Payoff dominance, a criterion for choosing between equilibrium points in games, is intuitively compelling, especially in matching games and other games of common interests, but it has not been justified from standard game-theoretic rationality assumptions. A psychological explanation of it is offered in terms of a form of reasoning that we call the Stackelberg heuristic in which players assume that their strategic thinking will be anticipated by their co-player(s). Two-person games are called Stackelberg-soluble if the players' strategies that (...) maximize against their co-players' best replies intersect in a Nash equilibrium. Proofs are given that every game of common interests is Stackelberg-soluble, that a Stackelberg solution is always a payoff-dominant outcome, and that in every game with multiple Nash equilibria a Stackelberg solution is a payoff-dominant equilibrium point. It is argued that the Stackelberg heuristic may be justified by evidentialist reasoning. (shrink)

Standard game theory cannot explain the selection of payoff-dominant outcomes that are best for all players in common-interest games. Theories of team reasoning can explain why such mutualistic cooperation is rational. They propose that teams can be agents and that individuals in teams can adopt a distinctive mode of reasoning that enables them to do their part in achieving Pareto-dominant outcomes. We show that it can be rational to play payoff-dominant outcomes, given that an agent group identifies. We (...) compare team reasoning to other theories that have been proposed to explain how people can achieve payoff-dominant outcomes, especially with respect to rationality. Some authors have hoped that it would be possible to develop an argument that it is rational to group identify. We identify some large—probably insuperable—problems with this project and sketch some more promising approaches, whereby the normativity of group identification rests on morality. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Matter and Mathematics: An Essentialist Account of the Laws of Nature by Andrew YOUNANDominic V. CassellaYOUNAN, Andrew. Matter and Mathematics: An Essentialist Account of the Laws of Nature. Washington, D.C.: The Catholic University of America Press, 2023. xii + 228 pp. Cloth, $75.00Andrew Younan’s work situates itself between two opposing philosophical accounts of the laws of nature. In one corner, there are the Humeans (or Nominalists); in the (...) other, the Anti-Humeans (or Platonists). The goal of the book is to find an explanation for the orderliness of the natural world that avoids falling into the difficulties of the two opposing philosophies. For example, the Humeans treat “events” as fundamental, and the laws of nature follow from these “events.” For the Humeans, reality is essentially random, with any order being something of our own contrivance. Whereas for the Anti-Humeans, the laws of nature are fundamental and are treated as causing events, turning the effect of necessity into the cause of material [End Page 166] characteristics. Looking to Aristotle and Thomas Aquinas, Younan proposes the recovery of a third option, the Essentialist position. This Essentialist position understands substances, that is, individual beings, as fundamental and all else (for example, events and laws of nature) follow from these individual beings. The thesis of the book, generally understood, is that Essentialism evades the critiques that the Humeans and Anti-Humeans put against one another while retaining what is right in each approach.The book is divided into two parts. The book’s first part deals with general objections and replies and is divided into three chapters. Chapters 1 and 2 address the two opposing accounts of nature mentioned, while chapter 3 argues for the benefits of recovering an Essentialist position. Chapter 1 examines the objection that Aristotelian natural philosophy is incompatible with modern science, an objection raised by Descartes. Chapter 2 addresses the objections of the Humeans, namely, that natural philosophy and, with it, causality and induction have been debunked. Chapter 3 looks at the fathers of quantum theory, specifically Heisenberg, and argues that a return to Aristotle’s understanding of nature would benefit the modern scientific project. The book’s second part is an argument for the Essentialist position and is divided into three chapters. Chapters 4 and 5 are the foundation for chapter 6. Chapter 4 is an abstractive account of mathematics, differing from Descartes and his conceptions, which draws on the texts of Aristotle and Aquinas’s Division and Methods. Chapter 5 situates necessity and its role in Aristotelian natural philosophy. Chapter 6 is the author’s attempt at defining what it is to be a law of nature.Younan argues that adopting an essentialist understanding of nature in a system where all knowledge begins in the senses has three significant “payoffs.” The first is that it avoids governance language, that is, it avoids making laws themselves causes of necessity; the second is that it avoids the assertion of a priori knowledge; the third is that it understands individual things as the fundamental primitives in nature, restoring the substance to its proper place as the thing that “stands under” accidental being.The book is concluded with an appendix that explores and rearticulates Thomas Aquinas’s fifth way under the consideration of everything the author had argued for in the book’s main text. Taking as established by the rest of the book that necessity and teleology go hand in hand, Younan argues for a creator God who establishes a universe freely but within certain parameters that follow upon being itself. Younan concludes, with Thomas Aquinas, that laws of nature are “ordinances of reason” that must come from a rational mind. To be as consistent as they are, the laws of nature must be promulgated by God, and they are discoverable within the nature of matter itself.Younan’s book often engages its interlocutors on the big-picture scale, frequently giving generalizations and not going into details to avoid getting bogged down in the weeds. The author is very aware of what he is doing. [End Page 167] It is appropriate since engaging the multiheaded hydra of the schools of thought that Younan... (shrink)

Even if game theory is broadened to encompass other-regarding preferences, it cannot adequately model all aspects of interactive decision making. Payoff dominance is an example of a phenomenon that can be adequately modeled only by departing radically from standard assumptions of decision theory and game theory – either the unit of agency or the nature of rationality. (Published Online April 27 2007).

