3 Presentations

• 
  11:15 AM - 11:40 AM

  Learning and Communication in Organizations

  • Qiaoxi Zhang, presenter, Universidad de Chile
  • Juan F. Escobar, Universidad de Chile

  We study how learning affects decision making in an organization. A principal chooses whether or not to invest in an unknown technology. An agent privately learns about the technology over time and decides when to offer unverifiable advice to the principal. While ex-post interests are aligned, ex-ante the principal values learning more than the agent. We discuss three types of informed decision making: dynamic mechanism design, delegation, and centralization. We characterize the optimal outcome for each and compare them in terms of welfare. The optimal mechanism delays the implementation of the agent's advice and sometimes imposes a deadline. Moreover, the optimal mechanism outperforms delegation and centralization in facilitating information transmission.

• 
  11:40 AM - 12:05 PM

  Dynamic Offer Proportional Beliefs in Sequential Bargaining with Uncertain Offer-Relative Values of Outside Options

  • Mantas Radzvilas, presenter, Sidney M. Edelstein Center, Hebrew University of Jerusalem

  In strategic bargaining games, a rational player is motivated to offer the opponent the smallest resource share which the opponent would be motivated to accept. In many real world bargaining problems, however, an identification of such an offer may be challenging due to uncertainty about opponent’s valuation of outside option(s), which, for example, may arise due to players having no information about the context of the game which determines how opponent identifies and evaluates the outside option(s) relative to possible bargaining gains, or due to possibility of opponent being motivated by context-dependent psychological or pro-social motivations, such as fairness norms or reciprocal emotional responses, in which case the value of the outside option(s) gets affected by the size and opponent’s perceived intention behind player’s offer.
  In this paper, I suggest a Bayesian-consistent strategic reasoning model for such games based on epistemic concepts of strategic caution and offer proportional beliefs, in which each player is assumed to be strategically cautious – assign positive probability of there being a resource share threshold, such that the outside option is preferred by the opponent over offers which fall below the threshold – and initially express naïve offer proportional beliefs – assign a uniform probability distribution over possible thresholds, thus believing that smaller offers a more likely to fall below the opponent’s unknown threshold than larger offers. At each information set of the game, the player revises the initial beliefs by taking into account opponent’s actions observed in previous information sets.
  I first study the conditions of agreement under common belief in strategic caution and offer proportional beliefs. I prove that players will always either reach an agreement, or end up with their outside options in the first period of the game, and that every reached agreement will be an h-relative equilibrium – a result of a terminal history of the game induced by a combination of subjectively optimal dynamic strategies. I specify the epistemic and material conditions under which the players will reach a strictly egalitarian agreement under common belief in strategic caution and offer proportional beliefs.
  I also study the dynamics of players negotiations over completely private strategic caution and offer proportional beliefs. I prove that players will reach an immediate agreement under a specific range of initial epistemic and material conditions, as well as specify the epistemic and material conditions under which the agreement can only be reached with a delay. I also prove that agreements reached in earlier stages of the game will always yield a more equitable allocation of resource that agreements reached in later stages of the game.

• 
  12:05 PM - 12:30 PM

  A learning approach for subgame perfect Nash equilibria

  • Francesco Caruso, presenter, University of Naples Federico II
  • Maria Carmela Ceparano, University of Naples Federico II
  • Jacqueline Morgan, University of Naples Federico II & Centre for Studies in Economics and Finance (CSEF)

  In one-leader one-follower two-stage games, multiple subgame perfect Nash equilibria (henceforth SPNE) could come up when the optimal reaction of the follower to any choice of the leader is not always unique (i.e. when the follower’s best reply correspondence is not single-valued). In this presentation we introduce a learning method in order to select an SPNE by using a learning approach with the following features: on the one hand, it has the advantage of relieving the leader of learning the follower’s best reply correspondence and it allows to overcome the difficulties deriving from the possible non single-valuedness of the best reply correspondence of the follower; on the other hand, it has a behavioral interpretation that covers various physical, physiological, psychological, and cognitive aspects of decision making processes. More precisely, we recursively define a sequence of SPNEs of perturbed games in which the follower’s best reply correspondence is single-valued (i.e. a sequence of SPNEs of classical Stackelberg games) and we show that the limit of such sequence of SPNEs generates an SPNE of the initial game. The payoff functions of the perturbed games are obtained by subtracting to the payoff functions of the initial game a quadratic term that represents a physical and behavioral cost to move, which is linked to the Moreau-Yosida regularization. Firstly, we illustrate the effectiveness of the learning method through an example, then we provide an existence result for SPNEs approached via this method, together with connections with other methods to construct SPNEs. The selection of an SPNE in one-leader two-follower two-stage games is also contemplated.