Between-game rule learning in dissimilar symmetric normal-form games

Rule learning posits that decision makers, rather than choosing over actions, choose over behavioral rules with different levels of sophistication. Rules are reinforced over time based on their historically observed payoffs in a given game. Past works on rule learning have shown that when playing a single game over a number of rounds, players can learn to form sophisticated beliefs about others. Here we are interested in learning that occurs between games where the set of actions is not directly comparable from one game to the next. We study a sequence of ten thrice-played dissimilar games. Using experimental data, we find that our rule learning model captures the ability of players to learn to reason across games. However, this learning appears different from within-game rule learning as previously documented. The main adjustment in sophistication occurs by switching from non-belief-based strategies to belief-based strategies. The sophistication of the beliefs themselves increases only slightly over time.     

Contribution to a public good under subjective uncertainty

This paper examines how voluntary contributions to a public good are affected by the contributors' heterogeneity in beliefs about the uncertain impact of their contributions. It assumes that contributors have Savagian preferences that are represented by a two‐state‐dependent expected utility function and different beliefs about the benefit that will result from the sum of their contributions. We establish general comparative statics results regarding the effect of specific changes in the distribution of beliefs on the (unique) Nash equilibrium provision of the public good, under certain conditions imposed on the preferences. We specifically show that the equilibrium public good provision is increasing with respect to both first‐ and second‐order stochastic dominance changes in the distribution of beliefs. Hence, increasing the contributors' optimism about the uncertain benefit of their contributions increases aggregate public good provision, as does any homogenization of these beliefs around their mean.     

Adaptive learning models of consumer behavior

In a model of dynamic duopoly, optimal price policies are characterized assuming consumers learn adaptively about the relative quality of the two products. A contrast is made between belief-based and reinforcement learning. Under reinforcement learning, consumers can become locked into the habit of purchasing inferior goods. Such lock-in permits the existence of multiple history-dependent asymmetric steady states in which one firm dominates. In contrast, belief-based learning rules must lead asymptotically to correct beliefs about the relative quality of the two brands and so in this case there is a unique steady state.     

Hypothetical Bias Reconsidered: Payment and Provision Uncertainties in a Threshold Provision Mechanism

We extend research on the consequentiality of stated preference choices to a threshold provision mechanism for public goods. We develop a simple theoretical model of option price to analyze how option price varies with payment and provision uncertainty. We explore whether threshold provision contributions are similarly influenced by payment and provision uncertainty using an induced value contribution experiment. Results suggest that: (1) the probability of payment has a negative effect on contributions; (2) the probability of provision has a positive effect on contributions. We offer subjective beliefs regarding payment and provision as a plausible systematic explanation for hypothetical bias.     

Ambiguity on audits and cooperation in a public goods game

We investigate the impact of various audit schemes on the provision of public goods, when contributing less than the average of the other group members is centrally sanctioned and the probability of an audit is unknown. We study how individuals update their beliefs about the probability of being audited, both before and after audits are permanently withdrawn. We find that when individuals have initially experienced systematic audits, they decrease both their beliefs and their contributions almost immediately after audits are withdrawn. In contrast, when audits were initially less frequent and more irregular, they maintain high beliefs and continue cooperating long after audits have been withdrawn. This identifies the compliance effect of irregularity and uncertainty due to learning difficulties. By increasing both the frequency of audits and the severity of sanctions, we also identify an educative effect of frequent and high sanctions on further cooperation.     

A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring

This paper extends the belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring. We first find that the previous belief-based techniques [T. Sekiguchi, Efficiency in repeated prisoners' dilemma with private monitoring, J. Econ. Theory 76 (1997) 345-361; V. Bhaskar, I. Obara, Belief-based equilibria in the repeated prisoners' dilemma with private monitoring, J. Econ. Theory 102 (2002) 40-69] cannot succeed when players' private monitoring technologies are sufficiently different. We then modify the previous belief-based approach by letting the player with smaller observation errors always randomize between cooperate and defect along the cooperative path of the play. We show that with vanishing observation errors, efficiency and a folk theorem can be approximated using our modified belief-based strategies.     

How time horizons and arbitrage cost influence the turnover premium?

