Higher Order Uncertainty and Information: Static and Dynamic Games

Weinstein and Yildiz (2007) have shown that in static games, only very weak predictions are robust to perturbations of higher order beliefs. These predictions are precisely those provided by interim correlated rationalizability (ICR). This negative result is obtained under the assumption that agents have no information on payoffs. This assumption is unnatural in many settings. It is therefore natural to ask whether Weinstein and Yildiz's results remain true under more general information structures. This paper characterizes the “robust predictions” in static and dynamic games, under arbitrary information structures. This characterization is provided by an extensive form solution concept: interim sequential rationalizability (ISR). In static games, ISR coincides with ICR and does not depend on the assumptions on agents' information. Hence the “no information” assumption entails no loss of generality in these settings. This is not the case in dynamic games, where ISR refines ICR and depends on the details of the information structure. In these settings, the robust predictions depend on the assumptions on agents' information. This reveals a hitherto neglected interaction between information and higher order uncertainty, raising novel questions of robustness.     

Pathological Outcomes of Observational Learning

This paper explores how Bayes‐rational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may type‐specific ‘herds’ eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history offers no decisive lessons for anyone, and each type's actions forever nontrivially split between two actions. To verify that our identified limit outcomes do arise, we exploit the Markov‐martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.     

Adjacent vertex distinguishing total colorings of outerplanar graphs

An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing total coloring of G is denoted by χ″ _a (G). In this paper, we characterize completely the adjacent vertex distinguishing total chromatic number of outerplanar graphs.     

Signaling to Partially Informed Investors in the Newsvendor Model

We analyze a signaling game between the manager of a firm and an investor in the firm. The manager has private information about the firm's demand and cares about the short‐term stock price assigned by the investor. Previous research has shown that under continuous decision choices and the Intuitive Criterion refinement, the least‐cost separating equilibrium will result, in which a low‐quality firm chooses its optimal capacity and a high‐quality firm over‐invests in order to signal its quality to investors. We build on this research by showing the existence of pooling outcomes in which low‐quality firms over‐invest and high‐quality firms under‐invest so as to provide identical signals to investors. The pooling equilibrium is practically appealing because it yields a Pareto improvement compared to the least‐cost separating equilibrium. Distinguishing features of our analysis are that: (i) we allow the capacity decision to have either discrete or continuous support, and (ii) we allow beliefs to be refined based on either the Undefeated refinement or the Intuitive Criterion refinement. We find that the newsvendor model parameters impact the likelihood of a pooling outcome, and this impact changes in both sign and magnitude depending on which refinement is used.     

The Effect of Changes in Risk Attitude on Strategic Behavior

We study families of normal‐form games with fixed preferences over pure action profiles but varied preferences over lotteries. That is, we subject players' utilities to monotone but nonlinear transformations and examine changes in the rationalizable set and set of equilibria. Among our results: The rationalizable set always grows under concave transformations (risk aversion) and shrinks under convex transformations (risk love). The rationalizable set reaches an upper bound under extreme risk aversion, and lower bound under risk love, and both of these bounds are characterized by elimination processes. For generic two‐player games, under extreme risk love or aversion, all Nash equilibria are close to pure and the limiting set of equilibria can be described using preferences over pure action profiles.     

Effect of charismatic signaling in social media settings: Evidence from TED and Twitter

Informal leaders in social media currently characterize a large part of political and economic communication on various challenges societies face, whether localized or transborder (e.g., COVID-19 pandemic, global warming). Scholars have theorized that charismatic signaling is effective in informal leadership settings; yet empirical evidence remains scarce in understanding a ubiquitous phenomenon that marks our times and plays an important role in shaping public opinion. In this article, we used two unique data sets extracted from social media to investigate the success of charisma for informal leaders, leaders who signal their beliefs and preferences to others but having no formal authority over them. Social media offers us a standardized medium as well as a natural environment to test our predictions. Using a sample of TED talks and tweets, we coded for objective markers of charisma and found that using more verbal charismatic signals predicted (a) higher views for TED talks as well as higher ratings for the extent to which the talk was found to be inspiring—beyond attractiveness and nonverbal behavior—and (b) more retweets. We discuss the implications of such results for both theory and practice in the media age.     

