Behavioral similarity,confederate strategy,and sex composition of dyad as determinants of interpersonal judgments and behavior in the prisoner's dilemma game

The study was designed to test three distinct theoretical models relating player's attitudes toward a confederate in the prisoner's dilemma game: a reinforcing outcome model, a cultural norm model, and a social comparison model. A secondary concern of the study was to determine if player's sex, confederate's sex, and the confederate's strategy interactively influence player's choice behavior. Forty-eight male and forty-eight female subjects played 100 trials of the prisoner's dilemma game with a confederate who played either a 74% cooperative or 74% competitive predetermined strategy and then filled out the Interpersonal Judgment Scale rating the confederate. Behaviorally similar confederates received more positive evaluations than dissimilar confederates supporting the social comparison hypothesis. Further, the strategy of the confederate did not influence choice behavior in mixed-sex dyads, suggesting that sex roles may inhibit behaviorally based male-female interaction. The generality of previous gaming research which has dealt almost exclusively with same-sex dyads is called into question.     

Maximum likelihood estimation for Luce's choice model

A terminology for general choice models based on the choice axiom is given. It applies to all kinds of choice experiments, such as confusion choice experiments, paired comparisons, triadic comparisons, directional rankings, scores on binary test items, and others. Maximum likelihood estimation for such general choice models is considered. Conditions for the uniqueness of maximum likelihood estimates are given, and it is shown that the estimates can be derived by iterative proportional fitting. This offers the opportunity of a general test of the choice axiom for all kinds of choice experiments using the likelihood ratio. The estimation and testing procedure is applied to data from a form recognition experiment, reported by W. A. Wagenaar (Nederlands Tijdschrift voor de Psychologie, 1968, 23, 96–108).     

Sequential search by groups with rank-dependent payoffs: An experimental study

In many sequential search situations, decisions are reached by groups. We examine behavior in such situations experimentally using an extension of the “secretary problem”. In our setup, group members (players) with non-aligned preferences inspect alternatives or “applicants” one at a time with no backward solicitation. A minimal information structure is assumed where players are only informed of the relative ranks of the alternatives as they inspect them sequentially. We present the equilibrium solution, and then use it as a benchmark for our analysis. We report the results from a controlled experiment showing that subjects over-searched relative to equilibrium. Decisions were affected by theoretically irrelevant observations including the relative rank of the previous alternative and the other player’s relative rank of the current alternative. For managers engaged in committee sequential search tasks, our findings highlight the importance of being aware to reach compromises early on, among other implications.     

The Intrinsic Quantum Nature of Nash Equilibrium Mixtures

In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics (QM), which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in a game, than the payoff matrix—the axiom of “no-supplementary data” holds—then the state of mind of a rational player is algebraically isomorphic to a pure quantum state. The “no supplementary data” axiom is captured in a Lukasiewicz’s three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. As a corollary, we show that in a mixed Nash equilibrium, the knowledge structure of a player implies that probabilities must verify the standard “Born rule” postulate of QM. The puzzling “indifference condition” wherein each player must be rationally indifferent between all the pure actions of the support of his equilibrium strategy is resolved by his state of mind being described by a “quantum superposition” prior a player is asked to make a definite choice in a “measurement”. Finally, these results demonstrate that there is an intrinsic limitation to the predictions of game theory, on a par with the “irreducible randomness” of quantum physics.     

Bargaining ability,the utility of playing a game,and models of coalition formation

A utility function for playing a given position in a game is developed as a natural extension of the utility function which defines the rewards available in the game. This function is determined by a player's opinion of his bargaining ability. A characterization of such utilities is obtained which generalizes previous results that the Shapley value and Banzhaf-Coleman index are both cardinal utility functions which reflect different bargaining abilities. The approach taken here is related to models of coalition formation.     

Competition and men’s face preferences

Several studies have examined potentially adaptive shifts and sources of individual differences in women’s face preferences, but relatively few studies have looked for similar findings in men. Evidence suggests that men of higher mate-value may be better placed to compete for relationships with higher-quality women, and that contest competition may influence men’s perceptions of dominance. Here, we looked at the effects of winning/losing in male–male competition on men’s face preferences. Participants were randomly and unknowingly assigned to either win or lose the first-person shooter video game Counter-Strike: Source against an unseen male confederate who could control the outcome through game cheats. We found that, compared to men assigned to the losing condition, men assigned to the winning condition had significantly (p = 0.012) higher preferences for women’s facial femininity. Results suggest that the outcomes of male–male competition may alter men’s mate preferences.     

