In a seminal paper, Aumann (1987, Econometrica 55, 1–18) showed how the choices of rational players could be analyzed in a unified state space framework. His innovation was to include the choices of the players in the description of the states, thus abolishing Savage’s (1954, The Foundations of Statistics. Wiley, New York) distinction between acts and consequences. But this simplification comes at a price: Aumann’s notion of Bayes rationality does not allow players to evaluate what would happen were they to (...) deviate from their actual choices. We show how the addition of a causal structure to the framework enables us to analyze such counterfactual statements, and use it to introduce a notion of causal rationality. Under a plausible causal independence condition, the two notions are shown to be equivalent. If we are prepared to accept this condition we can dispense with the causal apparatus and retain Aumann’s original framework. (shrink)

From an archaeological point of view, the recognition between religious and gaming activities is very uneasy. This is true also for the so-called Minoan pierres à cupules (or Minoan kernoi or “stone slabs with depressions”) whose most impressive specimen is surely the well known table à offrandes found in the Minoan palace at Mallia. After the most recent works on the subject (by H. Whittaker and N. Hillbom), the interpretation of the pierres à cupules as game board is now (...) prevailing; however, their possible religious function can not be disregarded. The paper aims to check the methodological problems involved in the study of these pierres, starting from the available archaeological evidence. (shrink)

How does a board of directors decide what is right? The contest over this question is frequently framed as a debate between shareholder value and stakeholder rights, between a utilitarian view of the ethics of corporate governance and a deontological one. This paper uses a case study with special circumstances that allow us to examine in an unusually clear way the conflict between shareholder value and other bases on which a board can act. In the autumn of 2010, (...) the board of Liverpool Football Club sold the company to another investing group against the explicit wishes of the owners. The peculiar circumstances of this case provide insight into the conflict between ethical approaches to board decisions, allowing us to see certain issues more clearly than we can in listed corporations with many shareholders. What the analysis suggests is that the board saw more than one type of utility on which to base its ethical decision, and that one version resonated with perceived duties to stakeholders. This alignment of outcomes of strategic value with duties contrasted with the utility of shareholder value. While there are reasons to be cautious in generalizing, the case further suggests reasons why boards may reject shareholder value, in opposition to mainstream notions of corporate governance, without rejecting utility as a base of their decisions. Further, the partial alignment of duty and utility facilitates a pragmatic decision rather than one based on a priori claims. (shrink)

How does a board of directors decide what is right? The contest over this question is frequently framed as a debate between shareholder value and stakeholder rights, between a utilitarian view of the ethics of corporate governance and a deontological one. This paper uses a case study with special circumstances that allows us to examine in an unusually clear way the conflict between shareholder value and other bases on which a board can act. In the autumn of 2010, (...) the board of Liverpool Football Club sold the company to another investing group against the explicit wishes of the owners. The peculiar circumstances of this case provide insight into the conflict between ethical approaches to board decisions, allowing us to see certain issues more clearly than we can in listed corporations with many shareholders. What the analysis suggests is that the board saw more than one type of utility on which to base its ethical decision, and that one version resonated with perceived duties to stakeholders. This alignment of outcomes of strategic value with duties contrasted with the utility of shareholder value. While there are reasons to be cautious in generalizing, the case further suggests reasons why boards may reject shareholder value, in opposition to mainstream notions of corporate governance, without rejecting utility as a base of their decisions. Further, the partial alignment of duty and utility facilitates a pragmatic decision rather than one based on a priori claims. (shrink)

