Robust equilibria under non-common priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.     

Payoff continuity in incomplete information games: a comment

Kajii and Morris (J. Econ. Theory 82 (1998) 267) provide necessary and sufficient conditions for two priors to be strategically close. The restrictiveness of these conditions establishes that strategic behavior can be highly sensitive to the assumed prior. Their results thus recommend care in the use of priors in economic modelling. Unfortunately, their proof of a central proposition fails for zero probability types. This comment corrects their proof to account for these cases.     

Robustness of equilibria in anonymous local games

This paper studies the robustness of symmetric equilibria in anonymous local games to perturbations of prior beliefs. Two priors are strategically close on a class of games if players receive similar expected payoffs in equilibrium under the priors, for any game in that class. I show that if the structure of payoff interdependencies is sparse in a well-defined sense, the conditions for strategic proximity in anonymous local games are strictly weaker than the conditions for general Bayesian games of Kajii and Morris (1998) [11] when attention is restricted to symmetric equilibria. Hence, by exploiting the properties of anonymous local games, it is possible to obtain stronger robustness results for this class.     

Proper scoring rules for general decision models

If a decision maker whose behavior conforms to the max-min expected utility model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there is a scoring rule inducing the agent to announce that prior. We also show that on the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors).     

The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibrium when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of some agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.     

Signaling without a common prior: Results on experimental equilibrium selection

The common prior assumption is pervasive in game-theoretic models with incomplete information. This paper investigates experimentally the importance of inducing a correct common prior in a two-person signaling game. Equilibrium selection arguments predict that different equilibria may be selected depending on whether the common prior is induced or not. Indeed, for a specific probability distribution of the sender?s type, the long-run behavior without an induced common prior is shown to be different from the long-run behavior when a common prior is induced, while for other distributions long-run behavior is similar under both regimes. We also present a learning model that allows players to learn about the other players? strategies and the prior distribution of the sender?s type. We show that this learning model accurately accounts for all main features of the data.     

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker?s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker?s set of priors is precisely all the weighted-averages of priors, where an expert?s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker?s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts? valuations.     

Large Scale Marine Protected Areas for Biodiversity Conservation Along a Linear Gradient: Cooperation, Strategic Behavior or Conservation Autarky?

In this paper we investigate effects of overlap in species between ecosystems along a linear gradient on the location of marine protected areas (MPAs) under full cooperation, strategic behavior and conservation autarky. Compared to the full cooperation outcome, both strategic behavior and conservation autarky lead to under-investment in biodiversity protection. Under strategic behavior, however, we observe the additional problem of ??location leakage?? i.e. countries invest less in species protected by others. Conservation autarky eliminates location leakage; in ecosystems with partly overlapping species compositions at country borders it even induces MPAs that are too large from a global perspective. We also find that, in our setting of a linear gradient without migrating species, countries focus their conservation efforts on species unique to their own country and that these species are relatively well protected compared to common species.     

Agreeable bets with multiple priors

This paper considers a two-agent model of trade with multiple priors. Firstly, we characterize the existence of an agreeable bet on some event in terms of the set of priors. It is then shown that the existence of an agreeable bet on some event is a strictly stronger condition than the existence of an agreeable trade, whereas the two conditions are equivalent in the standard Bayesian framework. Secondly, we show that the two conditions are equivalent when the set of priors is the core of a convex capacity. These results are also related to the no trade theorems under asymmetric information.     

First- and second-order subjective expectations in strategic decision-making: Experimental evidence

We study first- and second-order subjective expectations (beliefs) in strategic decision-making. We elicit probabilistically both first- and second-order beliefs and apply the method to a Hide-and-Seek experiment. We study the relationship between choice and beliefs in terms of whether observed choice coincides with the optimal action given elicited beliefs. We study the relationship between first- and second-order beliefs under a coherence criterion. Weak coherence requires that if an event is assigned, according to first-order beliefs, a probability higher/lower/equal to the one assigned to another event, then the same holds according to second-order beliefs. Strong coherence requires the probability assigned according to first- and second-order beliefs to coincide. Evidence of heterogeneity across participants is reported. Verbal comments collected at the end of the experiment shed light on how subjects think and decide in a complex environment that is strategic, dynamic and populated by potentially heterogeneous individuals.     