The fit of Holland’s RIASEC model to US occupations

Holland’s [Holland, J. L. (1959). A theory of occupational choice. Journal of Counseling Psychology, 6, 35-45; Holland, J. L. (1997). Making vocational choices: A theory of vocational personalities and work environments (3rd ed.). Odessa, FL: Psychological Assessment Resources, Inc.] RIASEC types were initially developed using a restricted range of occupational titles. Holland’s type classification system has been extended to encompass the full range of occupations in the US, using both statistical and expert rating methods. However, the extent that Holland’s classification model is sufficient to represent the full range of occupational interests has not been examined. Multidimensional scaling (MDS) was used to analyze college students’ (266 men, 572 women) interests in occupations representing approximately 85% of the US labor market. A two-dimensional MDS solution of the full set of occupations did not fit Holland’s model, but limiting the analysis to occupations used in Holland-based measures produced the expected RIASEC structure. In comparison, a three-dimensional solution included Prediger’s [Prediger, D. J. (1982). Dimensions underlying Holland’s hexagon: Missing link between interests and occupations? Journal of Vocational Behavior, 21, 259-287] dimensions (Things/People and Data/Ideas) consistent with Holland’s model, but also included prestige and sex-type dimensions that were not orthogonal to Prediger’s dimensions. These results demonstrate that the RIASEC types are not sufficient to represent the full range of occupational interests and are confounded with prestige and sex-type.     

Modelling simultaneous games in dynamic logic

We make a proposal for formalizing simultaneous games at the abstraction level of player’s powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of ‘concurrent game logic’ CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic.     

Discrete dynamic choice: An extension of the choice models of thurstone and luce

The present paper deals with the extension of two well-known static discrete choice theories to the dynamic situation in which individuals make choices at several points in (continuous) time. A dynamic version of Luce's Axiom, “independence from irrelevant alternatives”, is proposed and some of its implications are derived. In the static case Yellott (J. Math. Psych. 1977, 15, 109–146) and others have demonstrated that an independent random utility model generated from the extreme value distribution exp(?e^?ax?b) becomes equivalent to Luce's Axiom. Yellott also introduced an axiom called “invariance under uniform expansions of the choice set”, and he proved that within the class of random utility models with independent identically distributed utilities (apart from a location shift) this axiom is equivalent to Luce's Axiom. These results are extended to the dynamic situation and it is shown that if the utility processes are expressed by so-called extremal processes the corresponding choice model is Markovian. A nonstationary generalization is proposed which is a substantial interest in applications where the parameters of the choice process are influenced by previous choice experience or by time-varying exogenous variables. In particular, it is demonstrated that the nonstationary model is Markovian if and only if the joint choice probabilities at two points in time have a particular form. Thus, the paper provides a rationale for applying a specific class of Markov models as the point of departure when modelling mobility processes that involve individual discrete decisions over time.     

Framing prisoners and chickens: Valence effects in the prisoner’s dilemma and the chicken game

In an experimental study, we investigated how decisions in social dilemmas are affected by the valence of outcomes that are at stake. Prospect theory states that individuals are risk-averse when outcomes are framed as gains, and risk-seeking when outcomes are framed as losses. On the basis of this framework, previous research on social dilemmas has addressed the question of whether people are more cooperative in the negative domain than in the positive domain, but this research has led to inconsistent results. A possible explanation for this is that in many social dilemmas it is unclear whether cooperation or defection is the risky choice. In the current paper, we compare the well-studied prisoner’s dilemma with the less studied chicken game. Whereas in the prisoner’s dilemma it is unclear what constitutes the risky option, in the chicken game the risky option is quite clear. Consistent with predictions, we found in the chicken game more defection in the loss frame than in the gain frame, but no difference between the gain and loss frame in the prisoner’s dilemma. Moreover, choices were predicted by risk attitude in the chicken game, but not in the prisoner’s dilemma.     

The hidden persuaders break into the tired brain

There is a long-lasting debate on whether subliminal advertising actually works. In this context there are some studies suggesting that subjects’ motivation is a crucial point. Karremans et al. [Karremans, J. C., Stroebe, W., & Claus, J. (2006). Beyond Vicary’s fantasies: The impact of subliminal priming and brand choice. Journal of Experimental Social Psychology, 42, 792-798] showed that subjects were influenced in their intention to drink a specific brand of soft drink by a subliminally presented brand prime, but only if they were thirsty. In the present study, we adapted their paradigm to the concept of ‘concentration’ and embedded the subliminal presentation of a brand logo into a computer game. Actual subsequent consumption of dextrose pills (of the presented or a not presented brand) was measured dependent on the level of participants’ tiredness and the subliminally presented logo. We found the same pattern as Karremans et al. (2006): only tired participants consumed more of the subliminally presented than the not presented brand. Therefore, the findings confirm that subjects are influenced by subliminally presented stimuli if these stimuli are need-related and if subjects are in the matching motivational state.     

On Bourbaki’s axiomatic system for set theory

In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign \(\uptau \) in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck’s proposal of adding to Bourbaki’s system the axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group.     