Toward the end of Light in August, in the climactic scene in Chapter 1 where the authorities of justice pursue the elusive Joe Christmas through the streets of Jefferson, William Faulkner introduces a new character, Percy Grimm, a twenty-five-year-old captain in the State National Guard who has relentlessly acquired the rank of a special deputy for the search. As the town closes for the weekend, Grimm keeps vigil at a downtown store where other townsfolk have begun a poker game to (...) stay awake through the night as the search goes on. In their zeal to uphold law and justice, his men revel in their fantastic make-believe that they are doing the work of “a hidden and unsleeping and omnipotent eye watching the doings of men.” The poker game goes on through Saturday night until Christmas is spotted and given chase. As Grimm runs through the streets after the fleeing man, Faulkner presents to us the deputy's stream of thought from an omniscient point of view: “There was nothing vengeful about him either, no fury, no outrage. He was moving again almost before he had stopped, with that lean, swift, blind obedience to whatever Player moved him on the Board” (437). Through the rest of the chapter, Grimm, who has not participated in the poker game at all, thinks and acts as if he is engaged in a chess game, not as a player but as the stake or the pawn in a board game in which Jefferson is the board on which he and Christmas are being moved from place to place by two larger forces, he by the benevolent Providence and Christmas by the powers opposed to God. Finally, when Christmas is cornered and fatally shot in Reverend Hightower's kitchen, this fantasized game seems to end. (shrink)

This paper examines how board gender diversity affects corporate risk disclosure. We exploit an exogenous shock on firms’ risk environment created by the United Kingdom’s vote to leave the European Union and analyze related risk disclosure in annual reports of public firms in the UK. Using this unique setting, we mitigate concerns about omitted variables in concurrent studies. The findings suggest that board gender diversity is positively related to corporate risk disclosure. However, our results also indicate that the (...) proportion of female directors needs to reach a critical mass to impact the risk disclosure decision. Moreover, we find lower bid–ask spreads immediately after the referendum date for those firms that disclosed Brexit-related risks in their annual reports prior to the vote. Collectively, our results are consistent with board gender diversity promoting the disclosure of decision-relevant information through improved board group dynamics. (shrink)

Since the announcement and establishment of the Oversight Board (OB) by the technology company Meta as an independent institution reviewing Facebook and Instagram’s content moderation decisions, the OB has been subjected to scholarly scrutiny ranging from praise to criticism. However, there is currently no overarching framework for understanding the OB’s various strengths and weaknesses. Consequently, this article analyses, organises, and supplements academic literature, news articles, and Meta and OB documents to understand the OB’s strengths and weaknesses and how it (...) can be improved. Significant strengths include its ability to enhance the transparency of content moderation decisions and processes, to effect reform indirectly through policy recommendations, and its assertiveness in interpreting its jurisdiction and overruling Meta. Significant weaknesses include its limited jurisdiction, limited impact, Meta’s control over the OB’s precedent, and its lack of diversity. The analysis of a recent OB case in Ethiopia shows these strengths and weaknesses in practice. The OB’s relationship with Meta and governments will lead to challenges and opportunities shaping its future development. Reforms to the OB should improve the OB’s control over its precedent, apply OB precedent to currently disputed cases, and clarify the standards for invoking OB precedent. Finally, these reforms provide the foundation for an additional improvement to address the OB’s institutional weaknesses, by involving users in determining whether the OB’s precedent should be applied to decide current content moderation disputes. (shrink)

This is the first volume to apply insights from the material turn in philosophy to the study of play and games. At a time of renewed interest in analogue gaming, as scholars are looking beyond the digital and virtual for the first time since the inception of game studies in the 1990s, Material Game Studies not only supports the importance of the turn to the analogue, but proposes a materiality of play more broadly. Recognizing the entanglement of physical materiality (...) with cultural meaning, the authors in this volume apply a range of theoretical approaches, from material eco-criticism to animal studies, to examine games and play as existing within worlds of matter. Different chapters focus on the material properties of board, card and role-playing games, how they are designed and made, how they are touched and played with, and how they connect with other human and nonhuman things. Bringing together international scholars, Material Game Studies defines a new field of material game studies and demonstrates how it is a valuable addition to wider debates about the material turn and the place of embodied humans in a material world. (shrink)

