Disclosure and choice

An agent chooses among projects with random outcomes. His payoff is increasing in the outcome and in an observer's expectation of the outcome. With some probability, the agent can disclose the true outcome to the observer. We show that choice is inefficient: the agent favors riskier projects even with lower expected returns. If information can be disclosed by a challenger who prefers lower beliefs of the observer, the chosen project is excessively risky when the agent has better access to information, excessively risk{averse when the challenger has better access, and efficient otherwise. We also characterize the agent's worst-case equilibrium payoff

Optimal and Myopic Information Acquisition

We consider the problem of optimal dynamic information acquisition from many correlated information sources. Each period, the decision-maker jointly takes an action and allocates a fixed number of observations across the available sources. His payoff depends on the actions taken and on an unknown state. In the canonical setting of jointly normal information sources, we show that the optimal dynamic information acquisition rule proceeds myopically after finitely many periods. If signals are acquired in large blocks each period, then the optimal rule turns out to be myopic from period 1. These results demonstrate the possibility of robust and "simple" optimal information acquisition, and simplify the analysis of dynamic information acquisition in a widely used informational environment

Bayes Correlated Equilibrium and the Comparison of Information Structures in Games

The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the given information structure is equivalent to the set of a version of incomplete information correlated equilibrium which we dub Bayes correlated equilibrium . A game of incomplete information can be decomposed into a basic game, given by actions sets and payoff functions, and an information structure. We identify a partial order on many player information structures (individual sufficiency) under which more information shrinks the set of Bayes correlated equilibria

Correlated Equilibrium and the Comparison of Information Structures in Games

A game of incomplete information can be decomposed into a basic game and an information structure. The basic game defines the set of actions, the set of payoff states the payoff functions and the common prior over the payoff states. The information structure refers to the signals that the players receive in the game. We characterize the set of outcomes that can arise in Bayes Nash equilibrium if players observe the given information structure but may also observe additional signals. The characterization corresponds to the set of (a version of) incomplete information correlated equilibria which we dub Bayes correlated equilibria. We identify a partial order on many player information structures (individual sufficiency) under which more information shrinks the set of Bayes correlated equilibria. This order captures the role of information in imposing (incentive) constraints on behavior

Enforcing International Trade Agreements with Imperfect Private Monitoring: Private Trigger Strategies and the Possible Role of the WTO

International trade disputes often involve the WTO as a third party that generates impartial opinions on potential violations when countries receive imperfect and private signals of violations. To identify the role that the WTO plays in enforcing trade agreements, this paper first explores what countries can achieve without the WTO by characterizing optimal private trigger strategies (PTS) under which each country triggers a punishment phase by imposing an explicit tariff based on privately-observed imperfect signals of the other country's concealed trade barriers. It identifies the condition under which countries can restrain the use of concealed barriers based on PTS and establishes that countries will not reduce the cooperative protection level to its minimum attainable level under the optimal PTS. This paper then considers third-party trigger strategies (TTS) under which the WTO allows each country to initiate a punishment phase based on the WTO's judgment (i.e., its signals) about potential violations. The WTO thus changes the nature of punishment-triggering signals from private into public, enabling countries to use punishment phases of any length under TTS, which in turn facilitates a better cooperative equilibrium. The optimal TTS will involve an asymmetric and minimum punishment if the probability of a punishment phase being triggered is lower than a critical level, but it will entail punishments involving a permanent Nash tariff war if the probability of a punishment phase is higher than a certain level. A numerical comparison of the optimal TTS and optimal PTS indicates that the contribution of the WTO is likely to be significant when the signals of potential violations are relatively accurate, as this enables countries to use a more efficient punishment, such as an asymmetric and minimum punishment.Concealed Trade Barriers, Imperfect Private Monitoring, International Trade Agreements, Repeated Game, Trade Disputes, Trigger Strategies, WTO

Characterizing Belief-Free Review-Strategy Equilibrium Payoffs under ConditionalIndependence

This paper proposes and studies a tractable subset of Nash equilibria, belief-free review-strategy equilibria, in repeated games with private monitoring. The payoff set of this class of equilibria is characterized in the limit as the discount factor converges to one for games where players observe statistically independent signals. As an application, we develop a simple sufficient condition for the existence of asymptotically efficient equilibria, and establish a folk theorem for N-player prisoner’s dilemma. All these results are robust to a perturbation of the signal distribution, and hence remain true even under almost-independent monitoring.repeated game, private monitoring, conditional independence, belief-free review-strategy equilibrium, prisoner’s dilemma

Efficiency in Games With Markovian Private Information

We study repeated Bayesian games with communication and observable actions in which the players' privately known payoffs evolve according to an irreducible Markov chain whose transitions are independent across players. Our main result implies that, generically, any Pareto-efficient payoff vector above a stationary minmax value can be approximated arbitrarily closely in a perfect Bayesian equilibrium as the discount factor goes to 1. As an intermediate step, we construct an approximately efficient dynamic mechanism for long finite horizons without assuming transferable utility

Games of incomplete information without common knowledge priors

We relax the assumption that priors are common knowledge, in the standard model of games of incomplete information. We make the realistic assumption that the players are boundedly rational: they base their actions on finite-order belief hierarchies. When the different layers of beliefs are independent of each other, we can retain Harsányi’s type-space, and we can define straightforward generalizations of Bayesian Nash Equilibrium (BNE) and Rationalizability in our context. Since neither of these concepts is quite satisfactory, we propose a hybrid concept, Mirage Equilibrium, providing us with a practical tool to work with inconsistent belief hierarchies. When the different layers of beliefs are correlated, we must enlarge the type-space to include the parametric beliefs. This presents us with the difficulty of the inherent openness of finite belief subspaces. Appealing to bounded rationality once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternative generalizations of BNE and Rationalizability. Finally, we show that, when beliefs are degenerate point beliefs, the definition of Mirage Equilibrium coincides with that of the generalized BNE.inconsistent beliefs, games of incomplete information, finite belief hierarchy

Information Acquisition and Portfolio Under-Diversi¯cation

We solve the problem of an investor who chooses which assets' payoff to acquire information about before making an investment decision. Investors specialize because information has increasing returns: As an investor learns more about an asset, it becomes less risky and more desirable to hold; as he holds more of the asset, the value of information about it increases. Investors hold some fraction of their assets in a well diversified fund, about which they learn nothing, and hold the other fraction in a small set of highly-correlated assets that they specialize in learning about. In equilibrium, ex-ante identical investors acquire different information. Information is a strategic substitute because assets that many investors learn about have low expected returns. The theory can explain the empirical evidence that individual investors hold part of their equity portfolio in diversified mutual funds and the rest in a small number of highly-correlated assets. While such portfolios may appear under-diversified, they are optimal for investors who face constraints on how much information they can acquire