The profile structure for Luce's choice axiom

A geometric approach is introduced to explain phenomena that can arise with Luce's choice axiom; e.g., differences occur when determining the likelihood of a ranking by starting with the “best-first,” or “worst-first” alternative. As shown, the problem is caused by the way we compute pairwise probabilities: it forces “best-first” and “worst-first” computations to use different information from a profile. Thus agreement holds only should the different information agree: this happens only with complete indifference. An alternative “best-first” and “worst-first” comparison, which always holds, is developed. Ways to increase the applicability of the choice axiom are introduced; e.g., profiles admitted by Luce's formulation for ten alternatives have nine degrees of freedom; the approach described here allows millions of degrees of freedom. New ways to compute probabilities, which combine “best-first” and “worst-first” computations, are given: their properties are identified with a profile decomposition. A new way to compute pairwise probabilities, which eliminates all profile restrictions and problems associated with the choice axiom, is introduced; e.g., “best-first” and “worst-first” computations now agree. Three and four alternatives are emphasized for reasons of exposition, but most results extend to any number of alternatives.     

The lesson of Newcomb’s paradox

In Newcomb’s paradox you can choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to accurately deduce your choice, and uses that deduction to fill the two boxes. The way they do this guarantees that you made the wrong choice. Newcomb’s paradox is that game theory’s expected utility and dominance principles appear to provide conflicting recommendations for what you should choose. Here we show that the conflicting recommendations assume different probabilistic structures relating your choice and the algorithm’s prediction. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the probabilistic structure relating the problem’s random variables is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcomb’s paradox, the focus of much previous work, is irrelevant. We end by showing that Newcomb’s paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its ‘prediction’ after you make your choice rather than before.     

Proof and Dialogue in Aristotle

Jan ?ukasiewicz’s analysis of Aristotle’s syllogism drew attention to the nature of syllogisms as conditionals rather than premise-conclusion arguments. His further idea that syllogisms should be understood as theorems of an axiom system seems a step too far for many logicians. But there is evidence to suggest that Aristotle’s syllogism was to regularise some of the steps made in ‘dialogue games.’ This way of seeing the syllogism is explored in the framework of modern formal dialogue systems. A modern formal syllogistic game, DLSyll, is set out and analysed in use.     

Keep ‘hoping’ for rationality: a solution to the backward induction paradox

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe in a player’s rationality after updating with his irrationality.     

Second choices in a visual span of apprehension task

Four Ss were run in a visual span of apprehension experiment to determine whether second choices made following incorrect first responses are at the chance level, as implied by various high threshold models proposed for this situation. The relationships between response biases on first and second choices, and between first choice biases on trials with two or three possible responses, were also examined in terms of Luce’s (1959) choice theory. The results were: (a) second choice performance in this task appears to be determined by response bias alone, i.e., second choices were at the chance level; (b)first and second choice response biases were not related according to Luce’s choice axiom; and (c) the choice axiom predicted with reasonable accuracy the relationships between first choice response biases corresponding to trials with different numbers of possible response alternatives.     

Do infants bind mental states to agents?

Recent findings suggest that infants understand others’ preferential choice and can use the perspectives and beliefs of others to interpret their actions. The standard interpretation in the field is that infants understand preferential choice as a dispositional state of the agent. It is possible, however, that these social situations trigger the acquisition of more general, not person-specific knowledge. In a looking-time study we showed an Agent A demonstrating a choice, that only could have been interpreted as preferential based on the perspective (and thus the belief) of the agent, not the observer. Then we introduced a new agent (Agent B), who chose consistently or inconsistently with Agent A; also varying whether Agent B was an adult or a child. Results show that infants expected Agent B (both the adult and the child) to choose as Agent A, but only in the condition where according to Agent A’s knowledge two objects were present in familiarization(confirming previous evidence on the importance of contrastive choice). We interpret these results in the following way: (1) infants do not encode the perspectives of other agents as person-specific sources of knowledge and (2) they learn about the object, rather than the agent’s disposition towards that object. We propose that early theory of mind processes lack the binding of belief content to the belief holder. However, such limitation may in fact serve an important function, allowing infants to acquire information through the perspectives of others in the form of universal access to general information.     

Infinite Populations,Choice and Determinacy

This paper criticizes non-constructive uses of set theory in formal economics. The main focus is on results on preference aggregation and Arrow’s theorem for infinite electorates, but the present analysis would apply as well, e.g., to analogous results in intergenerational social choice. To separate justified and unjustified uses of infinite populations in social choice, I suggest a principle which may be called the Hildenbrand criterion and argue that results based on unrestricted axiom of choice do not meet this criterion. The technically novel part of this paper is a proposal to use a set-theoretic principle known as the axiom of determinacy (\(\mathsf {AD}\)), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of \(\mathsf {AD}\) from the point of view of the research area in question is its game-theoretic character.