This paper examines the varied cultural meanings of computer game play in competitive and professional computer gaming and live-streaming. To do so it riffs off Andrew Feenberg’s 1994 work exploring the changing meanings of the ancient board game of Go in mid-century Japan. We argue that whereas Go saw a de-aestheticization with the growth of newspaper reporting and a new breed of ‘westernized’ player, the rise of professionalized computer gameplay has upset this trend, causing a re-aestheticization of professional game (...) competition as a result of the many informal elements that contribute to the successes, and public perceptions, of professional players. In doing so we open up the consideration of the aesthetics of broadcasted gameplay, how they reflect back upon the players and the game, and locate this shift historically and culturally within the last two decades of computer games as a creative industry, entertainment industry, a media form, and as an embodied practice. (shrink)

The aim of this paper is to give an interpretation of the free and harmonious play of faculties. The dominant interpretations focus on how the imagination is free from the determination of understanding, but say little about the harmony that can exist between imagination and understanding; thus, in this paper an attempt is made to account for the free and harmonious relationship between these two faculties. Some of Kant’s lectures are reviewed to show the inclinations of the power of imagination (...) and understanding, respectively. As the power of imagination is inclined towards making many representations, understanding is necessary to truncate the multitudes of those representations, so that unity of the representation is achievable. Taking inspiration from the traditional board game of Go, it is possible to draw an interpretation of the play of faculties that takes into consideration both the freedom and the harmony that is present within the play. (shrink)

Non-determined game logic is the logic of two player board games where the game may end in a draw: unlike the case with determined games, a loss of one player does not necessarily constitute of a win of the other player. A calculus for non-determined game logic is given in [4] and shown to be complete. The calculus adds a new rule for the treatment of greatest fixpoints, and a new unfolding axiom for iterations of the universal (...) player. The technique of the completeness proof is inspired by the canonical model construction for propositional dynamic logic (PDL). In this paper, this is extended to the logic of determined games. It is proved that the calculus for nondetermined game logic, together with the axiom of determinacy, is complete for determined game logic. Next, it is shown that the axioms and rules of the new calculus can all be derived from the calculus proposed by Parikh in [5], for which the completeness was still open. This proves Parikh’s conjecture that his calculus is complete for determined games. (shrink)

Universal Game Theory - The theory that all of life is a game played by consciousness’es, (Living Beings). The board is a dream like structure of the universe. The progression is through an active process of intent witnessing, and passive meditation. Which releases the tension in the nerves of the body and leads to selfless actions, moral goodness, and eventually the finish, Enlightenment. Just like a wounded creature only cares about it’s own self. Man in tensionthrough self-centered thought only (...) thinks about his own predicaments. Even if he is thinking about others it is only through his own objectionable view from his false-created center. The enemy or deterrents in the game is the conditioning created by society for ambition, greed, control and general brain washing to give theindividual a false sense of identity, the ego. This is achieved by Religion; tradition, culture, education, reasoning, linear thought, and the creation of time. Leaving him/her in constant anxiety about millions of future contingencies. Through witnessing one realizes the whole futility of one dimensional thought which only leads to more and more thought. Simple or constructed elaborately, thought being time, a human construction. The final step of the Universal Game Theory is understanding the whole process of thought and the eventual revelation of Enlightenment, Bliss, ecstasy. Which the person then understands that he/she is the creator of the life/dream with which they are in. That point being a sexual ecstasy similar to what happens in death to men. i.e. Human males release semenwhen they die, having a sexual ecstasy at their last breath. (shrink)

Alongside the direct parallels and contrasts between traditional narrative fiction and games, there lie certain partial analogies that provide their own insights. This article begins by examining a direct parallel between narrative fiction and games—the role of fictional reliefs and reality checks in shaping aesthetic engagement—before arguing that from this a partial analogy can be developed stemming from a feature that distinguishes most games from most traditional fictions: the presence of rules. The relation between rules and fiction (...) in games has heretofore been acknowledged but not examined in detail, giving an impression of a tension that is constant. However, the paired concepts of formal reliefs and representation checks, once introduced, allow us to explain how rules and fiction interact to alter the ways in which players engage with games in a dynamic but limited way. (shrink)

