Strategic games with security and potential level players

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players.      

Probability and logic in belief systems

This paper seeks to develop a formal (mathematical) model of belief systems based on the axioms of probability theory and propositional logic. By a belief system we mean a set of propositions along with an actor's objective probability assignments to (beliefs in) them, together with the relationships among and between propositions and beliefs. Belief systems are regarded as being comprised of interrelated elements.In the paper are developed measures of the distance between sets of beliefs; of the congruence, coherence, and consistency of belief systems; and of the degree of polarization of belief systems-which are derived from one basic operation, symmetric difference.We show that these measures possess a number of useful and powerful mathematical properties. Also, a model is set forth by which, from an actor's subjective probability assignment to propositions and pairwise conjunctions of propositions, we may then impute to the actor subjectively perceived truth functional relationships between proposition.The potential uses and practical difficulties with the approach taken in the paper are also discussed, and the assertion is made that the measures developed enable us to simply distinguish between certain notions (e.g., congruence, consistency, coherence) too often and easily confused, provide us with the possibility of interval (or at least, quasi-interval level) measurement of certain properties of individual belief systems, and also allows us to make comparisons between the structures of different actors' belief systems.An earlier version of this paper was delivered at the 1969 American Political-Science Association, Chicago.     

Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories

Two experiments show that violations of expected utility due to ambiguity, found in general decision experiments, also affect belief aggregation. Hence we use modern ambiguity theories to analyze belief aggregation, thus obtaining more refined and empirically more valid results than traditional theories can provide. We can now confirm more reliably that conflicting (heterogeneous) beliefs where some agents express certainty are processed differently than informationally equivalent imprecise homogeneous beliefs. We can also investigate new phenomena related to ambiguity. For instance, agents who express certainty receive extra weight (a cognitive effect related to ambiguity-generated insensitivity) and generate extra preference value (source preference; a motivational effect related to ambiguity aversion). Hence, incentive compatible belief elicitations that prevent manipulation are especially warranted when agents express certainty. For multiple prior theories of ambiguity, our findings imply that the same prior probabilities can be treated differently in different contexts, suggesting an interest of corresponding generalizations.     

Joint Beliefs in Conflictual Coordination Games

The traditional solution concept for noncooperative game theory is the Nash equilibrium, which contains an implicit assumption that players probability distributions satisfy t probabilistic independence. However, in games with more than two players, relaxing this assumption results in a more general equilibrium concept based on joint beliefs (Vanderschraaf, 1995). This article explores the implications of this joint-beliefs equilibrium concept for two kinds of conflictual coordination games: crisis bargaining and public goods provision. We find that, using updating consistent with Bayes rule, players beliefs converge to equilibria in joint beliefs which do not satisfy probabilistic independence. In addition, joint beliefs greatly expand the set of mixed equilibria. On the face of it, allowing for joint beliefs might be expected to increase the prospects for coordination. However, we show that if players use joint beliefs, which may be more likely as the number of players increases, then the prospects for coordination in these games declines vis-à-vis independent beliefs.     

History as a coordination device

Coordination games often have multiple equilibria. The selection of equilibrium raises the question of belief formation: how do players generate beliefs about the behavior of other players? This article takes the view that the answer lies in history, that is, in the outcomes of similar coordination games played in the past, possibly by other players. We analyze a simple model in which a large population plays a game that exhibits strategic complementarities. We assume a dynamic process that faces different populations with such games for randomly selected values of a parameter. We introduce a belief formation process that takes into account the history of similar games played in the past, not necessarily by the same population. We show that when history serves as a coordination device, the limit behavior depends on the way history unfolds, and cannot be determined from a-priori considerations.     

Sociotropes, Systematic Bias, and Political Failure: Reflections on the Survey of Americans and Economists on the Economy

Objectives . Economic models of politics typically make two assumptions about voters: first, their motives are egocentric, not sociotropic; second, their beliefs are rational, not subject to systematic bias. Political scientists have presented strong evidence against the first assumption (Mansbridge, 1990), but have become increasingly willing to accept the second (Page and Shapiro, 1992; Marcus and Hanson, 1993). This article tests these two assumptions, then explores the tests' broader implications. Methods . I use the Survey of Americans and Economists on the Economy to test for egocentricity of motivation and rationality of belief. Results . Both standard assumptions fail for the case where the economic approach would seemingly be most relevant: economic beliefs. Conclusions . This is not necessarily cause for greater optimism about the efficiency of democracy: sociotropic voters with biased economic beliefs are more likely to produce severe political failures than are selfish voters with rational expectations.     