What are pictures good for? “Nothing” recurs as the apparently irrepress- ible reply of a motley collection iconophobes from Plato to the mediaeval iconoclasts, to parents concerned about comic books, to postmoderns in a lather over “scopic regimes”. In the aftermath of Nelson Goodman’s Languages of Art (1976), philosophers doubled down on theories of depiction and pictorial experience, but they have not rushed to work on the value of pictures. Those few who have written about pictorial value have taken for (...) granted an approach aptly dubbed “psychologism” (Wol- lheim 1987; Hopkins 1997; Lopes 2005). According to psychologism, we can understand pictorial value by appealing only to cognitive traits and capacities. Yet psychologism is enough out of step with studies of pic- tures outside philosophy that it dampens philosophy’s impact on the very scholars who could most use a defense of pictorial value. Here is a thesis: psychologism is false. Here is its payoff: an alternative to psychologism better suits the work of scholars outside philosophy. (shrink)

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’.

In a recent article in this journal, Duijf claims to have proved that team reasoning can be viewed as a payoff transformation. His formalization mimics team reasoning but ignores its essential agency switch. The possibility of such a payoff transformation was never in doubt, does not imply that team reasoning can be viewed as a payoff transformation, and makes no sense in a game in which payoffs represent players’ utilities. A theorem is proved here that a simpler (...) and more intuitive payoff transformation can mimic any theory that predicts what strategies players will choose in a well-defined game. (shrink)

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’.

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background (...) uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if (...) she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994). Frame characterization results are also provided. (shrink)

Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also common (...) knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (shrink)

We provide eductive foundations for the concept of forward induction, in the class of games with an outside option. The formulation presented tries to capture in a static notion the rest point of an introspective process, achievable from some restricted preliminary beliefs. The former requisite is met by requiring the rest point to be a Nash equilibrium that yields a higher payoff than the outside option. With respect to the beliefs, we propose the Incentive Dominance Criterion. Players should (...) consider one action more likely than another whenever the former is better than getting the outside option for more conjectures over his rival's actions. We apply this model to the case where the subgame is a coordination game with a conflict between payoff dominance and risk dominance. Our results provide support for dominance solvability, but not for Van Damme's notion of forward induction. We show how the forward induction logic helps to select the Pareto dominant equilibrium. This is the case whenever player 1's act of giving up the outside option reverses the incentive dominance relations among 1's pure actions in the subgame. (shrink)

How do rational agents coordinate in a single-stage, noncooperative game? Common knowledge of the payoff matrix and of each player's utility maximization among his strategies does not suffice. This paper argues that utility maximization among intentions and then acts generates coordination yielding a payoff-dominant Nash equilibrium. ‡I thank the audience at my paper's presentation at the 2006 PSA meeting for many insightful points. †To contact the author, please write to: Philosophy Department, University of Missouri, Columbia, MO 65211; e-mail: (...) [email protected]. (shrink)

Game theory's paradoxes stimulate the study of rationality. Sometimes they motivate the revising of standard principles of rationality. Other times they call for revising applications of those principles or introducing supplementary principles of rationality. I maintain that rationality adjusts its demands to circumstances, and in ideal games of coordination it yields a payoff-dominant equilibrium.

This paper presents the results of an experiment on mutual versus common knowledge of advice in a two-player weak-link game with random matching. Our experimental subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payoff-dominant equilibrium. Our results are somewhat surprising and can be summarized as follows: in all our treatments (...) both the choice of the efficiency-inducing action and the percentage of efficient equilibrium play are higher with respect to the control treatment, revealing that even a condition as weak as mutual knowledge of level 1 is sufficient to significantly increase the salience of the efficient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 induces, under suitable conditions, successful coordination more frequently than common knowledge. (shrink)

Psychological game theory encompasses formal theories designed to remedy game-theoretic indeterminacy and to predict strategic interaction more accurately. Its theoretical plurality entails second-order indeterminacy, but this seems unavoidable. Orthodox game theory cannot solve payoff-dominance problems, and remedies based on interval-valued beliefs or payoff transformations are inadequate. Evolutionary game theory applies only to repeated interactions, and behavioral ecology is powerless to explain cooperation between genetically unrelated strangers in isolated interactions. Punishment of defectors elucidates cooperation in social dilemmas but (...) leaves punishing behavior unexplained. Team reasoning solves problems of coordination and cooperation, but aggregation of individual preferences is problematic. (shrink)

