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Informationally optimal correlation

    Olivier Gossner, Rida Laraki and Tristan Tomala
    Mathematical Programming series B, 116: 147-172, 2009


    Abstract: 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 min max values of some repeated games with signals.


    Information independence and common knowledge

      Olivier Gossner, Ehud Kalai, and Robert Weber
      Econometrica, 77: 1317–1328, 2009


      Abstract: 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’s own) and (ii) type disassociation under common knowledge (the agents’ types are independent, conditional on some common-knowledge variable). Subjective independence is motivated by its implications in Bayesian games and in studies of equilibrium concepts. We find that a variable that disassociates types is more informative than any common-knowledge variable. With three or more agents, conditions (i) and (ii) are equivalent. They also imply that any variable which is common knowledge to two agents is common knowledge to all, and imply the existence of a unique common-knowledge variable that disassociates types, which is the one defined by Aumann.


      Entropy bounds on Bayesian learning

        Olivier Gossner, Tristan Tomalar
        Journal of Mathematical Economics, 44: 24-32, 2008


        Abstract: An observer of a process (x_t) believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(x_t|x1,…,x_{t−1}) and Q(x_t|x_1,…,x_{t−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 decision problems and to the merging of Q to P.


        Secret correlation in repeated games with imperfect monitoring

          Olivier Gossner, Tristan Tomala
          Mathematics of Operations Research, 32: 413–424, 2007


          Abstract: We characterize the maximum payoff that a team can guarantee against another in a class of repeated games with imperfect monitoring. Our result relies on the optimal tradeoff for the team between optimization of stage payoffs and generation of signals for future correlation.


          Optimal use of communicaiton resources

            Olivier Gossner, Penélope Hernández, and Abraham Neyman
            Econometrica, 74: 1603-1636, 2006


            Abstract: 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 equilibrium payoffs, which by definition entail no communication costs.


            Informational cascades elicit private information

              Olivier Gossner and Nicolas Melissas
              International Economic Review, 47: 297-325, 2006


              Abstract: 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 truthtelling incentive compatible. A separating equilibrium only exists for high-surplus projects. Both an investment subsidy and an investment tax can increase welfare. The more precise the sender’s information, the higher her incentives to truthfully reveal her private information.


              Empirical distributions of beliefs under imperfect observation

                Olivier Gossner and Tristan Tomala
                Mathematics of Operations Research, 31: 13-30, 2006


                Abstract: Let (x_n) be a process with values in a finite set X and law P, and let y_n = f(x_n) be a function of the process. At stage n, the conditional distribution p_n = P[x_n |x_1 … x_{n−1}], element of Pi = Delta(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 y_1 …, y_n holds a belief e_n = P[p_n |x_1,…,x_n] ∈ Delta(Pi) on the possible predictions of the perfect observer. Given X and f, we characterize the set of limits of expected empirical distributions of the process e_n when P ranges over all possible laws of (x_n).


                On the consequences of behavioural adaptations in the cost-benefits analysis of road safety measures

                  Olivier Gossner and Pierre Picard
                  Journal of Risk and Insurance, 7: 577-599, 2005


                  Abstract: 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–benefit rules for automobile safety regulation when drivers may adapt their risk-taking behavior in response to changes in the quality of the road network. The focus is on the financial externalities induced by accidents because of the insurance system as well as on the consequences of drivers’ risk aversion. We establish that road safety measures are Pareto improving if their monetary cost is lower than the difference between their (adjusted for risk aversion) direct welfare gain with unchanged behavior and the induced variation in insured losses due to drivers’ behavioral adaptation. The article also shows how this rule can be extended to take other accident external costs into account.



                  Dynamiques de Communication

                    Olivier Gossner, Penélope Hernández, Abraham Neyman
                    Revue Économique, 55: 509-516,2004


                    Abstract: Nous introduisons un modèle de communication avec état de la nature dynamique. En utilisant l’entropie comme mesure d’information, nous caractérisons les distributions empiriques espérées sur les actions qui sont réalisables. Nous présentons des applications aux jeux avec et sans intérêts communs.