A solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions. The first class consists of all convex combinations of the equal division solution and the center-of-gravity of the imputation-set value. The second class is the dual class consisting of all convex combinations of the equal division solution and the egalitarian non-separable contribution value. We provide characterizations of the two classes (...) of solutions using either population solidarity or a reduced game consistency in addition to other standard properties. (shrink)

A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on (...) variable and fixed player set. Specifications of several properties characterize specific solutions in this class. (shrink)

The aims of this paper are threefold: To show that game-playing (GP), the discipline of Artificial Intelligence (AI) concerned with the development of automated game players, has a strong epistemological relevance within both AI and the vast area of cognitive sciences. In this context games can be seen as a way of securely reducing (segmenting) real-world complexity, thus creating the laboratory environment necessary for testing the diverse types and facets of intelligence produced by computer models. This paper aims (...) to promote the belief that games represent an excellent tool for the project of computational psychology (CP). To underline how, despite this, GP has mainly adopted an engineering-inspired methodology and in doing so has distorted the framework of cognitive functionalism. Many successes (i.e. chess, checkers) have been achieved refusing human-like reasoning. The AI has appeared to work well despite ignoring an intrinsic motivation, that of creating an explanatory link between machines and mind. To assert that substantial improvements in GP may be obtained in the future only by renewed interest in human-inspired models of reasoning and in other cognitive studies. In fact, if we increase the complexity of games (from NP-Completeness to AI-Completeness) in order to reproduce real-life problems, computer science techniques enter an impasse. Many of AI’s recent GP experiences can be shown to validate this. The lack of consistent philosophical foundations for cognitive AI and the minimal philosophical commitment of AI investigation are two of the major reasons that play an important role in explaining why CP has been overlooked. (shrink)

Research suggests that institutions affect the levels of corruption in a country. We take these arguments a step further and examine whether it is the presence of inclusive institutions and/or the credible and consistent implementation of institutions that matter, as regards corruption. We use a novel approach to theoretically conceptualise and empirically operationalise institutions along two analytically distinct dimensions: the nature of the institutions (the de jure dimension), and the extent to which they are credibly and consistently implemented over time (...) (the de facto dimension), using a panel dataset for 148 countries covering 2012 to 2018. We find that formal institutions are most effective in reducing corruption when the rules are credibly and consistently implemented. Furthermore, this effect appears to operate differently at different levels of national income. The nature of the formal institutions appears important across income levels, but particularly so at the upper middle income level, while the credible and consistent implementation of these institutions is primarily influential at upper middle income levels. We explain why this may be the case and elaborate on the policy implications. (shrink)

The authors show. by means of a finitary version $\square_{\lambda D}^{fin}$ of the combinatorial principle $\square_\lambda^{h*}$ of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal A. if Mi and Ni are elementarily equivalent models of a language of size $\leq \lambda$ , then the second player has a winning strategy in the Ehrenfeucht- $Fra\uml{i}ss\acute{e}$ game of length $\lambda^{+}$ on $\pi_{i} M_{i}/D$ and (...) $\pi_{i} N_{i}/D$ . If in addition $2^{\lambda} = \labda^{+}$ and i < $\lambda$ implies | $M_{i}$ | +| $N_{i}$ | $\leq$ \lambda^{+} this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2]. (shrink)

The authors show, by means of a finitary version □finλ, D of the combinatorial principle □b*λ of [7], the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size ≤ λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ∏i Mi/D and ∏i Ni/D. (...) If in addition 2λ=λ+ and i <λ implies |Mi|+|Ni|≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2]. (shrink)