There are multiple theories for the causal relation between stock turnover and expected return. The risk theory argues that stocks with high turnover generally have high information uncertainty, and thus high subsequent returns are required to compensate for the increased risk. By contrast, the theory of heterogeneous beliefs considers that high-turnover stocks have high speculative values and tend to be overpriced. We find that the information contained in stock turnover is multidimensional and controlling time horizons and arbitrage cost contributes to the reconciliation of the theories of risk compensation and heterogeneous beliefs. Our result shows that expected return is positively correlated with short-term turnover, and negatively correlated with long-term one. The premium on short-term turnover is consistent with the explanations based on transaction cost and liquidity risk. The premium on long-term turnover is much more pronounced among stocks with high arbitrage cost and can be largely explained by the mispricing theory and heterogeneous beliefs.     

Beliefs and Public Good Provision with Anonymous Contributors

We analyze a static game of public good contributions where finitely many anonymous players have heterogeneous preferences about the public good and heterogeneous beliefs about the distribution of preferences. In the unique symmetric equilibrium, the only individuals who make positive contributions are those who most value the public good and who are also the most pessimistic; that is, according to their beliefs, the proportion of players who most like the public good is smaller than it would be according to any other possible belief. We predict whether the aggregate contribution is larger or smaller than it would be in an analogous game with complete information and heterogeneous preferences, by comparing the beliefs of contributors with the true distribution of preferences. A trade‐off between preferences and beliefs arises if there is no individual who simultaneously has the highest preference type and the most pessimistic belief. In this case, there is a symmetric equilibrium, and multiple symmetric equilibria occur only if there are more than two preference types.     

The institutional determinants of self-governance: a comment on Edward Stringham’s <Emphasis Type="Italic">Private Governance</Emphasis>

Many pages would be require to discuss Private Governance’s important contributions, so I focus on a relatively minor flaw: chapter 9 on moral beliefs is inconsistent with Stringham’s general treatment of private governance institutions as endogenous. Moral beliefs are essentially depicted as unchanging, but they actually are endogenous too. Individuals can pursue wealth through cooperative interaction, which requires trust, creating incentives to develop beliefs that encourage ethical and benevolent behavior. Alternatively wealth can be taken from others through force and/or guile. Beliefs to facilitate involuntary transfers also are institutionalized. For instance, in order to benefit from coercive wealth transfers “in good conscience,” recipients have incentives to see their victims as enemies to justify a moral “right” to transfers. Changing moral beliefs is costly, however, so they tend to be fixed in the short term. Once it becomes apparent that existing beliefs significantly conflict with an individual’s interests, she is forced to question those beliefs. The impetus for rationalizing new beliefs arises. The direction of evolution can be predicted with a rational decision-making model. To illustrate the endogeneity of moral beliefs, three institutional settings are examined: “dignity culture,” “honor culture,” and “victimhood culture”.     

Uncertainty causes rounding: an experimental study

Rounding is a common phenomenon when subjects provide an answer to an open-ended question, both in experimental tasks and in survey responses. From a statistical perspective, rounding implies that the measured variable is a coarsened version of the underlying continuous target variable. Since the coarsening process is non-random, inference from rounded data is generally biased. Despite the potentially severe consequences of rounding, little is known about its causes. In this paper, we focus on subjects’ uncertainty about the target variable as one potential cause for rounding behavior. We present a novel experimental method that induces uncertainty in a controlled way, thus providing causal evidence for the effect of subjects’ uncertainty on the extent of rounding. Then, we specify and estimate a mixture model that relates uncertainty and rounding. The results suggest that an increase in the exogenous level of uncertainty translates into higher variance of the subjects’ beliefs, which in turn results in more rounding.     

The minority game unpacked:

We conduct an experiment on a minority-of-three game in which each player is a team composed of three subjects. Each team can freely discuss its strategies in the game and decisions must be made via majority rule. Team discussions are recorded and their content analyzed to detect evidence of strategy co-evolution among teams playing together. Our main results show no evidence supporting the mixed strategy Nash equilibrium solution, and provide evidence more consistent with reinforcement learning models than with belief-based models. Exhibiting level-2 rationality (i.e., reasoning about others’ beliefs) is positively and significantly correlated with higher than average earnings in the game. In addition, teams that are more successful tend to become more self-centered over time, paying more attention to their own past successes than to the behavior of other teams. Finally, we find evidence of mutual adaptation over time, as teams that are more strategic induce competing teams to be more self-centered instead. Our results contribute to the understanding of coordination dynamics resting on heterogeneity and co-evolution of decision rules. In addition, they provide support at the decision process level to the validity of modeling behavior using reinforcement learning models.     

