Doubts and Equilibria

In real life strategic interactions, decision-makers are likely to entertain doubts about the degree of optimality of their play. To capture this feature of real choice-making, we present here a model based on the doubts felt by an agent about how well is playing a game. The doubts are coupled with (and mutually reinforced by) imperfect discrimination capacity, which we model here by means of similarity relations. We assume that each agent builds procedural preferences de ned on the space of expected payoffs-strategy frequencies attached to his current strategy. These preferences, together with an adaptive learning process lead to doubt-based selection dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed Strategy Doubt-Full Equilibria and Mixed Strategy Doubtless Equilibria and show the theoretical and the empirical relevance of these concepts.

Approximate knowledge of rationality and correlated equilibria

We extend Aumann's [3] theorem deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker notion, joint p-belief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i2I or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p su ciently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's [4] theorem on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.

Uncertain Information Structures and Backward Induction

In everyday economic interactions, it is not clear whether sequential choices are visible or not to other participants: agents might be deluded about opponents'capacity to acquire,interpret or keep track of data, or might simply unexpectedly forget what they previously observed (but not chose). Following this idea, this paper drops the assumption that the information structure of extensive-form games is commonly known; that is, it introduces uncertainty into players' capacity to observe each others' past choices. Using this approach, our main result provides the following epistemic characterisation: if players (i) are rational,(ii) have strong belief in both opponents' rationality and opponents' capacity to observe others' choices, and (iii) have common belief in both opponents' future rationality and op-ponents' future capacity to observe others' choices, then the backward induction outcome obtains. Consequently, we do not require perfect information, and players observing each others' choices is often irrelevant from a strategic point of view. The analysis extends {from generic games with perfect information to games with not necessarily perfect information{the work by Battigalli and Siniscalchi (2002) and Perea (2014), who provide different sufficient epistemic conditions for the backward induction outcome.

Long Run Trends in the Price of Energy and Energy Services

4 p.

Climate Change and Knowledge Communities

19 p.