基于策略熵的博弈分析研究

通过建立博弈问题的信息论模型和定义不同类型博弈问题的策略熵,论证了纳什均衡与最大熵之间的内在联系:最大策略熵是纳什均衡的充分必要条件。这表明纳什均衡不仅是利益的均衡同时也是信息均衡的结果。在此基础上,给出了基于熵最大化准则的纳什均衡估计与精炼的方法。     

The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private Information

The theory of global games has shown that coordination games with multiple equilibria may have a unique equilibrium if certain parameters of the payoff function are private information instead of common knowledge. We report the results of an experiment designed to test the predictions of this theory. Comparing sessions with common and private information, we observe only small differences in behavior. For common information, subjects coordinate on threshold strategies that deviate from the global game solution towards the payoff‐dominant equilibrium. For private information, thresholds are closer to the global game solution than for common information. Variations in the payoff function affect behavior as predicted by comparative statics of the global game solution. Predictability of coordination points is about the same for both information conditions.     

Robust Predictions in Games With Incomplete Information

We analyze games of incomplete information and offer equilibrium predictions that are valid for, and in this sense robust to, all possible private information structures that the agents may have. The set of outcomes that can arise in equilibrium for some information structure is equal to the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action–state distribution. We derive exact bounds on how prior knowledge about the private information refines the set of equilibrium predictions. We consider information sharing among firms under demand uncertainty and find new optimal information policies via the Bayes correlated equilibria. We also reverse the perspective and investigate the identification problem under concerns for robustness to private information. The presence of private information leads to set rather than point identification of the structural parameters of the game.     

ON THE POSSIBILITY OF INFORMATIONALLY EFFICIENT MARKETS

This paper presents conditions for a resolution of the Grossman–Stiglitz paradox of informationally efficient markets. We display a market with asymmetric information where a privately revealing equilibrium obtains in a competitive framework and where incentives to acquire information are preserved as long as the correlation in traders’ valuations is not too large. The equilibrium is efficient, and the problems associated with fully revealing rational expectations equilibria are precluded without resorting necessarily to noise traders. The robustness of the results to general information structures is established and the effect of market power is examined in a large market approximation to the competitive economy. The model is applied to explain changes in bidding behavior in central bank liquidity auctions in the crisis period. (JEL: D82, D84, G14, E59)     

Dynamic Global Games of Regime Change: Learning,Multiplicity, and the Timing of Attacks

Global games of regime change—coordination games of incomplete information in which a status quo is abandoned once a sufficiently large fraction of agents attack it—have been used to study crises phenomena such as currency attacks, bank runs, debt crises, and political change. We extend the static benchmark examined in the literature by allowing agents to take actions in many periods and to learn about the underlying fundamentals over time. We first provide a simple recursive algorithm for the characterization of monotone equilibria. We then show how the interaction of the knowledge that the regime survived past attacks with the arrival of information over time, or with changes in fundamentals, leads to interesting equilibrium properties. First, multiplicity may obtain under the same conditions on exogenous information that guarantee uniqueness in the static benchmark. Second, fundamentals may predict the eventual fate of the regime but not the timing or the number of attacks. Finally, equilibrium dynamics can alternate between phases of tranquility—where no attack is possible—and phases of distress—where a large attack can occur—even without changes in fundamentals.     

Efficient Use of Information and Social Value of Information

This paper analyzes equilibrium and welfare for a tractable class of economies (games) that have externalities, strategic complementarity or substitutability, and heterogeneous information. First, we characterize the equilibrium use of information: complementarity heightens the sensitivity of equilibrium actions to public information, raising aggregate volatility, whereas substitutability heightens the sensitivity to private information, raising cross‐sectional dispersion. Next, we define and characterize an efficiency benchmark designed to address whether the equilibrium use of information is optimal from a social perspective; the efficient use of information reflects the social value of aligning choices across agents. Finally, we examine the comparative statics of equilibrium welfare with respect to the information structure; the social value of information is best understood by classifying economies according to the inefficiency, if any, in the equilibrium use of information. We conclude with a few applications, including production externalities, beauty contests, business cycles, and large Cournot and Bertrand games.     

