Talk of ‘robustness’ remains vague, despite the fact that it is clearly an important parameter in evaluating models in general and game-theoretic results in particular. Here we want to make it a bit less vague by offering a graphic measure for a particular kind of robustness— ‘matrix robustness’— using a three dimensional display of the universe of 2 x 2 game theory. In a display of this form, familiar games such as the Prisoner’s Dilemma, Stag Hunt, Chicken (...) and Deadlock appear as volumes, making comparison easy regarding the extent of different game-theoretic effects. We illustrate such a comparison in robustness between the triumph of Tit for Tat in a spatialized environment (Grim 1995, Grim, Mar, and St. Denis 1998) and a spatialized modeling of the Contact Hypothesis regarding prejudice reduction (Grim, et. al 2005a, 2005b). The geometrical representation of relative robustness also offers a possibility for links between geometrical theorems and results regarding robustness in game theory. (shrink)

Evolutionary game theory and public goods games offer an important framework to understand cooperation during pandemics. From this perspective, the COVID-19 situation can be conceptualized as a dilemma where people who neglect safety precautions act as free riders, because they get to enjoy the benefits of decreased health risk from others’ compliance with policies despite not contributing to or even undermining public safety themselves. At the same time, humans appear to carry a suite of evolved psychological mechanisms aimed (...) at curbing free riding in order to ensure the continued provision of public goods, which can be leveraged to develop more effective measures to promote compliance with regulations. We also highlight factors beyond free riding that reduce compliance rates, such as the emergence of conspiratorial thinking, which seriously undermine the effectiveness of measures to suppress free riding. Together, the current paper outlines the social dynamics that occur in public goods dilemmas involving the spread of infectious disease, highlights the utility and limits of evolutionary game-theoretic approaches for COVID-19 management, and suggests novel directions based on emerging challenges to cooperation. (shrink)

During a cultural festival, artists and theaters act as a cartel by agreeing on pricing decisions that maximize the groups’ profit as a whole. We model the problem of sharing the profit created by a festival among organizing theaters as a cooperative game. In such a game, the worth of a coalition is defined as the theaters’ profit from the optimal fixation of prices. We show that this class of games is convex and we axiomatically characterize the Shapley (...) value for this class of games. We also provide an axiomatic basis for the downstream incremental solution. Finally, we apply this model to the NEXT festival, for which we have collected data. We propose an approach to derive the games’ vector from the data and we compute the different solutions. (shrink)

The game theoretical approach to R&D cooperation does not investigate the role of trust in the initiation and success of R&D cooperation: it either assumes that firms are non-opportunists or that the R&D cooperation is supported by an incentive mechanism that eliminates opportunism. In contrast, the present paper focuses on these issues by introducing incomplete information and two types of firms: opportunist and non-opportunist. Defining trust as the belief of each firm that its potential collaborator will (...) respect the contract, it identifies the trust conditions under which firms initiate R&D alliances and contribute to their success. The higher the spillovers, the higher the level of trust required to initiate R&D cooperation for non-opportunists, while the inverse holds for opportunists. (shrink)

Evolutionary game theory is ethically neutral: its assumption of ‘rationality’ has nothing to do with selfishness but is in fact entirely compatible with altruism. If altruism has an evolutionary explanation then this fact is of no theological relevance: in particular it is not any sort of evidence of a divine plan etc.

In this paper, I will discuss why in some circumstances people express their intentions indirectly: the use of Indirect Speech Acts. Based on Parikh’s games of partial information and Franke’s IBR model, I develop game-theoretic models of ISAs, which are divided into two categories, namely non-conventional ISAs and conventional ISAs. I assume that non-conventional ISAs involve two types of communication situations: communication under certain cooperation and that under uncertain cooperation. I will analyse the cases of ironical (...) request and implicit bribery as typical instances of non-conventional ISAs of each situation type, respectively. I then apply the models to analyse the use of conventional ISAs from an evolutionary perspective, which is inspired by Lewisian convention theory. The models yield the following predictions: the use of non-conventional ISAs under certain cooperation relies on the sympathy between interlocutors, which blocks their evolution towards conventional ISAs; in unc... (shrink)

