional distribution pn P(xnx1,,xn1), element of (X), is the belief that a perfect observer, who observes the process online, holds on its realization at stage n. A statistician observing the signals y1,,yn holds a beli...

We introduce cheap talk in a dynamic investment model with information externalities. We first show how social learning adversely affects the credibility of cheap talk messages. Next, we show how an informational cascade makes truth-telling incentive compatible. A separating equilibrium only exists for high-surplus projects. Both an investment subs...

We introduce cheap talk in a dynamic investment model with information externalities. We first show how social learning adversely affects the credibility of cheap talk messages. Next, we show how an informational cascade makes truth-telling incentive compatible. A separating equilibrium only exists for high-surplus projects. Both an investment subs...

Let (xt) be an n-periodic sequence in which the first n elements are drawn i.i.d. according to some rational distribution. We prove there exists a constant C such that whenever mlnm⩾Cn, with probability close to 1, there exists an automaton of size m that matches the sequence at almost all stages.

It is sometimes argued that road safety measures or automobile safety standards fail to save lives because safer highways or safer cars induce more dangerous driving. A similar but less extreme view is that ignoring the behavioral adaptation of drivers would bias the cost-benefit analysis of a traffic safety measure. This article derives cost-benef...

We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payoff is the average of a one-shot payoff over the joint sequence. We consider the maxmin value of the game played in pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First...

We study the maxmin value of a zero-sum repeated game where player 1 is restricted to pure strategies but privately observes the realizations of some random variables. This kind of problem was introduced by Gossner and Vieille (GV02) in the case where player 1 observes i.i.d. random variables. The paper solves the case where the law of the random v...

We introduce a model of communication with dynamic state of nature. We rely on entropy as a measure of information, characterize the set of expected empirical distributions that are achievable. We present applications to games with and without common interests.
Classification JEL : C61, C73, D82.

Le maxmin pour une certaine classe de jeux répétés à observation imparfaite est obtenu comme la solution d'un problème d'optimisation défini sur l'ensemble des distributions de probabilités sous contraintes d'entropie. Cette article offre une méthode pour résoudre un tel problème dans le cas d\\\'un jeu à trois joueurs où chaque joueur dispose de d...

Cahier de recherche du CEREMADE n° 421

We characterize the min max values of a class of repeated games with imperfect monitoring. Our result relies on the optimal trade-off for the team formed by punishing players between optimization of stage-payoffs and generation of signals for future correlation. Amounts of correlation are measured through the entropy function. Our theorem on min ma...

We study a repeated game in which one player, the prophet, acquires more information than another player, the follower, about the play that is going to be played. We characterize the optimal amount of information that can be transmitted online by the prophet to the follower, and provide applications to repeated games played by finite automata, and...

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments a la Blackwell. More specifically, we consider pairs consisting of a game with incomplete information G and an information structure L such tha...

Many results on repeated games played by finite automata rely on the complexity of the exact implementation of a coordinated play of length n. For a large proportion of sequences, this complexity appears to be no less than n. We study the complexity of a coordinated play when allowing for a few mismatches. We prove the existence of a constant C suc...

It is sometimes argued that road safety measures or automobile safety standards fail to save lives because safer highways or safer cars induce more dangerous driving. A similar but less extreme view is that ignoring the behavioral adaptation of drivers would bias the cost-benefit analysis of a traffic safety measure. This article derives cost-benef...

We consider a 3-player model of repeated game with standard monitoring in which player's strategies are implemented by polyno-mial time Turing machines. We prove that if a collection of trapdoor permutations exists, the set of equilibria of this game is the set of correlated equilibria of the original repeated game.

We introduce the notion of an information structure as being richer than another when for every game G, all correlated equilibrium distributions of G induced by are also induced by . In particular, if is richer than then can make all agents as well off as in any game. We also define to be faithfully reproducible from when all the players can comput...

We characterize the max min of repeated zero-sum games in which player one plays in pure strategies sonditional on the private observation of a fixed sequence random variables. Meanwhile we introduce a definition of a strategic distance between probability measures, and relate it to the standard Kullbach distance.

It is well known that, whereas in one-agent contexts the value of information is always positive, in strategic situations, this is not always the case. We will consider the class of games for which, under a specific information structure, there exists a unique Pareto payoff profile, and we show that any Nash-equilibrium payoff profile induced by a...

This article studies situations in which agents do not initially know the effect of their decisions, but learn from experience the payoffs induced by their choices and their opponents'. We chararacterize equilibrium payoffs in terms of simple strategies in which an exploration phase is followed by a payoff acquisition phase.

We consider the "and" communication mechanism that inputs messages from two players and outputs the public signal "yes" if both messages are "yes", and outputs "no" otherwise. We prove that no correlation can securely be implemented through finite or infinite repetition of this mechanism.

[fre] Protocoles de communication robustes. . Lorsque des possibilités de communication existent, un protocole désigne un ensemble de règles utilisées par les agents pour échanger de l'information. Nous définissons un protocole robuste comme un protocole duquel aucun agent n'a intérêt à dévier, et caractérisons ces protocoles. [eng] Robust protocol...

Correlated equilibria and communication equilibria are useful notions to understand the strategic effects of information and communication. Between these two models, a protocol generates information through communication. We define a secure protocol as a protocol from which no individual may have strategic incentives to deviate and characterize the...