A re-analysis of the occupational stress indicator

Abstract

This paper investigates the reliability of the Occupational Stress Indicator (OSI). Data from a sample of university staff, drawn from all areas of an urban university, are used to reassess the apparently low reliabilities of many of the OSI subscales reported by Cooper et al. (1988). In addition, factor analysis results are reported for the first time for the sources of pressure data. The reliability data reported here, while higher reliabilities than originally obtained, remain unacceptably low. A lack of stability in the device as it is currently formulated seems apparent. The paper also presents for the first time a detailed analysis of the sources of pressure scale, indicating a solution different from that proposed by Cooper et al. (1988). Certain areas of the OSI clearly need refinement; the inclusion of locus of control and type A behaviour as personality variables in particular is called into question. Observations regarding the particular strengths and weaknesses of this device, and suggestions for future refinements, are offered.     

Bayesian Learning,Smooth Approximate Optimal Behavior,and Convergence to ε‐Nash Equilibrium

In this paper, I construct players' prior beliefs and show that these prior beliefs lead the players to learn to play an approximate Nash equilibrium uniformly in any infinitely repeated slightly perturbed game with discounting and perfect monitoring. That is, given any ε > 0, there exists a (single) profile of players' prior beliefs that leads play to almost surely converge to an ε‐Nash equilibrium uniformly for any (finite normal form) stage game with slight payoff perturbation and any discount factor less than 1.     

Finite Order Implications of Common Priors

I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that in finite models, the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any finite N and any finite partitions model where priors have the same support, there is another finite partitions model with common priors that has the same nth order beliefs and knowledge for all n≤N.     

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.     

Beliefs in Repeated Games

Consider a two‐player discounted infinitely repeated game. A player's belief is a probability distribution over the opponent's repeated game strategies. This paper shows that, for a large class of repeated games, there are no beliefs that satisfy three properties: learnability, a diversity of belief condition called CSP, and consistency. Loosely, if players learn to forecast the path of play whenever each plays a strategy that the other anticipates (in the sense of being in the support of that player's belief) and if the sets of anticipated strategies are sufficiently rich, then neither anticipates any of his opponent's best responses. This generalizes results in Nachbar (1997).     

DO WOMEN PAY MORE FOR CREDIT? EVIDENCE FROM ITALY

By using a unique and large data set on loan contracts between banks and microfirms, we find robust evidence that women in Italy pay more for credit than men, although we do not find any evidence that women borrowers are riskier than men. The male/female differential remains even after controlling for a large number of characteristics of the type of business, the borrower, and the structure of the credit market. The result is not driven by lack of credit history, nor by women using a different type of bank than men, since the same bank charges different rates to male and female borrowers.     

Every Choice Function Is Backwards‐Induction Rationalizable

A choice function is backwards‐induction rationalizable if there exists a finite perfect‐information extensive‐form game such that for each subset of alternatives, the backwards‐induction outcome of the restriction of the game to that subset of alternatives coincides with the choice from that subset. We prove that every choice function is backwards‐induction rationalizable.     

Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree

An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ′ _a (G). Let mad(G)\mathop{\mathrm{mad}}(G) and Δ denote the maximum average degree and the maximum degree of a graph G, respectively.     

The Revealed Preference Theory of Stable and Extremal Stable Matchings

We investigate the testable implications of the theory of stable matchings. We provide a characterization of the matchings that are rationalizable as stable matchings when agents' preferences are unobserved. The characterization is a simple nonparametric test for stability, in the tradition of revealed preference tests. We also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market: extremal stable matchings. We find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers.     