“年少有为”还是“老当益壮”?——CEO职业生涯关注与战略变革

企业的战略变革是宏观经济转型和产业升级的重要微观基础,然而,变革活动的引领者CEO对自身职业生涯的认知会给战略变革带来怎样的影响是一个重要但仍具争议性的问题。本文整合高阶梯队理论和特质激活理论,以2007—2014年A股上市公司为样本,研究CEO职业生涯关注对战略变革的影响;采用CEO年龄和职业余期来代理CEO职业生涯关注,选择企业关键战略维度来构建战略变革的指标,对相关理论假设进行实证检验。研究发现,CEO职业生涯关注对战略变革有显著的正向影响;同时,在环境不确定性较低、经营期望落差较小、组织冗余较少以及CEO持股比例较高等组织内外部情境下,CEO职业生涯关注所能发挥的影响作用更大,对战略变革的促进效应也更为明显;进一步研究表明,在非国有企业中,CEO职业生涯关注对战略变革的影响更为显著;区分战略变革的类型,与战略变异相比,CEO职业生涯关注对战略背离的影响更为显著。本文不仅从新的视角拓展了战略变革动因的研究,而且对企业如何有效从内部驱动变革、推动企业转型发展有一定的启示意义。     

Non-Laplacian beliefs in a global game with noisy signaling

In standard global games, individual behavior is optimal if it constitutes a best response to agnostic—Laplacian—beliefs about the aggregate behavior of other agents. This paper considers a standard binary action global game augmented with noisy signaling by an informed policy-maker and shows that in this game, equilibrium beliefs depart in quite stark ways from the Laplacian benchmark. In the limit as signals become arbitrarily precise, so that all fundamental uncertainty is removed (leaving only strategic uncertainty), the equilibrium beliefs of the marginal individual concerning the aggregate action collapse to a discrete Bernoulli distribution, giving probability mass only to the polar extreme outcomes. By contrast in the underlying standard global game the marginal individual believes the aggregate action has a continuous uniform distribution, giving equal likelihood to all possible outcomes.     

The effect of endogenous timing on coordination under asymmetric information: An experimental study

This paper investigates the role of endogenous timing of decisions on coordination under asymmetric information. In the equilibrium of a global coordination game, where players choose the timing of their decision, a player who has sufficiently high beliefs about the state of the economy undertakes an investment without delay. This decision (potentially) triggers an investment by the other player whose beliefs would have led to inaction otherwise. Endogenous timing has two distinct effects on coordination: a learning effect (early decisions reveal information) and a complementarity effect (early decisions eliminate strategic uncertainty for late movers). The experiments that we conduct to test these theoretical results show that the learning effect of timing has more impact on the subjects' behavior than the complementarity effect. We also observe that subjects' welfare improves significantly under endogenous timing.     

企业合并中的所得税会计处理初探

企业合并中的所得税会计处理比较复杂,合并方(或购买方)在合并日从被合并方(或被购买方)取得的净资产,有的包括新增递延所得税资产和递延所得税负债,有的则不包括;合并方(或购买方)在企业合并过程中产生的合并差额,有的影响当期所得税或递延所得税,有的则不影响。本文通过对同一控制下企业合并和非同一控制下企业合并的合并方或购买方税务处理进行梳理,并应用案例进行解析,以便为会计理论界和会计实务界提供参考。     

Knightian decision theory and econometric inferences

An uncertainty averse Knightian decision maker has a set of probability distributions over outcomes and chooses something other than the status quo only if the change increases the expected payoff according to all the distributions. It is possible to define a standardized degree of uncertainty aversion. To each such degree, there corresponds a set of prior distributions over the parameters of a Gaussian linear regression model, these priors being centered on a uniform prior. The set of posterior means corresponding to this set of priors has the same properties as a standard confidence region.     

Intertemporal equilibria with Knightian uncertainty

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents? multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.     

Asymmetric information without common priors: an indirect evolutionary analysis of quantity competition

The common prior assumption justifies private beliefs as posterior probabilities when updating a common prior based on individual information. We dispose of the common prior assumption for a homogeneous oligopoly market with uncertain costs and firms entertaining arbitrary priors about other firms’ cost-type. We show that true prior beliefs can not be evolutionarily stable when truly expected profit measures (reproductive) success.     

Conservative belief and rationality

Playersʼ beliefs may be incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require playersʼ beliefs to be conservative, in the sense that all players must ascribe the actual world positive probability. We show that common conservative belief of rationality (CCBR) characterizes strategies in the support of a subjective correlated equilibrium where all playersʼ beliefs have common support. We also define a notion of strong rationalizability, and show that it is characterized by CCBR.     

Forecasting the Australian economy with DSGE and BVAR models

Reflecting the importance of commodities for the Australian economy, we construct a dynamic stochastic general equilibrium (DSGE) model of the Australian economy with a commodity sector. We assess whether its forecasts can be improved by using it as a prior for an empirical Bayesian vector autoregression (BVAR). We find that the forecasts from the BVAR tend to be more accurate than those from the DSGE model. Nevertheless, for output growth these forecasts do not outperform benchmark models, such as a small open economy BVAR estimated using the standard priors for forecasting. A Bayesian factor augmented vector autoregression produces the most accurate near-term inflation forecasts.     

Bayesian updates using precursor events

It is common practice among technological forecasters to use precursor events to anticipate technological change. However, the information obtained from precursor events is usually qualitative in nature. A previous paper demonstrated that information about prior “similar” innovations can be used to generate a probability distribution of lag times between a precursor event and the event to be forecast, thus making the forecasts more quantitative. This paper presents a method for using Bayes' Equation to update probability distributions of lag time using the occurrence of additional precursor events.