This paper proves a Folk Theorem for overlapping generations games in the case where the mixed strategies used by a player are not observable by the others, but only their realizations are public.

This paper proves a Folk Theorem for finitely repeated games with mixed strategies. To obtain this result, we first show a similar property for finitely repeated games with terminal payoffs.

This paper studies the communication in repeated common inter-est Sender-Receiver games when no common language is available to the players. The history of the game (i.e. the succession of actions and messages chosen by the players) constitutes the unique source of structure that can be used by the players to communicate. We are interested in under...

We study the relationship between a player's minmax payoff and his lowest equilibrium payoff (his reservation utility) in repeated games with imperfect monitoring. We provide a necessary and sufficient condition on the information structure under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show t...

We study a discrete-time dynamic programming problem involving a decision maker who chooses actions and observes random signals, and an observer who gets partial information about those actions and signals. The aim of the decision maker is to control the distribution of past actions and signals given the observer's information. We characterize the...

We study the relationship between a player’s (stage game) minmax payoff and the individually rational payoff in repeated games with imperfect monitoring. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show that, if the monitoring structure of an infinitely...

An information transaction entails the purchase of information. Formally, it consists of an information structure together with a price. We develop an index of the appeal of information transactions, which is derived as a dual to the agent's preferences for information. The index of information transactions has a simple analytic characterization in...

We study the robustness of equilibria with regards to small payoff perturbations of the dynamic game. We find that complete penal codes, that specify player's strategies after every history, can have at best limited robustness and may even fail to exist for some games. We define incomplete penal codes as partial descriptions of equilibrium strategi...

This note studies the relationship between a player's (stage game) minmax payo and the (lowest) individually rational payo in repeated games with imperfect monitoring. We characterize the signal structures under which these two payos coincide for any payo ma- trix. Under an identifiability assumption, we further show that, if the monitoring structu...

## Citations

... Some of these processes have been linked to the role of attention. Different formalizations have shown that attention can help to trade off the processes of satisficing and information accumulation (Gossner et al., 2021) and that attention reflecting an optimal accumulation strategy can reproduce several choice biases found in the literature (Callaway et al., 2021). ...

... However, this method has not been widely used due to the limited sensitivity of RT-qPCR in testing samples with low viral loads. It has also been suggested that RT-dPCR may be more effective than RT-qPCR in pooled samples due to its higher sensitivity, specificity, and precision; same-day turnaround time; and relatively low cost (23,164,165). To test the suitability of RT-dPCR for pooling, Martin et al. divided 448 COVID-19 hospital samples into three groups (14 pools of 32 samples/pool, 28 pools of 16 samples/pool, and 56 pools of 8 samples/pool) for RT-dPCR testing and directly compared the results to those of individual testing by RT-qPCR (165). ...

... Similar economies of testing were applied in the recent Covid-19 PCR tests (see e.g. [15,17]) and a large literature has is devoted to these ideas (see e.g. [14]). ...

Reference: Finding a Hidden Edge

... Being the information costly, the worker (weakly) prefers to remain ignorant: V (c ∪ d|υ) ≥ V (c ∪ d|ι), and the inequality is strict if κ > 0. 13 For the preference in (2), if d υ c and d υ l, adding the option l to c ∪ d does not increase the prescription value of c ∪ d, but it can increase the cost of information. 14The term C(µ, F ) corresponds to the instrumental value of receiving information µ in the choice problem F (see DeLara and Gossner, 2020;Frankel and Kamenica, 2019). Namely, the difference between the value of F for an individual who anticipates the use of information µ to select the best action from F , and the value of F in the absence of information arrival. ...

Reference: Identity, information and situations

... Misperception (of price) could be related to different factors. For instance, Acemoglu and Yildiz [36] mention that price misperception could be the consequence of ignorance (lack of information), or arising from failing memory (Gossner and Steiner [37]). In our experimental design, the lack of information does not exist, since participants are perfectly informed. ...

... This study postulates that improving cost information can improve GB adoption through the knowledge of why CMs exist. The rational economic decision discourse reviewed above affirmed the existence of imperfect information in the decision processes (Gossner and Steiner, 2018). In this study, we established the causes of distorted cost information in GB development to place the stakeholders in emerging green markets to engage in optimal misperception management. ...

... In the economics and finance literature, entropy also finds its applications. For example, Cabrales et al. (2013Cabrales et al. ( , 2017 uses Shannon entropy to measure the informativeness of different information structures for investors when making investment decisions. Sims (2006) and Miao et al. (2022) adopt the Shannon entropy to measure uncertainty and information capacity in the study of rational inattention. ...

Reference: Information extraction and artwork pricing

... See examples 1-3 in the working-paper version of this paper,Gossner and Steiner (2016), for formalizations. ...

... Automata in general have already been shown to be related to games and strategies in various works [31,32,38,39]. Andronikos et al. established a sophisticated connection between finite automata and the PQ Penny game, constructing automata for various interesting variations of the game [39]. ...

... An important question left open is how to actually determine the repeated-game min max payoff when it is below the stage-game min max payoff. Characterizations are only known for some classes of monitoring structures in [16,11,12]. When conditionally on each player's signal, other player's signals are independent, the equilibrium payoff set possesses a natural recursive structure, and methods from dynamic programming can be brought to bear. ...