The human “environment of evolutionary adaptedness” can only be inferred indirectly. In contrast, the behavior of some nonhuman animals can be compared among “natural” and various altered environments. As an example, male immigration tactics in unprovisioned versus provisioned macaque (Macaca) populations are compared using Tooby and Cosmides’s (1992) framework for evolutionary functional analysis. In unprovisioned populations, social groups contain few males, and immigrant male takeovers of alpha rank occur frequently. In provisioned populations, groups contain many males, and males almost invariably (...) enter social groups at very low rank and rise in rank only as more dominant males emigrate or die. Male conformity to the “seniority rule” is hypothesized to represent the behavioral output of an evolved decision-making algorithm (psychological mechanism) that takes into account (1) the net payoff of each rank in the dominance hierarchy and (2) the power of male group size as a predictor of the likelihood of successful immigrant takeover. (shrink)

In the Divide-the-Dollar (DD) game, two players simultaneously make demands to divide a dollar. Each player receives his demand if the sum of the demands does not exceed one, a payoff of zero otherwise. Note that, in the latter case, both parties are punished severely. A major setback of DD is that each division of the dollar is a Nash equilibrium outcome. Observe that, when the sum of the two demands x and y exceeds one, it is as if (...) Player 1's demand x (or his offer (1−x) to Player 2) suggests that Player 2 agrees to λx < 1 times his demand y so that Player 1's demand and Player 2's modified demand add up to exactly one; similarly, Player 2's demand y (or his offer (1−y) to Player 1) suggests that Player 1 agrees to λyx so that λyx+y = 1. Considering this fact, we change DD's payoff assignment rule when the sum of the demands exceeds one; here in this case, each player's payoff becomes his demand times his λ; i.e., each player has to make the sacrifice that he asks his opponent to make. We show that this modified version of DD has an iterated strict dominant strategy equilibrium in which each player makes the egalitarian demand 1/2. We also provide a natural N-person generalization of this procedure. (shrink)

Maximize Expected Choiceworthiness (MEC) is a theory of decision-making under moral uncertainty. It says that we ought to handle moral uncertainty in the way that Expected Value Theory (EVT) handles descriptive uncertainty. MEC inherits from EVT the problem of fanaticism. Roughly, a decision theory is fanatical when it requires our decision-making to be dominated by low-probability, high-payoff options. Proponents of MEC have offered two main lines of response. The first is that MEC should simply import whatever are the best (...) solutions to fanaticism on offer in decision theory. The second is to propose statistical normalization as a novel solution on behalf of MEC. This paper argues that the first response is open to serious doubt and that the second response fails. As a result, MEC appears significantly less plausible when compared to competing accounts of decision-making under moral uncertainty, which are not fanatical. (shrink)

Adapting a definition introduced by Milgrom (1981) we say that a signal about the environment is good news relative to some initial beliefs if the posterior beliefs dominate the initial beliefs in the sense of first-order stochastic dominance (the assumption being that higher values of the parameter representing the environment mean better environments). We give an example where good news leads to the adoption of a more pessimistic course of action (we say that action a, reveals greater pessimism than (...) action a„ if it gives higher payoff in bad environments and lower payoff in good environments). We then give sufficient conditions for a signal not to induce a more pessimistic choice of action. (shrink)

Corporate bond appeared in 1992-1994 in Vietnamese capital markets. However, it is still not popular to both business sectors and academic circles. This paper explores different dimensions of Vietnamese corporate bond market using a unique and perhaps, most complete data set. State not only intervenes in the bond markets with its powerful budget and policies but also competes directly with enterprises. The dominance of state-owned enterprises and large corporations also prevents small and medium enterprises from this debt financing vehicle. (...) Whenever a convertible term is available, bondholders are more willing to accept lower fixed income payoff. But they would not likely stick to it. On the one hand, prospective bondholders could value the holdings of equity when realized favourably ex ante. On the other hand, the applicable coupon rate for such bonds could turn out negative inflation-adjusted payoff when tight monetary policy is exercised and the corresponding equity holding turns out valueless, ex post. Given the weak primary market and virtually non-existent secondary market, the corporate bond market in Vietnam reflects our perception of the relationship-based and rent-seeking behaviour in the financial markets. For the corporate bonds to really work, they critically need a higher level of liquidity to become truly tradeable financial assets. Updated entries in 2010 affirm the findings and conclusions. (shrink)