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of game terms to a certain (...) ‘minimal canonical form’, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities. (shrink)

David Hume’s Treatise on Human Nature famously fell `deadborn from the press’ because it was too far ahead of its time. Basu’s book is one of a number published in recent years that suggest we are at last ready to put its precepts into action.1 Modern game theory provides a framework that makes Hume’s insights genuinely applicable, and I totally agree with Basu that this is not only the right way forward, but that it now looks increasingly likely that this (...) is the road that wil actualy be folowed ± not only in political economy, but across the board in the social sciences. (shrink)

The formal study of both astronomy and astrology in later medieval Europe was firmly based in the universities. Instruction in astrology is attested by the presence of an educational board game, known as the ludus astronomorum, in several university-related miscellanies of fifteenth-century English provenance. William Fulke also published an edition of the game a century later , which is attested in a number of Elizabethan libraries. The game serves to rehearse for its players the celestial motions and astrological principles (...) described by Ptolemy. It also employs principles of stellar rays described by al-Kindi in his De radiis stellarum. (shrink)

We prove that every abstractly defined game algebra can be represented as an algebra of consistent pairs of monotone outcome relations over a game board. As a corollary we obtain Goranko's result that van Benthem's conjectured axiomatization for equivalent game terms is indeed complete.

We prove that every abstractly defined game algebra can be represented as an algebra of consistent pairs of monotone outcome relations over a game board. As a corollary we obtain Goranko's result that van Benthem's conjectured axiomatization for equivalent game terms is indeed complete.

Understanding the spread of national public policies to increase the percentage of women on boards is often presented using different types of institutional theory logic. However, the importance of the political games influencing these decisions has not received the same attention. In this article, we look beyond the institutional setting by focusing on the role of actors. We explore processes that include who the critical actors that drive and determine these policies are, and what motivates them to push for (...) change. We employ a processual design approach using a longitudinal country-comparative case study exploring the case of Norway, England, Germany and Italy. We map the political games, both inside and outside legislative areas, including the micro-politics among various actors and groups of actors in the selected countries. Data are collected through participation observations, interviews and text analyses. The study contributes by filling important gaps in the literature by embedding the discussion about women on boards in politicking and national public policies and by introducing dynamic perspectives. Finally, by using a processual design approach, we capture the reality of the women on board debates at different points of time and in different actor and motivational contexts. The study has consequences for how policy-makers and businesses may follow up and act, based on the debates. (shrink)

Considerable work during the past two decades has focused on modeling the structure of semantic memory, although the performance of these models in complex and unconstrained semantic tasks remains relatively understudied. We introduce a two‐player cooperative word game, Connector (based on the boardgame Codenames), and investigate whether similarity metrics derived from two large databases of human free association norms, the University of South Florida norms and the Small World of Words norms, and two distributional semantic models based on large language (...) corpora (word2vec and GloVe) predict performance in this game. Participant dyads were presented with 20‐item word boards with word pairs of varying relatedness. The speaker received a word pair from the board (e.g., exam‐algebra) and generated a one‐word semantic clue (e.g., math), which was used by the guesser to identify the word pair on the board across three attempts. Response times to generate the clue, as well as accuracy and latencies for the guessed word pair, were strongly predicted by the cosine similarity between word pairs and clues in random walk‐based associative models, and to a lesser degree by the distributional models, suggesting that conceptual representations activated during free association were better able to capture search and retrieval processes in the game. Further, the speaker adjusted subsequent clues based on the first attempt by the guesser, who in turn benefited from the adjustment in clues, suggesting a cooperative influence in the game that was effectively captured by both associative and distributional models. These results indicate that both associative and distributional models can capture relatively unconstrained search processes in a cooperative game setting, and Connector is particularly suited to examine communication and semantic search processes. (shrink)