Usability of Online Services: The Role of Technology Readiness and Context*

An important prerequisite for the success of any online service is ensuring that customers' experience—via the interface—satisfies both sensory and functional needs. Developing interfaces that are responsive to customers' needs requires a perspective on interface design as well as a deep understanding of the customers themselves. Drawing upon research in consumer behavior concerning consumer beliefs about technology, we deploy an alternative way to describe customers based on psychographic characteristics. Technology readiness (TR), a multidimensional psychographic construct, offers a way to segment online customers based upon underlying positive and negative technology beliefs. The core premise of this study is that the beliefs form the foundation for expectations of how things should work and how specific online service interfaces are evaluated by customers. At the same time, usability evaluations of specific online services might be contingent on contextual factors, specifically the type of site (hedonic vs. utilitarian) and access method (Web vs. wireless Web). The aspects of usability examined here are those incorporated into the usability metric and instrument based on the Microsoft Usability Guidelines (MUG). The results of an empirical study with 160 participants indicate that (i) TR customer segments vary in usability requirements and (ii) usability evaluations of specific online service interfaces are influenced by complex interactions among site type, access method, and TR segment membership. As organizations continue to expand their online service offerings, managers must recognize that the interface exists to serve the customers, so their design must be matched to market needs and TR.     

Recoverable robust timetabling for single delay: Complexity and polynomial algorithms for special cases

In this paper, we study the problem of planning a timetable for passenger trains considering that possible delays might occur due to unpredictable circumstances. If a delay occurs, a timetable could not be able to manage it unless some extra time has been scheduled in advance. Delays might be managed in several ways and the usual objective function considered for such purpose is the minimization of the overall waiting time caused to passengers. We analyze the timetable planning problem in terms of the recoverable robustness model, where a timetable is said to be recoverable robust if it is able to absorb small delays by possibly applying given limited recovery capabilities. The quality of a robust timetable is measured by the price of robustness that is the ratio between the cost of the recoverable robust timetable and that of a non-robust optimal one.     

Certifiable Pre‐Play Communication: Full Disclosure

This article asks when communication with certifiable information leads to complete information revelation. We consider Bayesian games augmented by a pre‐play communication phase in which announcements are made publicly. We first characterize the augmented games in which there exists a fully revealing sequential equilibrium with extremal beliefs (i.e., any deviation is attributed to a single type of the deviator). Next, we define a class of games for which existence of a fully revealing equilibrium is equivalent to a richness property of the evidence structure. This characterization enables us to provide different sets of sufficient conditions for full information disclosure that encompass and extend all known results in the literature, and are easily applicable. We use these conditions to obtain new insights in games with strategic complementarities, voting with deliberation, and persuasion games with multidimensional types.     

CONVERGENCE: AN EXPERIMENTAL STUDY OF TEACHING AND LEARNING IN REPEATED GAMES

Nash equilibrium can be interpreted as a steady state where players hold correct beliefs about the other players’ behavior and act rationally. We experimentally examine the process that leads to this steady state. Our results indicate that some players emerge as teachers—those subjects who, by their actions, try to influence the beliefs of their opponent and lead the way to a more favorable outcome—and that the presence of teachers appears to facilitate convergence to Nash equilibrium. In addition to our experiments, we examine games, with different properties, from other experiments and show that teaching plays an important role in these games. We also report results from treatments in which teaching is made more difficult. In these treatments, convergence rates go down and any convergence that does occur is delayed.     

If You're so Smart,why Aren't You Rich? Belief Selection in Complete and Incomplete Markets

This paper provides an analysis of the asymptotic properties of Pareto optimal consumption allocations in a stochastic general equilibrium model with heterogeneous consumers. In particular, we investigate the market selection hypothesis that markets favor traders with more accurate beliefs. We show that in any Pareto‐optimal allocation whether each consumer vanishes or survives is determined entirely by discount factors and beliefs. Whereas equilibrium allocations in economies with complete markets are Pareto optimal, our results characterize the limit behavior of these economies. We show that, all else equal, the market selects for consumers who use Bayesian learning with the truth in the support of their prior and selects among Bayesians according to the size of their parameter space. Finally, we show that in economies with incomplete markets, these conclusions may not hold. With incomplete markets, payoff functions can matter for long‐run survival, and the market selection hypothesis fails.