The effects of (incentivized) belief elicitation in public goods experiments

Belief elicitation is an important methodological issue for experimental economists. There are two generic questions: 1) Do incentives increase belief accuracy? 2) Are there interaction effects of beliefs and decisions? We investigate these questions in the case of finitely repeated public goods experiments. We find that belief accuracy is significantly higher when beliefs are incentivized. The relationship between contributions and beliefs is slightly steeper under incentives. However, we find that incentivized beliefs tend to lead to higher contribution levels than either non-incentivized beliefs or no beliefs at all. We discuss the implications of our results for the design of public good experiments.     

资产收购与控制权转移对经营业绩的影响

控制权转移对公司经营业绩的影响是金融学界和会计学界关注的一个重要问题。本文在剔除控制权转移之后的收购资产对经营业绩的额外贡献的基础上 ,同时运用变化模型和配对模型来研究控制权转移公司在控制权转移前后的业绩变化 ,得出了两个不同的结论。控制权转移对公司业绩的影响只能采用配对模型 ,而变化模型则可以揭示控制权转移之后股东财富的变化。研究结论表明 ,控制权转移对公司业绩的影响不显著 ,但股东从控制权转移公司所得到的报酬 ,如果剔除控制权转移之后的收购资产对经营业绩的贡献 ,其显著为负 ;如果不剔除控制权转移之后的收购资产对经营业绩的贡献 ,则其与零没有显著差异 ;控制权转移之后的资产收购对公司业绩的变化具有显著的影响 ,在研究控制权转移对公司业绩的影响时 ,需要考虑控制权转移之后的资产收购行为。     

Rent extraction,revolutionary threat,and coups in non-democracies

This paper studies the political turnover process in autocracies due to coup d’états. We present a model in which autocratic rulers are politically constrained both by the elite and by the street. These political constraints are inter-related such that when leaders extract rent from the economy on behalf of the elite they increase the probability of facing a revolt in the street. We suppose that rulers differ in the efficiency with which they extract rents and citizens make inferences about the ruler’s type when idiosyncratic shocks occur. Equilibria are characterized in which elite-led coups serve to reset citizens’ beliefs about the leader’s type and pre-empt revolutions during periods of popular unrest. We then investigate the empirical implications using panel data on popular unrest and coups in sub-Saharan Africa. OLS and IV estimates support the causal mechanism highlighted in our theory. The magnitude of the effect is substantial – a one standard deviation increase in protest intensity increases the probability a coup occurs by a factor of almost three in our baseline IV specification.     

Endogenous uncertainty and market volatility

We advance the theory that the distribution of beliefs in the market is the most important propagation mechanism of economic volatility. Our model is based on the theory of Rational Beliefs (RB) and Rational Belief Equilibrium (RBE) developed by Kurz (1994, 1997). We argue that the diverse market puzzles which are examined, such as the equity premium puzzle, are all driven by the structure of market expectations. In support of our view, we present an RBE model with which we study financial markets. The model is able to simulate the correct order of magnitude of: (i) the long term mean and standard deviation of the price\dividend ratio; (ii) the long term mean and standard deviation of the risky rate of return on equities; (iii) the long term mean and standard deviation of the riskless rate; (iv) the long term mean equity premium. In addition, the model predicts (v) the GARCH property of risky asset returns; (vi) the observed pattern of the predictability of long returns on assets, and (vii) the Forward Discount Bias in foreign exchange markets. The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs such that some agents are optimistic and some pessimistic about future capital gains. The model has a unique parameterization under which the model makes all the above predictions simultaneously. The parameterization requires the optimists to be in the majority but the rationality of belief conditions of the RBE require the pessimists to have a higher intensity level. In simple terms, the large equity premium and the low equilibrium riskless rate are the result of the fact that at any moment of time there are agents who hold extreme pessimistic beliefs and they have a relatively stronger impact on the market. The paper also studies the effect of correlation of beliefs among investors. It shows that the main effect of such correlation is on the dynamic patterns of asset prices and returns and is hence important for studying such phenomena as stochastic volatility. Received: May 16, 2000; revised version: November 15, 2000     