Banks have an important social responsibility to serve the real economy and to maintain financial stability, and they also need to be responsible to borrowers and others. Against the backdrop of the COVID-19 pandemic affecting the global economy and increasing financial risks, it is particularly important for banks to assume social responsibilities. This study theoretically analyzed the outstanding applicability of stakeholder governance theory. Using a two-stage game method, the optimal pressure intensity of the social responsibility stakeholders was calculated, and the (...) dynamic performance of shareholders was deduced. We found that the establishment of the social responsibility stakeholder governance mechanism will prompt the bank to fulfill its social responsibilities; rational social responsibility stakeholders will not lead to poor bank management due to excessive behavior; and shareholders with social responsibility can self-consciously choose the investment projects with lower negative externalities. The conclusions can be summarized as follows: The participation of stakeholder and the establishment of the social responsibility function of the board of directors can help promote a bank's social responsibility performance. This work studied the social responsibility of banks from the new perspective of stakeholder governance, expands the theoretical boundaries, and puts forward relevant suggestions to enhance the application value of this research. (shrink)

While there are avid chess players in Japan, China, Korea and throughout the East, far more popular is the deceptively simple game of Go, in which black and white pieces called stones are used to form intricate, interlocking patterns that sprawl across the board. So subtle and beautiful is this ancient game that, to hear aficionados describe it, Go is to chess what Asian martial arts like aikido are to a boxing match.

Hellenistic and Roman acrostich inscriptions are usually full of verbal and visual clues, which point the reader in the direction of the ‘hidden message’ contained in the vertical lines of the text. The authors of such inscriptions want their audiences to appreciate the skill that has gone into their composition. There are several complementary ways in which the presence of an acrostich might be signalled to the reader or viewer and their attention directed towards it. These include direct verbal statements, (...) or more subtle allusions, within the text of the inscription. But, even without having read its text, the viewer of an inscription containing a ‘hidden message’ is often immediately aware that some kind of wordplay is at work. Acrostichs, palindromes and various kinds of word square are all graphically striking, or their appearance may be enhanced to make them more so. Regular spacing, the repetition of the acrostich in a separate column and the use of painted or incised grids are all ways in which the layout of the text on the stone can invite the viewer to play a word game. In some cases, as I will argue in this paper, acrostich makers envisaged—even intended—the participants in this game to include the illiterate as well as the literate. (shrink)

Current arguments to increase shareholder power in the large public U.S. corporation need to take account of the well-established historical practice of extensive delegation by shareholders of business decision-making and agenda-control to management and the board, what might be characterized as an absolute delegation rule. This practice sharply limits the power of shareholders to put either business or governance proposals to the shareholders for dispositive resolution. The paper, originally published in 1991 but newly relevant, argues that the rule is (...) based on potential pathologies in shareholder voting rather than the inherent information asymmetry between shareholders and managers. Rational shareholders who know of this asymmetry (and know that others know) would simply vote against most shareholder proposals. But shareholder voting gives rise to potential cycling problems, as shifting shareholder majorities vie for preferred policies, and potential opportunism, as shareholders engage in side deals with management and other shareholders to extract rents in corporate decision-making. Since shareholding patterns are in part a response to control rights, deviations from the absolute delegation rule will predictably lead to greater block ownership, for defensive and offensive reasons. These concerns need to be addressed in arguments for the expansion of shareholder power. (shrink)

Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130: 78-94,2006). In particular, we show that subjectivestate-space models (henceforth HMS structures) can be embedded (...) within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse. (shrink)

This issue was published in the framework of a program that has been made possible by the generous support of the American people through the United States Department of State. The contents are the responsibility of the authors and do not necessarily reflect the views of the Department of State or the United States Government.