Does natural selection favor veridical percepts—those that accurately depict objective reality? Perceptual and cognitive scientists standardly claim that it does. Here we formalize this claim using the tools of evolutionary game theory and Bayesian decision theory. We state and prove the “Fitness-Beats-Truth Theorem” which shows that the claim is false: If one starts with the assumption that perception involves inference to states of the objective world, then the FBT Theorem shows that a strategy that simply seeks to maximize expected-fitness (...) class='Hi'>payoff, with no attempt to estimate the “true” world state, does consistently better. More precisely, the FBT Theorem provides a quantitative measure of the extent to which the fitness-only strategy dominates the truth strategy, and of how this dominance increases with the size of the perceptual space. The FBT Theorem supports the Interface Theory of Perception, which proposes that our perceptual systems have evolved to provide a species-specific interface to guide adaptive behavior, and not to provide a veridical representation of objective reality. (shrink)

Aside from making a few weak, and hopefully widely shared claims about the value of privacy, transparency, and accountability, we will offer an argument for the protection of privacy based on individual self-interest and prudence. In large part, this argument will parallel considerations that arise in a prisoner’s dilemma game. After briefly sketching an account of the value of privacy, transparency, and accountability, along with the salient features of a prisoner’s dilemma games, a game-theory analysis will be offered. In a (...) game where both players want privacy and to avoid transparency and the associated accountability, the dominant action will be to foist accountability and transparency on the other player while attempting to retain one’s own privacy. Simply put, if both players have the ability or power to make the other more accountable and transparent, they will do so for the same reasons that player’s defect in a prisoner’s dilemma game. Ultimately this will lead to a sub-optimal outcome of too much accountability and transparency. While there are several plausible solutions to prisoner dilemma games, we will offer both technical, as well as, law and policy solutions. We need to change the payoffs of the game so that is it in everyone’s interest to balance privacy and accountability rather than foisting transparency on others. (shrink)

Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...) Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory. (shrink)

It is usually assumed in game theory that agents who interact strategically with each other are rational, know the strategies open to other agents as well as their payoffs and, moreover, have common knowledge of all the above. In some games, that much information is sufficient for the players to identify a "solution" and play it. The most commonly adopted solution concept is that of Nash equilibrium. A Nash equilibrium is defined a combination of strategies, one for each player, such (...) that no player can profit from a deviation from his strategy if the opponents stick to their strategies. Nash equilibrium is taken to have predictive power, in the sense that in order to predict how rational agents will in fact behave, it is enough to identify the equilibrium patterns of actions. Barring the case in which players have dominant strategies, to play her part in a Nash equilibrium a player must believe that the other players play their part, too. But an intelligent player must immediately realize that she has no ground for this belief. Take the case of a one-shot, simultaneous game. Here all undominated strategies are possible choices, and the beliefs supporting them are possible beliefs, even if this game has a.. (shrink)

Solution concepts for game play implicitly assume what information is relevant for choosing moves. Maximin and Eliminating Dominated Strategies use payoff order; mixed strategies and Harsanyi's risk dominance use payoff values. "Cooperative" strategies use previous choices, ignoring payoffs altogether. We first define the 12 symmetric 2 × 2 games as a continuous payoff space then use this space to evaluate strategies based on different types of information. Strategic success is shown to be sensitive to actual payoffs (...) and seldom consistent for all games of an ordinally defined category such as Chicken. A new hybrid strategy using both payoff and choice information is introduced and shown to produce efficient outcomes in all symmetric 2×2 games when employed by both players. It does well in evolutionary tournaments against strategies of other types, especially in the difficult distribution games including Battle-of-the-Sexes. (shrink)

A growing body of empirical evidence suggests the existence of a Paradox of Choice, whereby a larger choice set leads to a lower expected payoff to the decisionmaker. These empirical findings contradict traditional choice-theoretic results in microeconomics and even social psychology, suggesting profound yet unexplained aspects of choice settings/behavior. The Paradox remains largely as a theoretically-rootless empirical phenomenon. We neither understand the mechanisms and conditions that generate it, nor whether the Paradox stems from choice behavior, choice setting, or both. (...) We present a general search model of consumer choice under incomplete information to examine the theoretical existence and conditions for the Paradox. The model departs from traditional microeconomic choice theory in assuming no “cognitive free lunches.” Search and evaluative efforts require time, focus, and opportunity cost in the model, as in real life. The model shows that conditions for Paradox readily exist, diminishing returns to potential value of the choice in choice set size is a necessary condition for a Paradox outcome, that a Paradox outcome can occur with or without a “choice overload” response by the decisionmaker, and that avoidance of a Paradox outcome is an impossibility in some choice settings (primitive to setting regardless of choice behavior). Lastly, we develop a pareto-improving choice set reduction algorithm that eliminates weakly dominated choice set elements and presents the restricted choice set to the decisionmaker. As such, it is shown that the algorithm acts to treat or mitigate the Paradox of Choice, as well as to pareto-improve choice-supporting evaluation more generally. Like established AI recommender systems, the novel algorithm filters choices. In the present case, the filtering is based upon identification of weakly dominated choice set elements. (shrink)