试论宗教信仰的政治意蕴

信仰源于人类的本性需要,宗教信仰也是如此,对宗教信仰的社会作用应给以科学评价。宗教信仰之所以得到许多国家的认同和支持,在于其具有深刻的政治意蕴。它不仅是统治者进行政治统治的理论辩护工具,而且是进行社会控制和稳定社会秩序的调节器,特别是凝聚民族力量的强力粘合剂,一些重要政治运动的传播机。因此,在对待宗教信仰的态度上,我们一方面应该实行宗教信仰自由政策,另一方面必须反对封建迷信、抵制和铲除邪教。同时,维护宗教信仰的民族性特点,坚决反对利用宗教信仰作掩护的民族分裂主义。     

Overconfidence in tournaments: evidence from the field

This paper uses a field survey to investigate the quality of individuals’ beliefs of relative performance in tournaments. We consider two field settings, poker and chess, which differ in the degree to which luck is a factor and also in the information that players have about the ability of the competition. We find that poker players’ forecasts of relative performance are random guesses with an overestimation bias. Chess players also overestimate their relative performance but make informed guesses. We find support for the “unskilled and unaware hypothesis” in chess: high-skilled chess players make better forecasts than low-skilled chess players. Finally, we find that chess players’ forecasts of relative performance are not efficient.     

Belief system foundations of backward induction

Two justifications of backward induction (BI) in generic perfect information games are formulated using Bonanno's (1992; Theory and Decision 33, 153) belief systems. The first justification concerns the BI strategy profile and is based on selecting a set of rational belief systems from which players have to choose their belief functions. The second justification concerns the BI path of play and is based on a sequential deletion of nodes that are inconsistent with the choice of rational belief functions.     

Beliefs in Conspiracy Theories Among African Americans: A Comparison of Elites and Masses*

Objective. Several studies have reported a widespread belief in conspiracy theories among African Americans. Such theories have been shown to have possible deleterious effects, especially when they deal with HIV/AIDS. It has been conjectured that African‐American elites could play a role in dispelling these beliefs, unless, of course, they believe in these theories themselves. To examine this possibility the present study examines the conspiratorial beliefs of African‐American locally elected officials in Louisiana and compares them with a previous study of African‐American churchgoers in the same state. Methods. A systematic sample of 400 African‐American locally elected officials was drawn from a list of all African‐American elected officials in the state and 170 officials completed and returned the mail survey. Confirmatory factor analysis and OLS regression were used to analyze the attitude structure and determinants of beliefs, respectively. Results. The locally elected officials believe in these theories as much as the churchgoers and the structures of their beliefs are also very similar. In some very important ways, however, the predictors of these beliefs differ between the two samples. Conclusions. Our findings suggest that beliefs in conspiracy theories are widespread and that African‐American locally elected officials will not seek to dispel these beliefs.     

Them and Us: Hidden Ideologies-Differences in Degree or Kind?

This article looks at three measuring instruments—the Right-Wing Authoritarianism Scale, the Social Dominance Orientation Scale, and the Attitudes About Reality Scale—used to examine covert ideology and its relationship to social and political beliefs and behaviors. These scales share similar ideological components involving abdication of moral responsibility to an outside agent, belief that one's own ideology represents the only form of truth, and negative beliefs about individuals who are not members of one's own group. Evidence is provided to suggest that radical fundamentalists and some groups within U.S. society share ideological beliefs that differ in degree rather than kind. These beliefs make it easy for them to divide the world into "us" and "them" and exacerbate the present conflict.     

Professional and personal hierarchies of ethical principles

We explore social workers’ perception of the importance and rank ordering of ethical principles. Do they have a generally agreed upon hierarchy of ethical principles? Do they apply similar hierarchies of ethical principles when facing different cases? Are their professional and personal hierarchies of ethical principles similar? The findings based on a structured questionnaire indicated that while social workers attach high importance to most ethical principles closely associated with social work, they do not hold a universal hierarchy of ethical principles. Social workers change their ethical hierarchies in different professional situations but there is no difference between their professional and personal ethical hierarchies. Implications for practice and education are discussed.     

Faith and Politics: The Influence of Religious Beliefs on Political Participation*

Objective. The relationship between religion and political participation has not been rigorously investigated, typically employing only basic measures of church attendance or denomination. In this study, we utilize precise measures of various religious behaviors, traditions, and beliefs to examine their influence on political participation. Methods. Using data from the Baylor Religion Survey 2005, we demonstrate that merely including measures of church attendance or denomination camouflages much of religion's influence on political participation. Results. We find that religious beliefs are significantly related to national political participation. For religious activities, identifying with a religious tradition reduces participation, but participation in church activities increases political participation. Conclusion. Different types of religious beliefs influence political participation differently. Although some macro religious beliefs significantly increase macro political behavior, believers in an involved God are less likely to participate politically. Individualistic, micro beliefs have no affect on national politics. Thus, the scope of the religious belief fits with the scope of the political activity, in that more macro concerns translate to national political participation.     