In spectrum sharing cognitive radio networks, unauthorized users are allowed to use the spectrum of authorized users to improve spectrum utilization. Due to limited spectrum resources, how to formulate a reasonable spectrum allocation scheme is very important. As a mathematical analysis tool, game theory can solve the problem of resource allocation well. In recent years, it has been applied to the research of resource allocation in spectrum sharing networks by some literatures. In a cellular network consisting of multiple cellular (...) users and full-duplex end-to-end communication users D2D, the self-interference caused by full-duplex communication and the interference caused by the D2D users to the cellular users will significantly reduce system throughput. In order to reduce the interference in the network, this paper introduces a power control algorithm based on Stackelberg game, which sets the cellular users and D2D users as the leaders and followers, respectively. The cellular users and the D2D users compete with each other to minimize the cost, and we propose new utility functions. We build an optimization problem under the outage probability constraint and power constraint and the transmission power of the users is obtained by using the Lagrangian dual decomposition method. The simulation results show that the proposed game algorithm improves network performance compared with other existing schemes. (shrink)

Using an idea of Sargsyan, we show how to reduce the consistency strength of the assumptions employed to establish a theorem concerning a uniform level of indestructibility for both strong and supercompact cardinals.

In the framework of transferable utility games, we modify the 2-person Davis–Maschler reduced game to ensure non-emptiness of the imputation set of the adapted 2-person reduced game. Based on the modification, we propose two new axioms: reduced game monotonicity and reduced dominance. Using RGM, RD, NE, Covariance under strategic equivalence, Equal treatment property and Pareto optimality, we are able to characterize the kernel.

The mathematical tools of game theory are frequently used in the social sciences and economic consultancy. But how do they explain social phenomena and support prescriptive judgments? And is the use of game theory really necessary? I analyze the logical form of explanatory and prescriptive game theoretical statements, and argue for two claims: (1) explanatory game theory can and should be reduced to rational choice theory in all cases; and (2) prescriptive game theory gives (...) bad advice in some cases, is reducible to rational choice theory in other cases, while it makes no sense in yet other cases. (shrink)

There are many social psychological theories regarding the nature of prejudice, but only one major theory of prejudice reduction: under the right circumstances, prejudice between groups will be reduced with increased contact. On the one hand, the contact hypothesis has a range of empirical support and has been a major force in social change. On the other hand, there are practical and ethical obstacles to any large-scale controlled test of the hypothesis in which relevant variables can be manipulated. Here (...) we construct a spatialized model that tests the core hypothesis in a large array of game-theoretic agents. Robust results offer a new kind of support for the contact hypothesis: results in simulation do accord with a hypothesis of reduced prejudice with increased contact. The spatialized game-theoretic model also suggests a deeper explanation for at least some of the social psychological phenomena at issue. (shrink)

Consistency and optimality together with converse consistency provide an illuminating and novel characterization of the equilibrium concept (Peleg and Tijs, 1996). But (together with non-emptiness) they preclude refinements of the equilibrium notion and selection of a unique equilibrium (Norde et al., 1996). We suggest two escape routes: By generalizing the concept of strict equilibrium we question the practical relevance of the existence requirement for refinements. To allow for equilibrium selection we suggest more complex reduced games which capture (...) the inclinations of ``players who already left''. (shrink)

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he (...) concedes a contradictory set of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

The need for cognitive closure is a construct postulated by Kruglanski that explains the motivational aspects which influence decision-making and its impact on the social environment. Initially, it was assessed through a unidimensional scale, later criticized for its poor satisfactory reliability and validity. Regarding these criticisms, Pierro and Kruglanski developed a new 14-item scale to measure two dimensions, which were not previously evaluated: urgency tendency and permanence tendency. Although the Revised Test of Need for Cognitive Closure is more economical in (...) terms of assessment time, it would be optimal to develop a reduced test that can assess faster while maintaining validity and reliability. The present research aims to reduce the Revised Test of Need for Cognitive Closure scale to the Argentinian context. To this end, we worked on a non-experimental design, assessing this scale within a sample of 690 Argentinian university students, and proceeded to perform reliability, as well as confirmatory factor analysis, convergent validity, and factorial invariance analysis. The results indicate a bi-factorial structure of a Need for Cognitive Closure instrument with eight items and two dimensions: urgency tendency and permanence tendency, suggesting good reliability in both of them. In addition, well convergent validity was checked with other validated instruments, and finally, the factor loadings were shown to be invariant. In conclusion, it was demonstrated the reliability and validity of reducing the Revised Test of Need for Cognitive Closure in our social environment. (shrink)