In the game theory literature, Garrett Hardin’s famous allegory of the “tragedy of the commons” has been modeled as a variant of the Prisoner’s Dilemma, labeled the Herder Problem (or, sometimes, the Commons Dilemma). This brief paper argues that important differences in the institutional structures of the standard Prisoner’s Dilemma and Herder Problem render the two games different in kind. Specifically, institutional impediments to communication and cooperation that ensure a dominant strategy of defection in the classic Prisoner’s Dilemma are absent (...) in the Herder Problem. Their absence does not ensure that players will achieve a welfare-enhancing, cooperative solution to the Herders Problem, but does create far more opportunity for players to alter the expected payoffs through cooperative arrangements. In a properly modeled Herder Problem—along the lines of an assurance game—defection would not always be the dominant strategy. Consequently, the Herder Problem is not in the nature of a Prisoner’s Dilemma. (shrink)

Sengupta and Sengupta consider a payoff configuration of a TU game as a viable proposal if it challenges each legitimate contender. Lauwers prove that the set of viable proposals is nonempty for every game. In the present paper, we prove that the set of viable proposals coincides with the coalition structure core if there exists an undominated proposal; otherwise, it coincides with the set of accessible proposals. This characterization result implies that a proposal is a viable proposal if and (...) only if it is undominated or accessible. Moreover, we prove that the set of viable proposals includes the minimal dominant set, which is another nonempty extension of the coalition structure core introduced by Kóczy and Lauwers. In particular, we prove that the set of viable proposals of a cohesive game coincides with the minimal dominant set. (shrink)

We investigate how changes to the payoffs of cooperative behavior affect the evolutionary dynamics. Paradoxically, the larger the benefits of cooperation, the less likely it is to evolve. This holds true even in cases where cooperation is strictly dominant. Increasing the benefits from prosocial behavior has two effects: first, in some circumstances it promotes the evolution of spite; and second, it can decrease the strength of selection leading to nearly neutral evolution of strategies. In light of these results we must (...) reevaluate standard philosophical perspectives on the evolution of cooperation and morality. (shrink)

How do firms make sense of creating shared value projects? In their sense-making processes, do they extend the meaning spectrum to include human rights? What are the dominant cognitive frames through which firms make sense of CSV projects, and are some frames more likely to have transformative power? We pose these questions in the context of small-scale firms in a low-to-middle income country—a context where CSV policies have been promoted extensively over the last decade in the expectation of improved economic (...) competitiveness, growth, and sustainable development processes. We employ a grounded theory approach to identify three dominant cognitive frames used by our respondents to make sense of CSV. The most prevalent frame prioritizes economic over social and environmental goals, and considers social, environmental, and human rights benefits to trickle down from economic growth and wealth generation. In the second frame, economic actors follow a win–win logic according to which environmental sustainability is pursued only if there are clear and foreseeable economic payoffs. The third frame is a niche that emphasizes the attainment of certain human rights goals, despite a perceived lack of immediate economic returns. Our work casts doubt on the capacity of CSV projects to stimulate sustainable development processes without radically changing entrepreneurs’ cognitive frames from growth first to humanizing the business. (shrink)

The use of evolutionary game theory to explain the evolution of human norms and the behavior of humans who act according to those norms is widespread. Both the aims and motivation for its use are clearly articulated by Harms and Skyrms (2008) in the following passage: "A good theory of evolution of norms might start by explaining the evolution of altruism in Prisoner’s Dilemma, of Stag Hunting, and of the equal split in the symmetric bargaining game. These are not well-explained (...) by classical game theory based on rational choice. From a technical point of view, they present different theoretical challenges. In the bargaining game, there are an infinite number of equilibria with no principled (rational choice) way to select the cooperative one. In Stag Hunt there are only two, but the non-cooperative one is selected by risk-dominance. In Prisoner’s Dilemma the state of mutual cooperation is not a Nash equilibrium at all, and cooperation flies in the face of the rational-choice principle that one does not choose less rather than more. In contrast to rational choice theory, the most common tool of evolutionary game theory is the replicator dynamics, in which the propagation rate of each strategy is determined by its current payoffs. These dynamics have a rationale in both biological and cultural evolutionary modeling, and sometimes tell us things that rational choice theory does not." We agree with the first sentence in this quotation: a good theory about the behavior under norms ought to explain altruism in the Prisoner’s Dilemma (PD), playing Stag in Stag Hunt (SH), and offering equal splits in the symmetric Nash bargaining game (NB). We also agree with Harms and Skyrms about the difference in technical challenges each of these games poses. Finding a single mechanism, even one as broadly understood as evolution, that could solve these challenges en masse is no doubt a tall order. Nonetheless, in this paper, we present a single, simple, modification to SH, NB, and a general n-player PD that does just that: we introduce deontological autonomy into the models. (shrink)