The likelihood of various stock market return distributions, part 2: Empirical results

The present article shows how Bayesians should shift beliefs among a family of models concerning the probability distribution of daily changes in the Standard & Poor 500 Index, given a particular sample. The preceding article in this issue showed that classical (R.A. Fisher, Neyman-Pearson) inference can be highly misleading for Bayesians, as can the assumption of a diffuse prior. The present article discusses how to bound Bayesian shifts in belief for compound hypotheses generally, as well as the specific shifts in beliefs among simple and compound hypotheses implied by the particular sample.     

Judgment aggregation and minimal change: a model of consensus formation by belief revision

When a group of agents attempts to reach an agreement on certain issues, it is usually desirable that the resulting consensus be as close as possible to the original judgments of the individuals. However, when these judgments are logically connected to further beliefs, the notion of closeness should also take into account to what extent the individuals would have to revise their entire belief set to reach an agreement. In this work, we present a model for generation of agreement with respect to a given agenda which allows individual epistemic entrenchment to influence the value of the consensus. While the postulates for the transformation function and their construction resemble those of AGM belief revision, the notion of an agenda is adapted from the theory of judgment aggregation. This allows our model to connect both frameworks.     

A new model of the development of deception: Disentangling the role of false‐belief understanding in deceptive ability

“Deception” is defined predominantly as the intentional attempt to create false‐beliefs in others. However, the intentionality behind early acts of deception and its relation to false‐belief understanding remain unresolved. In this article, we offer a three‐stage theoretical model of the development of deception in human ontogeny. We posit that at any age, human deception is an intentional action, but its form changes according to the level of the deceiver's intentionality. As the primary function of deception is to influence the behaviour of others, we argue that first‐stage deceptions‐in‐action involves only in the analysis of behaviours and perceptual access, not beliefs. In our view, the ability to deceive and false‐belief understanding are eventually inter‐connected, but false‐belief understanding is not essential for the earliest form of deception. Based on empirical findings, which suggest that by observing the results of early deceptions children build their knowledge of mental states as causes of human actions, we claim that the second stage of deception is representational deception. Further, as the understanding of beliefs becomes more advanced, the effectiveness of children's deception increases, and new forms of reflective deception (the third stage) emerge. Future directions for research are outlined, and limitations of the current model are discussed.     

Children's Attention to Others' Beliefs during Persuasion: Improvised and Selected Arguments to Puppets and People

Until now children's attention to the beliefs of people they wish to persuade has been examined experimentally via tasks that were artificial in important respects. To determine whether such research has underestimated children's psychological perspective taking, two studies that manipulated task elements pertinent to ecological validity were conducted. Children in three age groups (3, 4/5, and 6/7 years) were asked (forced‐choice and open‐ended formats) how best to persuade puppets and people, with differing beliefs, to pet and play with various toy animals. Children offered as many or more belief‐relevant arguments in response to forced‐choice as to open‐ended questions. Only the oldest group attended to beliefs more when persuading a person compared with a puppet. Even on more realistic tasks, significant improvement with age across task formats confirmed a developmental trajectory in line with extant reports of children's belief reasoning. The findings support the idea that enhanced social competence corresponds specifically to children's increasing attention to beliefs in social interactions such as persuasion.     

The Foreign Policy Beliefs of Political Campaign Contributors: A Post-Cold War Analysis

Objective. In this article we address two questions raised by the literature on the structure of foreign policy beliefs. First, has the end of the Cold War brought about any major changes in these belief systems? Second, how do ideology and economic interests shape these beliefs? Methods. We analyze data from a 1996 survey of U.S. presidential campaign contributors conducted by the Ray Bliss Center to determine the foreign policy belief systems of contributors. We then compare those results to the belief systems found in a 1988 survey of contributors. Results. We find that Cold War belief systems are quite durable. There was surprisingly little change in the structure or content of contributors' foreign policy beliefs between 1988 and 1996. We also find that both ideology and economic interests help shape these beliefs and examine the circumstances under which each of these two considerations appears to have the most important effects. Conclusions. Policymakers face new challenges since the end of the Cold War, but domestic political elites still approach foreign policy with a Cold War perspective. Also, although ideology is very important in determining how individuals think about foreign policy, material interests also make a difference for campaign contributors.     

Belief formation in a signaling game without common prior: an experiment

Using belief elicitation, the paper investigates the process of belief formation and evolution in a signaling game in which a common prior is not induced. Both prior and posterior beliefs of Receivers about Senders’ types are elicited, as well as beliefs of Senders about Receivers’ strategies. In the experiment, subjects often start with diffuse uniform beliefs and update them in view of observations. However, the speed of updating is influenced by the strength of initial beliefs. An interesting result is that beliefs about the prior distribution of types are updated slower than posterior beliefs, which incorporate Senders’ strategies. In the medium run, for some specifications of game parameters, this leads to outcomes being significantly different from the outcomes of the game in which a common prior is induced. It is also shown that elicitation of beliefs does not considerably change the pattern of play in this game.