We analyse the decision of an agent with time-inconsistent preferences to consume a good that exerts an externality on future welfare. The extent of the externality is initially unknown, but may be learned via a costless sampling procedure. We show that when the agent cannot commit to future consumption and learning decisions, incomplete learning may occur on a Markov perfect equilibrium path of the resulting intra-personal game. In such a case, each agent's incarnation stops learning for some values of the posterior distribution of beliefs and acts under self-restricted information. This conduct is interpreted as strategic ignorance. All equilibria featuring this property strictly Pareto dominate the complete learning equilibrium for any posterior distribution of beliefs.

An individual (the leader) with free access to information decides how much public evidence to collect. Conditional on this information, another individual with conflicting preferences (the follower) undertakes an action that affects the payoff of both players. In this game of incomplete but symmetric information, we characterize the rents obtained by the leader as a result of his control of the generation of public information. These rents capture the degree of influence exerted by a chairman on a committee from his capacity to keep discussions alive or call a vote. Similar insights are obtained if the leader decides first how much private information he collects, and then how much verifiable information he transmits to the follower.

To understand the thinking process in private information games, we use "Mousetracking" to record which payoffs subjects attend to. The games have three information states and vary in strategic complexity. Subjects consistently deviate from Nash equilibrium choices and often fail to look at payoffs which they need to in order to compute an equilibrium response. Choices and lookups are similar when stakes are higher. When cluster analysis is used to group subjects according to lookup patterns and choices, three clusters appear to correspond approximately to level-3, level-2, and level-1 thinking in level-k models, and a fourth cluster is consistent with inferential mistakes (as, for example, in QRE or Cursed Equilibrium theories). Deviations from Nash play are associated with failure to look at the necessary payoffs. The time durations of looking at key payoffs can predict choices, to some extent, at the individual level and at the trial-by-trial level. Downloaded fromBROCAS ET AL. STRATEGIC THINKING IN PRIVATE INFORMATION GAMES 945players do not make rational inferences in private information games. Understanding strategic thinking in private information games is important because they are such popular tools for modelling contracting, bargaining, consumer and financial markets, and political interactions. If there is widespread strategic naïvete, then distortions due to hidden information can be larger than predicted by equilibrium analysis, and ideal policy responses may be different (e.g. Crawford, 2003).In this article, we consider two-person betting games with three states and two-sided private information. Players privately observe a state-partition (either one or two of the three states) and choose whether to bet or not bet. Unless both players bet, they earn a known sure payoff. If both bet, they earn the payoff corresponding to the realized state. These games capture the essence of two-sided adverse selection. We also get information about decision processes by hiding the payoffs in opaque boxes. These are only revealed by a 'lookup', when the computer mouse is moved into the box and a mouse button is held down. As in earlier experiments, subjects get feedback about the state after each trial, so they can learn.Lab and field evidence suggest there are strategic thinking limits in many different games with private information. 1 This evidence can be explained by two types of theories. (1) Imperfect choice; or (2) Imperfect attention.By imperfect choice, we mean stochastic response to payoffs (rather than optimization) or a simplification of some structural feature of likely behaviour. Quantal response equilibrium (QRE) assumes players' beliefs are statistically accurate but players respond noisily to expected payoffs (McKelvey and Palfrey, 1995). Two other theories assume optimization, but also assume an imperfection in recognizing aspects of behaviour. In cursed equilibrium (CE), players correctly forecast the distribution of actions chosen by other players, but underestimate the link between the private...