In this paper, we provide a game-theoretic examination of indirect utilitarianism by comparing the expected payoffs of attempts to apply a deontological principle and a utilitarian principle within the context of the Prisoner’s Dilemma (PD). Although many of the best-known utilitarians and consequentialists have accepted some indirect form of their respective views, the results in this paper suggest that they have been overly quick to dismiss altogether the benefits of directly enacting utilitarian principles. We show that for infallible moral agents, (...) what we call ‘non-autonomous agents’, direct utilitarianism dominates indirect utilitarianism via deontology in terms of achieving the maximized utilitarian outcome, but only in underlying games where the maximized utilitarian outcome involves unequal payoffs. In other situations, indirect utilitarianism implemented through Kantian deontology either ties or dominates direct utilitarianism in terms of achieving the maximized utilitarian outcome. We also examine the two different moralities on the assumption that fallibility, which is a form of autonomy, is an aspect of moral agency by introducing Endogenized Morality Models (EMM’s). We believe that just as indirect utilitarians worry about the cost of applying moral principles, so too they should worry about the fact that humans have both pro-social and materialistically selfish motivations and hence are fallible moral agents. We show that there are conditions under which fallible autonomous utilitarians achieve higher expected material and psychic payoffs than fallible autonomous deontologists and conditions under which they do not. (shrink)

In the Nash demand game n players announce utility demands, the demands are implemented if they are jointly feasible, and otherwise no one gets anything. If the utilities set is the simplex, the game is called “divide-the-dollar”. Brams and Taylor studied variants of divide-the-dollar, on which they imposed reasonableness conditions. I explore the implications of these conditions on general NDGs. In any reasonable NDG, the egalitarian demand profile cannot be obtained via iterated elimination of weakly dominated strategies. Further, a reasonable (...) NDG may fail to have a Nash equilibrium, even in mixed strategies. In the 2-person case, existence of pure strategy equilibrium is equivalent to the existence of a value, in the sense that each player can secure the egalitarian payoff level independent of his opponent’s play. This result does not extend to reasonable NDGs with more than two players. Interestingly, there are results for reasonable NDGs that hold for two and three players, but not for n≥4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 4$$\end{document} players. (shrink)

“Randomized dictatorship,” one of the simplest ways to solve bargaining situations, works as follows: a fair coin toss determines the “dictator”—the player to be given his first-best payoff. The two major bargaining solutions, that of Nash and that of Kalai and Smorodinsky, Pareto-dominate this process. However, whereas the existing literature offers axiomatizations of the Nash solution in which this ex ante domination plays a central role, it does not provide an analogous result for Kalai–Smorodinsky. This paper fills in this (...) gap: a characterization of the latter is obtained by combining the aforementioned domination with three additional axioms: Pareto optimality, individual monotonicity, and a weakened version of the Perles–Maschler super additivity axiom. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Three Probes into St. Francis of Assisi's Second Letter to the Faithful1Robert J. Karris, OFMFrancis' Second Letter to the Faithful2 is so rich that it would take a lengthy book to probe most of its treasures. My goal is to make three probes: 1) from a literary analysis of this letter of exhortation, 2) from the results of a more thorough search for the biblical sources behind its eighty-eight (...) lines, and 3) from the insights achieved through literary and theological parallels to its contents.3 I accomplish my goals by going systematically through this letter, which I contend has introduction, positive exhortations, conclusion to positive exhortations and bridge to second part of the letter, negative exhortations, aka polemic, the example story of the unrepentant rich man, and ending.4 At the very beginning, I remind myself and my readers of something that we might take for granted: The dominant figure of this letter is "our Lord Jesus Christ," an expression and reality that pulses through its eighty-eight lines. Take, as [End Page 79] an example, n. 49–50, which are staggering in scope: "And they (who persevere in penance) will be children of the heavenly Father, whose works they are doing. And they are spouses, brothers, and mothers of our Lord Jesus Christ."Methodology: Search for Literary and Theological ParallelsEarly on in my doctoral studies, I learned the importance and value of investigating New Testament texts by means of their literary parallels.5 For example, there were significant interpretive payoffs to be gained by comparing St. Paul's use of polemic in the Pastoral Epistles (1–2 Timothy and Titus) to that employed by the Stoics.6 Paul probably never met a Stoic philosopher in his life, but their means of no-holds-barred polemic was "in the air" he breathed. Daniel J. Harrington expresses well this common methodology in New Testament Studies: "In literature a parallel involves some point or points of similarity between two texts where literary dependence is unlikely or not proved. Parallels to New Testament texts can be taken from any body of literature and from any period of history…"7So what parallels do I suggest as background for the interpretation of Francis' 2LtF? There may be many, since Francis' letter is dealing with fundamental human and Christian realities: sin and virtue. I have selected what I call The Big Three:In his De Virtutibus et Vitiis Liber,8 Alcuin of York (d. 800) wrote a letter to Count Guy, who is engaged in martial activities. Alcuin has followed Guy's request for paternal admonition and prays that his writing may help Guy to perpetual salvation (n. 6). Alcuin writes briefly about 35 topics: wisdom, faith, charity, hope, zeal of reading, peace, mercy, remission, patience, humility, compunction of the heart, confession, repentance, not delaying conversion to God, fear of God, fasting, almsgiving, chastity, avoiding fraud, judges, false witnesses, envy, pride, proneness to anger, not seeking human praise, perseverance in good works, eight principal vices, greed, fornication, avarice, anger, [End Page 80] weariness (acedia), sorrow, cenodoxia (vainglory), and the four virtues.9 It is abundantly clear that Francis does not engage in 35 topics, but his exhortations do overlap with a number of Alcuin's, e.g., almsgiving, judges, perseverance in good works.In his Liber exhortationis,10 Archbishop St. Paulinus of Aquileia (d. 802) wrote to Count or Duke Henry of Fruilli. His treatise has 66 chapters and covers virtually all spiritual and moral topics. Of singular interest is Chapter 8, "On Friendship with God and Keeping God's Commandments." His final chapter is a long prayer to resist the wiles of the devil and to persevere in virtue. Saints Paulinus of Aquileia and Francis of Assisi's 2LtF have numerous points in common.11Archbishop Hincmar of Reims (d. 882) wrote a very polished and regarded letter, De cavendis vitiis et virtutibus exercendis to King Charles the Bald.12 It has ten chapters. The first seven deal chiefly with vices such as avarice, pride, voluptuousness, gluttony, envy, anger, and jealousy. They also encourage virtuous deeds such as almsgiving, works of mercy, fidelity, and prayer. Chapters 8... (shrink)