Cursed Equilibrium

There is evidence that people do not fully take into account how other people's actions depend on these other people's information. This paper defines and applies a new equilibrium concept in games with private information, cursed equilibrium, which assumes that each player correctly predicts the distribution of other players' actions, but underestimates the degree to which these actions are correlated with other players' information. We apply the concept to common‐values auctions, where cursed equilibrium captures the widely observed phenomenon of the winner's curse, and to bilateral trade, where cursedness predicts trade in adverse‐selections settings for which conventional analysis predicts no trade. We also apply cursed equilibrium to voting and signalling models. We test a single‐parameter variant of our model that embeds Bayesian Nash equilibrium as a special case and find that parameter values that correspond to cursedness fit a broad range of experimental datasets better than the parameter value that corresponds to Bayesian Nash equilibrium.     

Incentives for information sharing in duopoly with capacity constraints

We study the ex ante incentives for firms to share their private information in a Cournot duopoly with capacity constraints. In both demand and cost information sharing games, we show that the incentives can be reversed when some equilibrium solutions are binding on capacity. Especially, we identify some conditions under which partial information sharing is the dominant strategy under both games. Numerical examples are provided for illustration. In addition, we show that information sharing does not necessarily increase social welfare.     

Optimal Use of Communication Resources

We study a repeated game with asymmetric information about a dynamic state of nature. In the course of the game, the better‐informed player can communicate some or all of his information to the other. Our model covers costly and/or bounded communication. We characterize the set of equilibrium payoffs and contrast these with the communication equilibrium payoffs, which by definition entail no communication costs.     

Repeated Games Where the Payoffs and Monitoring Structure Are Unknown

This paper studies repeated games with imperfect public monitoring where the players are uncertain both about the payoff functions and about the relationship between the distribution of signals and the actions played. We introduce the concept of perfect public ex post equilibrium (PPXE), and show that it can be characterized with an extension of the techniques used to study perfect public equilibria. We develop identifiability conditions that are sufficient for a folk theorem; these conditions imply that there are PPXE in which the payoffs are approximately the same as if the monitoring structure and payoff functions were known. Finally, we define perfect type‐contingently public ex post equilibria (PTXE), which allows players to condition their actions on their initial private information, and we provide its linear programming characterization.     

Belief‐Free Equilibria in Games With Incomplete Information

We define belief‐free equilibria in two‐player games with incomplete information as sequential equilibria for which players' continuation strategies are best replies after every history, independently of their beliefs about the state of nature. We characterize a set of payoffs that includes all belief‐free equilibrium payoffs. Conversely, any payoff in the interior of this set is a belief‐free equilibrium payoff. The characterization is applied to the analysis of reputations.     

Isotone Equilibrium in Games of Incomplete Information

An isotone pure strategy equilibrium exists in any game of incomplete information in which each player's action set is a finite sublattice of multidimensional Euclidean space, types are multidimensional and atomless, and each player's interim expected payoff function satisfies two “nonprimitive conditions” whenever others adopt isotone pure strategies: (i) single‐crossing in own action and type and (ii) quasi‐supermodularity in own action. Conditions (i), (ii) are satisfied in supermodular and log‐supermodular games given affiliated types,and in games with independent types in which each player's ex post payoff satisfies supermodularity in own action and nondecreasing differences in own action and type. This result is applied to provide the first proof of pure strategy equilibrium existence in the uniform price auction when bidders have multi‐unit demand, nonprivate values, and independent types.     

Cognition and Behavior in Normal‐Form Games: An Experimental Study

This paper reports experiments designed to study strategic sophistication, the extent to which behavior in games reflects attempts to predict others’ decisions, taking their incentives into account. We study subjects’ initial responses to normal‐form games with various patterns of iterated dominance and unique pure‐strategy equilibria without dominance, using a computer interface that allowed them to search for hidden payoff information, while recording their searches. Monitoring subjects’ information searches along with their decisions allows us to better understand how their decisions are determined, and subjects’ deviations from the search patterns suggested by equilibrium analysis help to predict their deviations from equilibrium decisions.     

Toward a Strategic Foundation for Rational Expectations Equilibrium

A step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information. If there are sufficiently many buyers and sellers, and their bids are restricted to a sufficiently fine discrete set of prices, then, generically, there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents. In particular, the large double‐auction equilibrium is almost efficient and almost fully aggregates the agents' information.     

