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Preferences under ignorance

    Olivier Gossner and Christoph Kuzmics
    International Economic Review, 60: 241-257, 2018

     
    Abstract: 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 alternatives can be rationalized by a DM with strict preferences over all alternatives. Under this model, the DM has preferences for preferences while being ignorant of what preferences are “right”.

    PreferencesUnderIgnorance

    On the cost of misperception: General results and behavioural applications

      Olivier Gossner and Jakub Steiner
      Journal of Economic Theory, 177: 816-847, 2018

       
      Abstract: 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 documented in the behavioural and psychological literatures. We include illusion of control, order effect, overprecision, and overweighting of small probabilities as illustrative examples.

      optimism

      A normalized value for information purchases

        Antonio Cabrales, Olivier Gossner and Roberto Serrano
        Journal of Economic Theory, 170: 266-288, 2017
         

        Abstract: 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 normalized value of the information purchase: it is the risk-aversion level of the unique CARA agent who is indifferent between accepting and rejecting the pur- chase, and it is characterized by a “duality” principle that states that agents with a stronger preference for information should engage more often in information purchases. No agent more risk-averse than the index finds it profitable to acquire the information, whereas all agents less risk-averse than the index do. Given an empirically measured range of degrees of risk aversion in a competitive economy with no-arbitrage investments, our model therefore comes close to describing an inverse demand for information, by predicting what pieces of information are acquired by agents and which ones are not. Among several desirable properties, the normalized value formula induces a complete ranking of information structures that extends Blackwell’s classic ordering.

        value for information purchases

        The complexity of interacting automata

          Olivier Gossner, Penelope Hernández, and Ron Peretz
          International Journal of Game Theory, 45:461-496, 2016
           

          Abstract: 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 m log m. We investigate implications of these results on the correlated min–max value of repeated games played by automata.

          Interacting automata

          Finite-sample exact tests for linear regressions with bounded dependent variables

            Olivier Gossner and Karl Schlag
            Journal of Econometrics, 177: 75-94, 2013

             
            Abstract: 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 m log m. We investigate implications of these results on the correlated min–max value of repeated games played by automata.

            exact_linear_regressions

            Entropy and the value of information to investors

              Antonio Cabrales, Olivier Gossner, Roberto Serrano
              American Economic Review, 103: 360-377, 2013

               
              Abstract: Consider any investor who fears ruin when 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 α investment dominates information structure β if, whenever he is willing to buy β at some price, he is also willing to buy α at that price. We show that this informativeness ordering is complete and is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth, or investment problem. We also show that no prior-independent informativeness ordering based on similar premises exists.

              Entropy_Investors

              Reasoning-based introspection

                Olivier Gossner and Elias Tsakas
                Theory and Decision, 73: 513-523, 2012

                 
                Abstract: 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 redundant.

                PrimitiveKnowledge

                Performing best when it matters most: evidence from professional tennis

                  Julio González-Días, Olivier Gossner and Brian Rogers
                  Journal of Economic Behavior and Organizations, 84: 767-781, 2012
                   

                  Abstract: 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. We establish persistent heterogeneity in critical abilities. We find a significant statistical relationship between identified critical abilities and overall career success, which validates the identification procedure and suggests that response to pressure is a significant factor for success.

                  Tennis

                  Impermanent types and permanent reputations

                    Olivier Gossner, Mehmet Ekmekci, Andrea Wilson
                    Journal of Economic Theory, 147: 142-178, 2012
                      

                    Abstract: 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 on the convergence rates of the discount factor to one and of the rate of replacement to zero, both bounds converge to the Stackelberg payoff if the type space is sufficiently rich. These limiting conditions hold in particular if the game is played very frequently.

                    impermanent-types

                    When is the individually rational payoff in a repeated game equal to the minmax payoff?

                      Olivier Gossner and Johannes Hörner
                      Journal of Economic Theory, 145: 63-84, 2010

                       

                      Abstract: We study the relationship between a player’s lowest equilibrium payoff in a repeated game with imperfect monitoring and this player’s min max 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 monitoring structure of an infinitely repeated game “nearly” satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.

                      minmax-repeatedgames