Most human societies exhibit a distinct class structure, with an elite, middle classes, and a bottom class, whereas animals form simple dominance hierarchies in which individuals with higher fighting ability do not appear to form coalitions to “oppress” weaker individuals. Here, we extend our model of primate coalitions and find that a division into a bottom class and an upper class is inevitable whenever fitness-enhancing resources, such as food or real estate, are exploitable or tradable and the members of (...) the bottom class cannot easily leave the group. The model predicts that the bottom class has a near flat, low payoff and always comprises at least half the society. The upper class may subdivide into one or more middle class(es), resulting in improved payoff for the topmost members (elite). The model predicts that the bottom class on its own is incapable of mounting effective counter-coalitions against the upper class, except when receiving support from dissatisfied members of the middle class(es). Such counter-coalitions can be prevented by keeping the payoff to the lowest-ranked members of the middle classes (through concessions) well above that of the bottom class. This simple model explains why classes are also absent in nomadic hunter-gatherers and predominate in (though are not limited to) societies that produce and store food. Its results also agree well with various other known features of societies with classes. (shrink)

The paper presents a variation of the EMAIL Game, originally proposed byRubinstein (American Economic Review, 1989), in which coordination ofthe more rewarding-risky joint course of actions is shown to obtain, evenwhen the relevant game is, at most, ``mutual knowledge.'' In the exampleproposed, a mediator is introduced in such a way that two individualsare symmetrically informed, rather than asymmetrically as in Rubinstein,about the game chosen by nature. As long as the message failure probabilityis sufficiently low, with the upper bound being a (...) function of the gamepayoffs, conditional beliefs in the opponent's actions can allow playersto choose a more rewarding-risky action. The result suggests that, forefficient coordination to obtain, the length of interactive knowledge onthe game, possibly up to ``almost common knowledge,'' does not seem to bea major conceptual issue and that emphasis should be focused instead onthe communication protocol and an appropriate relationship between thereliability of communication channels and the payoffs at stake. (shrink)

We consider Effort Games, a game-theoretic model of cooperation in open environments, which is a variant of the principal-agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; carrying out certain subsets of the tasks completes the project successfully, while carrying out other subsets does not. The probability of carrying out a task is higher when the agent in charge of it exerts effort, at a certain cost for that agent. A central authority, called (...) the principal, attempts to incentivize agents to exert effort, but can only reward agents based on the success of the entire project.We model this domain as a normal form game, where the payoffs for each strategy profile are defined based on the different probabilities of carrying out each task and on the boolean function that defines which task subsets complete the project, and which do not. We view this boolean function as a simple coalitional game, and call this game the underlying coalitional game. We suggest the Price of Myopia as a measure of the influence the model of rationality has on the minimal payments the principal has to make in order to motivate the agents in such a domain to exert effort.We consider the computational complexity of testing whether exerting effort is a dominant strategy for an agent, and of finding a reward strategy for this domain, using either a dominant strategy equilibrium or using iterated elimination of dominated strategies. We show these problems are generally #P-hard, and that they are at least as computationally hard as calculating the Banzhaf power index in the underlying coalitional game. We also show that in a certain restricted domain, where the underlying coalitional game is a weighted voting game with certain properties, it is possible to solve all of the above problems in polynomial time. We give bounds on PoM in weighted voting effort games, and provide simulation results regarding PoM in another restricted class of effort games, namely effort games played over Series-Parallel Graphs. (shrink)