Twenty-two experienced action video-game players (AVGPs) and 18 non-VGPs were tested on a pen-and-paper line bisection task that was untimed. Typically, right-handers bisect lines 2 % to the left of true centre, a bias thought to reflect the dominance of the right-hemisphere for visuospatial attention. Expertise may affect this bias, with expert musicians showing no bias in line bisection performance. Our results show that experienced-AVGPs also bisect lines with no bias with their right hand and a significantly reduced (...) bias with their left hand compared to non-AVGPs. Bisections by experienced-AVGPs were also more precise than those of non-AVGPs. These findings show the cognitive proficiencies of experienced-AVGPs can generalize beyond computer based tasks, which resemble their training environment. (shrink)

Contents. Introduction. 1. Preliminaries. 2. Normal Form Games. 3. Extensive Games. 4. Applications of Game Theory. 5. The Methodology of Game Theory. Conclusion. Appendix. Bibliography. Index. Does game theory—the mathematical theory of strategic interaction—provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory—the first monograph on the philosophy of game theory—is an attempt to combine insights from epistemic logic (...) and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. I prove new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and explore in detail the logical form of game theory as it is used in explanatory and normative contexts. I argue that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, I argue, has been rather successful in achieving this aim. "The 'epistemic' approach to game theory has emerged over the past twenty-five years. What is this approach? How does it differ from the conventional equilibrium-based approach to game theory? What have been its strengths and weaknesses to date? To find out, read this comprehensive and excellently written account". Adam Brandenburger, J. P. Valles Professor of Business Economics and Strategy, Stern School of Business, New York University "Reading Boudewijn de Bruin's book should be rewarding both for game theorists interested in the conceptual foundations of their discipline and for philosophers who want to learn more about formal analysis of strategic interaction. It provides an in-depth logical study of the currently dominant epistemic approaches to non-cooperative games, with an eye both to the attractions and to the serious challenges facing the Epistemic Programme". Wlodek Rabinowicz, Professor of Practical Philosophy, Department of Philosophy, Lund University . (shrink)

John Maynard Smith was the founder of evolutionary game theory. He has also been the major influence on the direction of this field, which now pervades behavioural ecology and evolutionary biology. In its original formulation the theory had three components: a set of strategies, a payoff structure, and a concept of evolutionary stability. These three key components are still the basis of the theory, but what is assumed about each component is often different to the original assumptions. We review (...) modern approaches to these components. We emphasis that if a game is considered in isolation, and arbitrary payoffs are assumed, then the payoffs may not be consistent with other components of the system which are not modelled. Modelling the whole system, including not only the focal game, but also the future behaviour of the players and the behaviour of other population members, allows a consistent model to be constructed. We illustrate this in the case of two models of parental care, showing how linking a focal game to other aspects of the system alters what is predicted. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in (...) general the game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.

We study the equilibrium behavior of informed traders interacting with market scoring rule (MSR) market makers. One attractive feature of MSR is that it is myopically incentive compatible: it is optimal for traders to report their true beliefs about the likelihood of an event outcome provided that they ignore the impact of their reports on the profit they might garner from future trades. In this paper, we analyze non-myopic strategies and examine what information structures lead to truthful betting by traders. (...) Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a dynamic game. We consider finite-stage and infinite-stage game models. For each model, we study the logarithmic market scoring rule (LMSR) with two different information structures: conditionally independent signals and (unconditionally) independent signals. In the finite-stage model, when signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE). Moreover, it is the unique Weak Perfect Bayesian Equilibrium (WPBE) of the game. In contrast, when signals of traders are unconditionally independent, truthful betting is not a WPBE. In the infinite-stage model with unconditionally independent signals, there does not exist an equilibrium in which all information is revealed in a finite amount of time. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any WPBE for.. (shrink)

