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)

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.’.

Moral philosophers of late have been examining the implications of experimental social psychology for ethics. The focus of attention has been on situationism—the thesis that we routinely underestimate the extent to which minor situational variables influence morally significant behavior. Situationism has been seen as a threat to prevailing lay and philosophical theories of character, personhood, and agency. In this paper, I outline the situationist literature and critique one of its upshots: the admonition to carefully select one’s situational contexts. Besides being (...) limited in application, this strategy accentuates an untenable person/situation dichotomy. The deeper lesson of situationism lies in highlighting the interconnectedness of all social behavior—how we are inextricably involved in the actions of others, and how minor tweaks in our own behavior can lead to major payoffs in our moral lives. Situationism is better seen as an opportunity for moral progress than a threat to individual autonomy. (shrink)

This article discusses the set of Harsanyi payoff vectors of a cooperative TU-game, also known as the Selectope. We reconsider some results on Harsanyi payoff vectors within a more general framework. First, an intuitive approach is used, showing that the set of Harsanyi payoff vectors is the core of an associated convex game. Next, the set of individual rational Harsanyi payoff vectors, the Harsanyi imputations in short, is considered. Existence conditions are provided, and if non-empty, we (...) provide a description as the core of a well-defined convex game, and show that it is an externally stable set. (shrink)

I explore a game-theoretic analysis of social interactions in which each agent’s well-being depends crucially on the well-being of another agent. As a result of this, payoffs are interdependent and cannot be fixed, and hence the overall assessment of strategies becomes ungrounded. A paradigmatic example of this general phenomenon occurs when both players are ‘reflective altruists’, in a sense to be explained. I argue that ungroundedness cannot be captured by standard games with incomplete information, but that it requires the concept (...) of an underspecified game; underspecified games have radically underdetermined matrices. Players locked in ungroundedness will be assumed to engage simultaneously in an implicit second-order game in which they try to coordinate their first-order matrices. If they fail to coordinate, their first-order interaction cannot be recast as a game in the first place. (shrink)

Human migration is nonrandom. In small scale societies of the past, and in the modern world, people tend to move to wealthier, safer, and more just societies from poorer, more violent, less just societies. If immigrants are assimilated, such nonrandom migration can increase the occurrence of culturally transmitted beliefs, values, and institutions that cause societies to be attractive to immigrants. Here we describe and analyze a simple model of this process. This model suggests that long run outcomes depend on the (...) relative strength of migration and local adaptation. When local adaption is strong enough to preserve cultural variation among groups, cultural variants that make societies attractive always predominate, but never drive alternative variants to extinction. When migration predominates, outcomes depend both on the relative attractiveness of alError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapternative variants and on the initial sizes of societies that provide and receive immigrants. (shrink)

In “Stereotyping as Discrimination: Why Thoughts Can Be Discriminatory,” I propose that stereotyping someone—even if you manage to keep your thoughts hidden and don’t act on them—can constitute a form of discrimination (2021b). What, Alex Madva asks, are the practical implications of this claim? Even if I am correct that stereotyping constitutes a form of discriminatory treatment, it’s still possible that people should keep on speaking and acting as if “discrimination” refers exclusively to behaviors and policies. He invites me to (...) explore the “potential payoffs and perils” of referring to thoughts and perceptions as discriminatory, especially as they relate to legal practice and social-scientific inquiry (2021, 46). (shrink)

Most research on transmission biases in cultural evolution has treated different biases as distinct strategies. Here I present a model that combines both frequency dependent bias (including conformist bias) and payoff bias in a single decision-making calculus and show that such an integrated learning strategy may be superior to relying on either bias alone. Natural selection may operate on humans’ relative dependence on frequency and payoff information, but both are likely to contribute to the spread of variants with (...) high payoffs. Importantly, the magnitude of conformist bias affects the evolutionary dynamics, and I show that an intermediate level of conformity may be most adaptive and may spontaneously evolve as it resists the invasion of low-payoff variants yet enables the fixation of high-payoff variants in the population. (shrink)

This article discusses the set of Harsanyi payoff vectors of a cooperative TU-game, also known as the Selectope. We reconsider some results on Harsanyi payoff vectors within a more general framework. First, an intuitive approach is used, showing that the set of Harsanyi payoff vectors is the core of an associated convex game. Next, the set of individual rational Harsanyi payoff vectors, the Harsanyi imputations in short, is considered. Existence conditions are provided, and if non-empty, we (...) provide a description as the core of a well-defined convex game, and show that it is an externally stable set. (shrink)