Reputation in Continuous‐Time Games

We study reputation dynamics in continuous‐time games in which a large player (e.g., government) faces a population of small players (e.g., households) and the large player's actions are imperfectly observable. The major part of our analysis examines the case in which public signals about the large player's actions are distorted by a Brownian motion and the large player is either a normal type, who plays strategically, or a behavioral type, who is committed to playing a stationary strategy. We obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. We find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type. By contrast, when it is common knowledge that the large player is the normal type, every public equilibrium of the continuous‐time game is payoff‐equivalent to one in which a static Nash equilibrium is played after every history. Finally, we examine variations of the model with Poisson signals and multiple behavioral types.     

Identification and Estimation of a Discrete Game of Complete Information

We discuss the identification and estimation of discrete games of complete information. Following Bresnahan and Reiss (1990, 1991), a discrete game is a generalization of a standard discrete choice model where utility depends on the actions of other players. Using recent algorithms to compute all of the Nash equilibria to a game, we propose simulation‐based estimators for static, discrete games. We demonstrate that the model is identified under weak functional form assumptions using exclusion restrictions and an identification at infinity approach. Monte Carlo evidence demonstrates that the estimator can perform well in moderately sized samples. As an application, we study entry decisions by construction contractors to bid on highway projects in California. We find that an equilibrium is more likely to be observed if it maximizes joint profits, has a higher Nash product, uses mixed strategies, and is not Pareto dominated by another equilibrium.     

商业银行信息披露监控机制的构建研究

商业银行充分有效的信息披露是进一步完善市场经济机制、强化对银行的市场约束,提高金融透明度的必然要求,也是国际银行监管发展的趋势。运用博弈论与信息经济学的原理,研究商业银行信息披露监控中的一阶段博弈和多阶段的重复博弈问题。根据博弈结果,认为按既定的行为规则下设计信息披露监控机制,可以构成稳定的均衡,博弈的双方都有遵守机制的内在动力。     

Level‐k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private‐Value Auctions?

This paper proposes a structural nonequilibrium model of initial responses to incomplete‐information games based on “level‐k” thinking, which describes behavior in many experiments with complete‐information games. We derive the model's implications in first‐ and second‐price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level‐k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common‐value auctions and overbidding in those independent‐private‐value auctions without the uniform value distributions used in most experiments.     

Reinforcement‐based vs. Belief‐based Learning Models in Experimental Asymmetric‐information Games

This paper examines the abilities of learning models to describe subject behavior in experiments. A new experiment involving multistage asymmetric‐information games is conducted, and the experimental data are compared with the predictions of Nash equilibrium and two types of learning model: a reinforcement‐based model similar to that used by Roth and Erev (1995), and belief‐based models similar to the ‘cautious fictitious play’ of Fudenberg and Levine (1995, 1998) These models make predictions that are qualitatively similar cycling around the Nash equilibrium that is much more apparent than movement toward it. While subject behavior is not adequately described by Nash equilibrium, it is consistent with the qualitative predictions of the learning models. We examine several criteria for quantitatively comparing the predictions of alternative models. According to almost all of these criteria, both types of learning model outperform Nash equilibrium. According to some criteria, the reinforcement‐based model performs better than any version of the belief‐based model; according to others, there exist versions of the belief‐based model that outperform the reinforcement‐based model. The abilities of these models are further tested with respect to the results of other published experiments. The relative performance of the two learning models depends on the experiment, and varies according to which criterion of success is used. Again, both models perform better than equilibrium in most cases.     

Selecting Cheap‐Talk Equilibria

There are typically multiple equilibrium outcomes in the Crawford–Sobel (CS) model of strategic information transmission. This paper identifies a simple condition on equilibrium payoffs, called NITS (no incentive to separate), that selects among CS equilibria. Under a commonly used regularity condition, only the equilibrium with the maximal number of induced actions satisfies NITS. We discuss various justifications for NITS, including perturbed cheap‐talk games with nonstrategic players or costly lying. We also apply NITS to other models of cheap talk, illustrating its potential beyond the CS framework.