Background Retraction is a mechanism for alerting readers to unreliable material and other problems in the published scientific and scholarly record. Retracted publications generally remain visible and searchable, but the intention of retraction is to mark them as “removed” from the citable record of scholarship. However, in practice, some retracted articles continue to be treated by researchers and the public as valid content as they are often unaware of the retraction. Research over the past decade has identified a number of (...) factors contributing to the unintentional spread of retracted research. The goal of the Reducing the Inadvertent Spread of Retracted Science: Shaping a Research and Implementation Agenda (RISRS) project was to develop an actionable agenda for reducing the inadvertent spread of retracted science. This included identifying how retraction status could be more thoroughly disseminated, and determining what actions are feasible and relevant for particular stakeholders who play a role in the distribution of knowledge. -/- Methods These recommendations were developed as part of a year-long process that included a scoping review of empirical literature and successive rounds of stakeholder consultation, culminating in a three-part online workshop that brought together a diverse body of 65 stakeholders in October–November 2020 to engage in collaborative problem solving and dialogue. Stakeholders held roles such as publishers, editors, researchers, librarians, standards developers, funding program officers, and technologists and worked for institutions such as universities, governmental agencies, funding organizations, publishing houses, libraries, standards organizations, and technology providers. Workshop discussions were seeded by materials derived from stakeholder interviews (N = 47) and short original discussion pieces contributed by stakeholders. The online workshop resulted in a set of recommendations to address the complexities of retracted research throughout the scholarly communications ecosystem. -/- Results The RISRS recommendations are: (1) Develop a systematic cross-industry approach to ensure the public availability of consistent, standardized, interoperable, and timely information about retractions; (2) Recommend a taxonomy of retraction categories/classifications and corresponding retraction metadata that can be adopted by all stakeholders; (3) Develop best practices for coordinating the retraction process to enable timely, fair, unbiased outcomes; and (4) Educate stakeholders about pre- and post-publication stewardship, including retraction and correction of the scholarly record. -/- Conclusions Our stakeholder engagement study led to 4 recommendations to address inadvertent citation of retracted research, and formation of a working group to develop the Communication of Retractions, Removals, and Expressions of Concern (CORREC) Recommended Practice. Further work will be needed to determine how well retractions are currently documented, how retraction of code and datasets impacts related publications, and to identify if retraction metadata (fails to) propagate. Outcomes of all this work should lead to ensuring retracted papers are never cited without awareness of the retraction, and that, in public fora outside of science, retracted papers are not treated as valid scientific outputs. (shrink)

In its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player's decision problem, a solution valid for all real-world instantiations, regardless of context. "Permissiveness" would constrain the theory to designate as admissible for a player any conjecture consistent with the function's designation of admissible strategies for the other players. Given (...) permissiveness and other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between [math] principles over [math]-models of [math]. They also introduced a version of this game that similarly captures provability over [math]. We generalize and extend this game-theoretic framework to other formal systems, and establish a certain compactness result that shows that if an implication (...) [math] between two principles holds, then there exists a winning strategy that achieves victory in a number of moves bounded by a number independent of the specific run of the game. This compactness result generalizes an old proof-theoretic fact noted by H. Wang (1981), and has applications to the reverse mathematics of combinatorial principles. We also demonstrate how this framework leads to a new kind of analysis of the logical strength of mathematical problems that refines both that of reverse mathematics and that of computability-theoretic notions such as Weihrauch reducibility, allowing for a kind of fine-structural comparison between [math] principles that has both computability-theoretic and proof-theoretic aspects, and can help us distinguish between these, for example by showing that a certain use of a principle in a proof is “purely proof-theoretic”, as opposed to relying on its computability-theoretic strength. We give examples of this analysis to a number of principles at the level of [math], uncovering new differences between their logical strengths. (shrink)

A philosophical theory of explanation should provide solutions to a series of problems, both descriptive and normative. The aim of this essay is to establish the claim that this can be best done if one theorizes in terms of explanatory games rather than focusing on the explication of the concept of explanation. The position that is adopted is that of an explanatory pluralism and it is elaborated in terms of the rules that incorporate the normative standards that guide the processes (...) of discovery and justification of explanations as well as the modes of their communication, dissemination, and adoption. They constitute the rules of the explanatory game that the participants are playing. The philosophical project consists in describing and normatively appraising the rules that constitute these games. (shrink)