The analysis of Political Action Committee activities is dominated by the perspective that PAC contributions are a rational investment in political candidates; they yield valuable short-term payoffs. PACs buy access to officeholders and their votes on important legislation. Despite broad acceptance of this morally suspect theory, the evidence upon which it is based is weak. An alternative perspective — what we call the principled approach — both fits the evidence and rejects the morally repugnant interpretation of the relationship between business (...) and politics that permeates the rational investment perspective. (shrink)

Studies consistently report that individuals believe they are far more ethical than co-workers, superiors, or managers in other firms. The present study confirms this finding when comparing undergraduate students' own ethical standards to their perceptions of the standards held by most managers or supervisors. By maintaining a holier than thou ethical perception, new and future managers might rationalize their unethical behavior as being necessary for success in an unethical world. A prisoner's dilemma type problem can be said to exist when (...) choosing an unethical behavior becomes each player's dominant strategy and the interaction of dominant behaviors is Pareto inferior. Dispelling the holier than thou perception may encourage students to revise their personal behavior payoffs such that the collective benefits that emanate from ethical conduct are favored and the prisoner's dilemma problem is converted into a coordination problem. (shrink)

[David Charles] Aristotle, it appears, sometimes identifies well-being with one activity, sometimes with several, including ethical virtue. I argue that this appearance is misleading. In the Nicomachean Ethics, intellectual contemplation is the central case of human well-being, but is not identical with it. Ethically virtuous activity is included in human well-being because it is an analogue of intellectual contemplation. This structure allows Aristotle to hold that while ethically virtuous activity is valuable in its own right, the best life available for (...) humans is centred around, but not wholly constituted by, intellectual contemplation. /// [Dominic Scott] In Nicomachean Ethics X 7-8, Aristotle distinguishes two kinds of eudaimonia, primary and secondary. The first corresponds to contemplation, the second to activity in accordance with moral virtue and practical reason. My task in this paper is to elucidate this distinction. Like Charles, I interpret it as one between paradigm and derivative cases; unlike him, I explain it in terms of similarity, not analogy. Furthermore, once the underlying nature of the distinction is understood, we can reconcile the claim that paradigm eudaimonia consists just in contemplation with a passage in the first book requiring eudaimonia to involve all intrinsic goods. (shrink)

In _ Psychiatry in the Scientific Image, _Dominic Murphy looks at psychiatry from the viewpoint of analytic philosophy of science, considering three issues: how we should conceive of, classify, and explain mental illness. If someone is said to have a mental illness, what about it is mental? What makes it an illness? How might we explain and classify it? A system of psychiatric classification settles these questions by distinguishing the mental illnesses and showing how they stand in relation to one (...) another. This book explores the philosophical issues raised by the project of explaining and classifying mental illness. Murphy argues that the current literature on mental illness -- exemplified by the Diagnostic and Statistical Manual of Mental Disorders -- is an impediment to research; it lacks a coherent concept of the mental and a satisfactory account of disorder, and yields too much authority to commonsense thought about the mind. He argues that the explanation of mental illness should meet the standards of good explanatory practice in the cognitive neurosciences, and that the classification of mental disorders should group symptoms into conditions based on the causal structure of the normal mind. (shrink)

For centuries, philosophers have identified beauty with what brings pleasure. Dominic McIver Lopes challenges this interpretation by offering an entirely new theory of beauty - that beauty engages us in action, in concert with others, in the context of social networks - and sheds light on why aesthetic engagement is crucial for quality of life.

Birth asphyxia is the most common single cause of death in term newborn infants. The majority of deaths in developed countries follow decisions to withdraw intensive care. Recent technological advances, particularly the use of magnetic resonance imaging (MRI) of the brain, may affect the process of prognostication and decision-making. There is little existing evidence about how prognosis is determined in newborn infants and how this relates to treatment withdrawal decisions.An exploratory qualitative study was performed using in-depth semi-structured interviews with a (...) sample of ten neonatologists from tertiary intensive care units in the UK. Participants were purposively selected to ensure a range of experience and type of unit. They were asked about the process of prognostication for infants with birth asphyxia and decisions about treatment withdrawal. Interviews were transcribed and thematically analysed.MRI played a significant role in decision-making about life-sustaining treatment for a number of clinicians. Clinicians did not identify particular ethical concerns related to MRI, though wider discussion revealed issues relating to uncertainty around predictions, the timing of prognostication and decision-making, and difficulty in predicting quality of life. (shrink)