The relative input of payoffs and probabilities into risk judgment The study was designed to investigate the relative input of payoffs and probabilities into risk judgment on the basis of the analysis of information search pattern. The modified version of MouselabWeb software was used as an investigative tool. The amount, the kind and the order of information accessed by subjects to evaluate risk was collected from ordinary respondents and respondents trained in mathematics and statistics. In the latter group were 75 (...) students and young researchers working at National Aeronautics and Space Administration. The ordinary subjects were 67 Polish students of social sciences. As expected, the NASA group considered more information than ordinary students and searched for more information about probabilities. However, the ratio of information about payoffs to probabilities was close to 1 in both groups. Moreover, average risk rates were similar in both groups. It was also observed that risk rates were positively related with the amount of information about probabilities considered by subjects. (shrink)

This is a translation of "Minor Tweaks, Major Payoffs" (2010) prepared by 黃玉娥 for the Journal of Chinese Philosophy and Culture for a special issue edited by Brian Bruya on cognitive science and early Chinese philosophy.

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)

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).

Philosophers working on time-biases assume that people are hedonically biased toward the future. A hedonically future-biased agent prefers pleasurable experiences to be future instead of past, and painful experiences to be past instead of future. Philosophers further predict that this bias is strong enough to apply to unequal payoffs: people often prefer less pleasurable future experiences to more pleasurable past ones, and more painful past experiences to less painful future ones. In addition, philosophers have predicted that future-bias is restricted to (...) first-person preferences, and that people’s third-person preferences are time-neutral. Philosophers disagree vigorously about the normative status of these preferences—i.e., they disagree about whether first-person future-bias is rationally permissible. Time-neutralists, for example, have appealed to the predicted asymmetry between first- and third-person preferences to argue for the rational impermissibility of future-bias. We empirically tested these predictions, and found that while people do prefer more past pain to less future pain, they do not prefer less future pleasure to more past pleasure. This was so in both first and third-person conditions. This suggests that future-bias is typically non-absolute, and is more easily outweighed in the case of positive events. We connect this result to the normative debate over future-bias. (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.’.

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)

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)

Human migration is nonrandom. In small scale societies of the past, and in the modern world, people tend to move to wealthier, safer, and more just societies from poorer, more violent, less just societies. If immigrants are assimilated, such nonrandom migration can increase the occurrence of culturally transmitted beliefs, values, and institutions that cause societies to be attractive to immigrants. Here we describe and analyze a simple model of this process. This model suggests that long run outcomes depend on the (...) relative strength of migration and local adaptation. When local adaption is strong enough to preserve cultural variation among groups, cultural variants that make societies attractive always predominate, but never drive alternative variants to extinction. When migration predominates, outcomes depend both on the relative attractiveness of alternative variants and on the initial sizes of societies that provide and receive immigrants. (shrink)

We extend Tomasello's framework by addressing the functional challenge of obligation. If the long-run social consequences of a decision are sufficiently costly, obligation motivates the actor to forgo potential immediate benefits in favor of long-term social interests. Thus, obligation psychology balances the downstream socially-mediated payoffs from a decision. This perspective can predict when and why obligation will be experienced.

We explore the idea that eye-movement strategies in reading are precisely adapted to the joint constraints of task structure, task payoff, and processing architecture. We present a model of saccadic control that separates a parametric control policy space from a parametric machine architecture, the latter based on a small set of assumptions derived from research on eye movements in reading (Engbert, Nuthmann, Richter, & Kliegl, 2005; Reichle, Warren, & McConnell, 2009). The eye-control model is embedded in a decision architecture (...) (a machine and policy space) that is capable of performing a simple linguistic task integrating information across saccades. Model predictions are derived by jointly optimizing the control of eye movements and task decisions under payoffs that quantitatively express different desired speed-accuracy trade-offs. The model yields distinct eye-movement predictions for the same task under different payoffs, including single-fixation durations, frequency effects, accuracy effects, and list position effects, and their modulation by task payoff. The predictions are compared to—and found to accord with—eye-movement data obtained from human participants performing the same task under the same payoffs, but they are found not to accord as well when the assumptions concerning payoff optimization and processing architecture are varied. These results extend work on rational analysis of oculomotor control and adaptation of reading strategy (Bicknell & Levy, ; McConkie, Rayner, & Wilson, 1973; Norris, 2009; Wotschack, 2009) by providing evidence for adaptation at low levels of saccadic control that is shaped by quantitatively varying task demands and the dynamics of processing architecture. (shrink)

Are the recent findings of Behavioural Game Theory (BGT) on unselfish behaviours relevant for the progress of game theory? Is the methodology of BGT, centred around the attempt to study theoretically players’ utility functions in the light of the feedback that experimental evidence can produce on the theory, a satisfactory one? Or is the creation of various types of ‘social preferences’ just wasteful tinkering? This article compares BGT with the methodology of Rational Game Theory (RGT). BGT is viewed as a (...) more promising and constructive approach, with regard to the relationship between experimental data and theoretical modelling. However, I also argue that today RGT and BGT are closer to one another than often thought. (shrink)

Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion Nash equilibria is discussed in detail. Finally, (...) for2×2bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing as their own confidence levels when players employ the optimistic value criterion. (shrink)

Decision making can be studied using hypothetical payoffs because it is hypothetical to its very core. However, the core process can be influenced by contextual features. As there is no theory for these contextual features, a “do-it-both-ways” rule amounts to a waste of money. If we had such a theory, doing it both ways would be unnecessary.

Science has needed a dispassionate valuation of psychoactive drugs, but a motivational analysis should be conducted with respect to long-term reward rather than reproductive fitness. Because of hyperbolic overvaluation of short-term rewards, an individual's valuation depends on the time she forms it and the times she will revisit it, sometimes making her best long-term interest lie in total abstinence.

We test people's ability to optimize performance across two concurrent tasks. Participants performed a number entry task while controlling a randomly moving cursor with a joystick. Participants received explicit feedback on their performance on these tasks in the form of a single combined score. This payoff function was varied between conditions to change the value of one task relative to the other. We found that participants adapted their strategy for interleaving the two tasks, by varying how long they spent (...) on one task before switching to the other, in order to achieve the near maximum payoff available in each condition. In a second experiment, we show that this behavior is learned quickly and remained stable for as long as the payoff function did not change. The results of this work show that people are adaptive and flexible in how they prioritize and allocate attention in a dual-task setting. However, it also demonstrates some of the limits regarding people's ability to optimize payoff functions. (shrink)

Pepper & Nettle offer a nuanced and humane view on poverty that should be required reading for policy makers, particularly those interested in “behaviour change” policy. We suggest, however, that the emphasis on “future-discounting” in this paper downplays the importance of differences in the payoffs to behavioursin the presentand how these payoffs may be realised in different currencies.

I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show how the equilibrium concepts differ, computing necessary and (...) sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. (shrink)

Bentley et al.’s two-dimensional conceptual map is complementary to cultural evolution research that has sought to explain population-level cultural dynamics in terms of individual-level behavioral processes. Here, I qualify their scheme by arguing that different social learning biases should be treated distinctly, and that the transparency of decisions is sometimes conflated with the actual underlying payoff structure of those decisions.

In a series of papers, Forber and Smead :151–166, 2014, Biol Philos 30:405–421, 2015) and Smead and Forber :698–707, 2013) make a valuable contribution to the study of cooperation in finite populations by analyzing an understudied model: the prisoner’s delight. It always pays to cooperate in the one-shot prisoner’s delight, so this model presents a best-case scenario for the evolution of cooperation. Yet, what Forber and Smead find is highly counterintuitive. In finite populations playing the prisoner’s delight, increasing the benefit (...) of cooperation causes selection to favor defection. Here, I extend their model by considering the effects of non-linear payoffs. In particular, I show that interesting subtleties arise when payoffs are synergistic. Indeed, analysis reveals that increasing the benefit of cooperation does not always favor the spread of defection if payoffs are synergistic. I conclude by drawing some general considerations about robustness analysis in evolutionary models. (shrink)

In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the most coalitional (marginal) stable solutions. Inspired (...) by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models. (shrink)

This study focuses on the question of neural differences in the evaluation of hypothetical and real payoffs. Hypothetical payoffs are not incentive compatible and are, therefore, not considered to be reliable. Behavioral differences between the evaluation of hypothetical and real payoffs can be attributed to this incentive effect. Because real payoff mechanisms are not always applicable in the field, it is necessary to know in which way both types of payoffs affect evaluation processes. In order to delineate the cognitive (...) processes related to hypothetical bias, we conducted a within-subject EEG experiment with hypothetical and real payoffs. A certainty equivalent elicitation method for measuring risk attitudes was performed in which subjects had to indicate whether they preferred playing a lottery or receiving a sure payoff instead. At the behavioral level, subjects were more risk averse for real payoff choices, confirming a hypothetical bias. EEG-derived event-related potentials provide evidence that the processes underlying these differences in evaluations differ. A higher N2 component for hypothetical payoffs revealed increased cognitive control for hypothetical decisions. These neuronal underpinnings indicate additional evaluation processes in hypothetical choice paradigms, which can explain the shift in risk attitude toward the expected value of a lottery. (shrink)

This article describes and evaluates the application of an explicitly critical realist methodology to a quantitative doctoral research project on the causes of family homelessness in Australia. It...