The present study consists of a cross-cultural analysis of the role of irony in the Blue Cliff Record. The analysis is structured in four chapters, one devoted to methodological concerns and three to equivalent types and functions of irony within the text, a pivotal literary work of the Chan Buddhist tradition. In relation to Chan studies, a discussion of irony is particularly important since the wide corpus of Chan literature includes a significant number and a consistent variety of ironic features (...) such as puns, wordplay, extravagant acts, and so forth. The idea of the present paper is that the ironic temperament of Chan is not a contingent circumstance, but a functional strategy purposely employed in textual compositions and oral communication with soteriological purposes. (shrink)

This text is the result of academic research aimed at achieve the goal of finding viable ways to reduce social inequalities in the Brazilian context through the education. Our main focus was the pursuit of reducing violence through education and the ways in which education can promote development and security human in general. In order to achieve this goal with clarity and consistency, I address theoretical and practical issues. The part theory clarifies the essential concepts and establishes the background (...) for the rest of the work. The practical part is a application of these concepts in the Brazilian educational scenario / Este texto é o resultado de uma pesquisa acadêmica que visa atingir o objetivo de encontrar formas viáveis para reduzir as desigualdades sociais no contexto brasileiro por meio da educação. Nosso foco principal foi a busca da redução da violência por intermédio da educação e as maneiras pelas quais a educação pode promover o desenvolvimento e a segurança humana no geral. Para alcançar essa meta com clareza e consistência, abordo questões de cunho teórico e prático. A parte teórica esclarece os conceitos essenciais e estabelece o pano de fundo para o restante do trabalho. A parte prática é uma aplicação desses conceitos no cenário educacional brasileiro. (shrink)

Industrial development in recent decades has led to using information and communication technologies to support personnel selection processes. One of the most notable examples is game-related assessments, supposedly as accurate as conventional tests but which generate better applicant reactions and reduce the likelihood of adverse impact and faking. However, such claims still lack scientific support. Given practitioners’ increasing use of GRA, this article reviews the scientific literature on gamification applied to personnel selection to determine whether the current state of (...) the art supports their use in professional practice and identify specific aspects on which future research should focus. Following the PRISMA model, a search was carried out in the Web of Science and Scopus databases, identifying 34 valid articles, of which 85.3% are empirical studies that analyze five areas: validity; applicant reactions; design of GRA; personal characteristics and GRA; and adverse impact and faking. Together, these studies show that GRA can be used in personnel selection but that the supposed advantages of GRA over conventional tests are fewer than imagined. The results also suggest several aspects on which research should focus, which could help define the situations in which the use of GRA may be recommended. (shrink)

Minimal adversariality consists in the opposition of contradictory conclusions in argumentation, and its usual metaphorical expression as a game between combating arguers has seen it be criticized from a number of perspectives: the language used, whether cooperation best attains the argumentative telos of epistemic betterment, and the ideal nature of the metaphor itself. This paper explores primarily the idealization of deductive argumentation, which is problematic due to its attenuated applicability to a dialectic involving premises and justificatory biases that are (...) left hidden and unelucidated. To clarify the issue and offer up a solution, we consider minimal adversariality as an involuntary state of affairs before relating this interpretation to a link between rational persuasion and the attainment of epistemic betterment. Through this we see how the idealizing tendencies of minimal adversariality can be reduced even in argumentation involving premises whose justifications for any arguer are inaccessible to any other arguer. (shrink)

By studying the logic that unites play, the rules of games and the body of players, this article intends to highlight a spatial mimesis through play and games. It consists of carrying out a Ricœurian anthropology of play and game, taking Ricœur's analysis of the relationship between time and narrative as a model. The article then shows that play prefigures the physical space as a lived space, that game configures a space of rules and that the player's body (...) is refigured by the spatiality of the rules of the game. This application of the ternary model of Ricœurian mimesis thus allows a unified understanding of play and games by space, and of space by play and games. (shrink)