Coordination and correlation in Markov rational belief equilibria

Summary This paper studies the effect of correlation in the rational beliefs of agents on the volatility of asset prices. We use the technique of generating variables to study stable and non-stationary processes needed to characterize rational beliefs. We then examine how the stochastic interaction among such variables affects the behavior of a wide class of Rational Belief Equilibria (RBE). The paper demonstrates how to construct a consistent price state space and then shows the existence of RBE for any economy for which such price state space is constructed. Next, the results are used to study the volatility of asset prices via numerical simulation of a two agents model. If beliefs of agents are uniformly dispersed and independent, we would expect heterogeneity of beliefs to have a limited impact on the fluctuations of asset prices. On the other hand, our results show that correlation across agents can have a complex and dramatic effect on the volatility of prices and thus can be the dominant factor in the fluctuation of asset prices. The mechanism generating this effect works through the clustering of beliefs in states of different levels of agreement. In states of agreement the conditional forecasts of the agents tend to fluctuatetogether inducing more volatile asset prices. In states of disagreement the conditional forecasts fluctuatein diverse directions tending to cancel each other's effect on market demand and resulting in reduced price volatility.This research was supported, in part, by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the Research Incentive Fund of Stanford University. The authors thank Carsten K. Nielsen and Ho-Mou Wu for valuable discussions on an earlier draft. Carsten K. Nielsen also made an important contribution to the development of Section 3.     

Stock market development and real economic activity in Peru

We explore the causal effect of stock market development on real economic activity in Peru by setting up a simple growth model that underpins long-run identifying restrictions for vector autoregressive models. This allows us to identify stock market shocks and to uncover the dynamic response of real output per capita. Using annual time series data for the period 1965–2013, we find that stock market shocks have had a short-run causal effect on real GDP per capita only after 1991, a result that is consistent with standard Granger causality tests; however, the contribution of stock market shocks to output growth dynamics has been small. Thus, policy actions aimed at further developing the Peruvian stock market may have a positive impact on the dynamics of economic growth.     

Political contribution caps and lobby formation: Theory and evidence

The perceived importance of “special interest group” money in election campaigns motivates widespread use of caps on allowable contributions. We present a bargaining model in which the effect of a cap that is not too stringent on the amount a lobby can contribute improves its bargaining position relative to the politician. It thus increases the payoff from lobbying, which will therefore increase the equilibrium number of lobbies when lobby formation is endogenous. Caps may then also increase aggregate contributions from lobbies and increase politically motivated government spending. We present empirical evidence from U.S. states that support various predictions of the model. We find a positive effect on the number of PACs formed from enacting laws constraining PAC contributions. Moreover, the estimated effect is non-linear, as predicted by the theoretical model. Very stringent caps reduce the number of PACs, but as the cap increases above a threshold level, the effect becomes positive. Contribution caps in the majority of U.S. states are above this threshold.     

Identification of firms’ beliefs in structural models of market competition

Firms make decisions under uncertainty and differ in their ability to collect and process information. As a result, in changing environments, firms have heterogeneous beliefs on the behaviour of other firms. This heterogeneity in beliefs can have important implications on market outcomes, efficiency and welfare. This paper studies the identification of firms’ beliefs using their observed actions—a revealed preference and beliefs approach. I consider a general structural model of market competition where firms have incomplete information and their beliefs and profits are nonparametric functions of decisions and state variables. Beliefs may be out of equilibrium. The framework applies both to continuous and discrete choice games and includes as particular cases models of competition in prices or quantities, auction models, entry games and dynamic games of investment decisions. I focus on identification results that exploit an exclusion restriction that naturally appears in models of competition: an observable variable that affects a firm's cost (or revenue) but does not have a direct effect on other firms’ profits. I present identification results under three scenarios—common in empirical industrial organization—on the data available to the researcher.     

Weak Moral Motivation Leads to the Decline of Voluntary Contributions

We develop a model that accounts for the decay of the average contribution observed in experiments on voluntary contributions to a public good. The novel idea is that people's moral motivation is “weak.” Their judgment about the right contribution depends on observed contributions by group members and on an intrinsic “moral ideal.” We show that the assumption of weakly morally motivated agents leads to the decline of the average contribution over time. The model is compatible with persistence of overcontributions, variability of contributions (across and within individuals), the “restart effect” and the observation that the decay in contributions is slower in longer games. Furthermore, it offers a rationale for conditional cooperation.