The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of Yale University, (...) called the ALL Project (Accelerated Learning of Logic). Following the introduction, the game of VALIDITY is described, first with reference to the propositional calculus, and then in connection with the first-order predicate calculus with identity. Sections in the text are devoted to discussions of the various rules of derivation employed in both calculi. Three appendices follow the main text; these provide a catalogue of sequents and theorems that have been proved for the propositional calculus and for the predicate calculus, and include suggestions for the classroom use of VALIDITY in university-level courses in mathematical logic. (shrink)

Formal analyses of Pascal’s Wager have almost all been decision-theoretic, with a human as the sole decision-maker. This paper analyses Pascal’s Wager in a game-theoretic setting in which the deity whose existence the human is considering wagering on is also a decision-maker. There is an equilibrium in which the human chooses to wager that the deity exists and Pascal’s Wager thus operates, but also one in which the human does not wager. Thus, in a game-theoretic setting, Pascal’s Wager (...) is indeterminate: wagering and not wagering are both consistent with equilibrium behaviour. (shrink)

We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = R$ and (...) the Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this. We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω^2 with payoff in $R^R\Pi _1^1$ or with σ-projective payoff. (shrink)

We propose a solution concept for games that are played among players with present-biased preferences that are possibly naive about their own, or about their opponent’s future time inconsistency. Our perception-perfect outcome essentially requires each player to take an action consistent with the subgame perfect equilibrium, given her perceptions concerning future types, and under the assumption that other present and future players have the same perceptions. Applications include a common pool problem and Rubinstein bargaining. When players are naive about their (...) own time inconsistency and sophisticated about their opponent’s, the common pool problem is exacerbated, and Rubinstein bargaining breaks down completely. (shrink)

Emotional stimuli are consistently better remembered than neutral stimuli. However, the reported effects of emotional stimuli on source memory are less consistent. In four experiments, we examined spatial and temporal source memory and free recall for emotional words previously studied in an fMRI experiment. In the fMRI experiment, the unpleasant but not the pleasant words were shown to activate the amygdala. In the experiments reported here, spatial and temporal source memory were reduced for the unpleasant words compared to pleasant (...) and neutral words. Reduced spatial memory for unpleasant words was observed across studies that varied the specific stimuli, task conditions, and incidental versus intentional encoding instructions. Free recall was enhanced for the pleasant and unpleasant words compared to neutral words. The results demonstrate reduced source memory for unpleasant words even when item recall is enhanced. Our findings are consistent with prior reports of amygdala-mediated amnestic effects evoked by unpleasant stimuli. (shrink)

Working under large cardinal assumptions such as supercompactness, we study the Borel reducibility between equivalence relations modulo restrictions of the nonstationary ideal on some fixed cardinal κ. We show the consistency of Eλ-clubλ++,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλλ++ in the space λ++, being continuously reducible to Eλ+-club2,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλ+λ++ in the space 2λ++. Then we show that for κ ineffable Ereg2,κ, the relation of equivalence (...) modulo the nonstationary ideal restricted to regular cardinals in the space 2κ is Σ11-complete. We finish by showing that, for Π21-indescribable κ, the isomorphism relation between dense linear orders of cardinality κ is Σ11-complete. (shrink)

Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It is shown that the same mathematical tool, namely modal logic, can be used to explicitly model both views.

Solomon’s article and Binmore’s response exemplify a standard exchange between the game theorist and those critical of applying game theory to ethics. The critic of game theory lists a number of problems with game theory and the game theorist responds by arguing that the critic’s objections are based on a misrepresentation of the theory. Binmore claims that the game theorist is in the position of the innocent man who, when asked why he beats his (...) wife, must explain that he doesn’t beat his wife at all (Binmore, 2). However, even if we agree that the denial is true, we might still like to know why, if you are not beating your wife, do others consistently accuse you of doing so? Or, to get away from this rather sexist metaphor, why are critics of game theory like Solomon (according to game theorists) consistently getting game theory wrong?While, as I argue in the first section, critics of game theory such as Solomon may misrepresent game theory, this misrepresentation is not entirely their own fault. The way in which game theory is traditionally presented is misleading. For example, students are usually first introduced to game theory through the prisoner’s dilemma. It is compelling drama, but lousy PR for the use of ethics in game theory. (You want to know what to do? Let’s see how two thieves reason.) However, while Binmore is right to argue that game theory neither assumes nor entails the theory of human nature that Solomon finds objectionable, Solomon is also right to argue that game theory is promulgated and applied with what appear to be a robust set of assumptions about human motivation. I argue in the second section, however, that in fact neither these applications of game theory, nor game theory itself, is committed to a particular theory of human motivation. Thus, while game theory is not able to provide a complete ethical theory (assuming that a theory of human motivation is essential to such a theory), it is not contrary to ethics. In the final section I note that Aristotle, rather than being the alternative to using game theory in business ethics, as Solomon suggests, actually points the way to an ethical theory that can combine a discussion of both game theory and “those nagging and controversial questions about what it is that people do and ought to care about” (Solomon, 7). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Game ChangeMaximo CortezOn November 17, 1983, I was born with a condition called mixed gonadal dysgenesis, and ambiguous genitalia. My gender was not of a big concern at that time. The more urgent matter was that I had a heart murmur, which was repaired when I was twelve months old. [End Page E5]It was not until I turned five, and by issue of the Texas Children’s Protective Services (...) (CPS), that my mother was forced to authorize providers to perform normalization surgeries on me. An anonymous caller tipped the CPS that my mother was raising a boy as a girl. The state intervened and explained to my mother that she would have to consent to these surgeries or else she would lose custody of me. This included a gonadectomy and a clitorectomy. Without any consent, these surgeries were performed “in my best interests.” My mother was an epileptic, Hispanic, Mormon, single parent.I was raised to be a socially acceptable female, though as early as five, I played with “boy” toys and enjoyed TV programs aimed at male youth, like Teenage Mutant Ninja Turtles. It was not until I had those normalization surgeries performed on me that I felt different. I knew that something major had happened to me. I woke up in a hospital bed in a gown. I raised the covers and noticed that I had an “X” carved in my groin area. Doctors mutilated my clitoris by reducing its size, which made me feel alienated and angry that something was wrong with my body.I had a surgery performed on me that was to be kept secret and never talked about. This sense of fear and shame was instilled in me shortly after the surgery. I do not recall any psychological evaluations or counseling to help me cope with such surgeries. Seeing everyone else my age going through puberty during my teenage years, I felt behind. I wasn’t becoming a boy with a deep voice or facial hair. Instead, I visited the doctor’s office with my mom and was told that I would be taking oral estrogen to become a woman. I wasn’t until that moment that I understood I was seeing a doctor to foster the development of female secondary characteristics. I felt betrayed by the medical community and by my own mother.Just a few years later, I saw a urologist to find out whether I was ready for a vaginal construction surgery (vaginoplasty). Thankfully the urologist suggested that I was not ready to move forward with an invasive and irreversible vaginal construction surgery. I never pursued it as an adult, as I have always felt male gendered.Social sexual relationships have always been difficult for me but more so with my attraction to women. I first realized my attraction to women in early middle school. Being raised Mexican and a Mormon and knowing that I was homosexual created a lot of conflict for me. I felt that I was a male–gendered person forced into a castrated, mutilated, and medically created female body. I suffered through depression from an early age and it continues today. My conservative Mormon upbringing brought me much shame. The Mormon religion, as most people understand it, expresses a great intolerance to homosexuals and transgender people. I felt like I was a heterosexual male in a female’s body, but the Mormons would never accept me.My later teenage years and mid–twenties were a dark time in my life. I even attempted suicide in my early twenties. My depression was treated with antidepressants and talk therapy. Once I began testosterone, I gradually stopped taking antidepressants. When I was only on estrogen, I felt very moody, angry, and in an emotional funk. I would cry easily and would become very irritable and emotional without cause. With testosterone therapy, I began to think more clearly, had balanced emotions, and began to think more logically.I began to research intersex online and found a women’s androgen insensitivity (AIS) support group. At one of their national conferences, I met another intersex individual who was raised as a female and who had transitioned to male. Like me... (shrink)