Game-Theoretic Models of Bargaining provides a comprehensive picture of the new developments in bargaining theory. It especially shows the way the use of axiomatic models has been complemented by the new results derived from strategic models. The papers in this volume are edited versions of those given at a conference on Game Theoretic Models of Bargaining held at the University of Pittsburgh. There are two distinct reasons why the study of bargaining is of fundamental importance in (...) economics. The first is that many aspects of economic activity are directly influenced by bargaining between and among individuals, firms, and nations. The second is that bargaining occupies an important place in economic theory, since the 'pure bargaining problem' is at the opposite pole of economic phenomena from the case of 'perfect competition'. This volume is an outgrowth of the renewed interest in the strategic approach to the theory of bargaining and to the general theory of non-cooperative games. (shrink)

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)

This is an entry into the contemporary debate over contractarian theories of political obligation, with a particular focus on the "liberal" feminist critiques. It analyzes three prominent feminist critics of contractarianism, Susan Moller Okin, Carole Pateman and Nancy Hirschmann, selected because they each try to remain within the main premises and methodology of contractarian liberalism. The conclusion is that Okin's critique is too generous, Pateman's is radically incomplete, and Hirschmann's is too radical. ;It reviews the few remarks in the works (...) of Thomas Hobbes directed to issues of gender and families, and speculates that his originality might have been stimulated by a contemporary debate about gender in Seventeenth Century England. An appendix reviews the debate for its political contents. ;The analysis then turns to contractarianism in the contemporary mode of game theory. The contractarian exercise establishes the state of nature scenario, introduces male and female players, and characterizes the females as smaller, weaker, and vulnerable in childbirth and nursing. It then varies the players' moral psychologies along the egoism/altruism continuum. The exercise then applies the assumptions of contractarian game theory to analyze how a two-gender population would deal with the problems of violence and heterosexual sexual intercourse. The analysis concludes that the best strategy for females in contractarian terms is collective action and that institutions of the social contract state can be evaluated according to whether the institutions inhibit or advance that possibility. It then applies such an analysis to the theories of Robert Nozick and John Rawls and finally to three institutions of the liberal contractarian state: territorial representation, sexual individualism and individualism in employment. ;The work concludes that both theories and institutions are inadequate to provide for gender equality, because each is hostile to female collective action, the theories because of their insistence on the primacy of freedom over equality and the institutions because of their particular effects on the elements of cooperation. (shrink)

The conceptual foundations, features, and scope of the notion of rationality are increasingly being affected by developments in embodied cognitive science. This article starts from the idea of embodied rationality, and aims to develop a frame in which a debate with the classical, possibly bounded, notion of rationality-as-consistency can take place. To this end, I develop a game theoretic description of a real time interaction setup in which participants' behaviors can be used to compare the enactive approach, which (...) underlies embodied rationality, with game theoretic approaches to human interaction. The Perceptual Crossing Paradigm is a minimal interaction interface where two participants each control an avatar on a shared virtual line, and are tasked with cooperatively finding each other among distractor objects. It is well known that the best performance on this task is obtained when both participants let their movements coordinate with the objects they encounter, which they do without any prior knowledge of efficient interaction strategies in the system. A game theoretic model of this paradigm shows that this task can be described as an Assurance game, which allows for comparing game theoretical approaches and the enactive approach on two main fronts. First, accounting for the ability of participants to interactively solve the Assurance game; second, accounting for the evolution of choice landscapes resulting from evolving normative realms in the task. Similarly to the series of paradoxes which have fueled debates in economics in the past century, this analysis aims to serve as an interpretation testbed which can fuel the current debate on rationality. (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in (...) terms of those games. The measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation . New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling . Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19 , 95–125). (shrink)

Hobbes’s own justification for the existence of governments relies on the assumption that, without a government, our lives in the state of nature would result in a state of war of every man against every man. Many contemporary scholars have tried to explain why universal war is unavoidable in Hobbes’s state of nature by utilizing modern game theory. However, most game-theoretic models that have been presented so far do not accurately capture what Hobbes deems to be the (...) primary cause of conflict in the state of nature – which is uncertainty, rather than people’s egoistic psychology. Any game- theoretic model that does not incorporate uncertainty into the picture is, therefore, I claim, the wrong model. In this paper, I use Bayesian game-theory to show how universal conflict can break-out in the state of nature - even when the majority of the population would strictly prefer to cooperate and seek peace with other people - due to uncertainty about the other person’s type. Along the way, I show that the valuation of one’s own life is one of the central mechanisms that drives Hobbes’s pessimistic conclusion. (shrink)

In recent years, a number of authors have used gametheoretic reasoning to explain why purely self-interested agentswould ever conform their economic activities with the requirements of justice, when by doing so they forego opportunities to reapunilateral net gains by exploiting others. In this paper, I argue that Hume's justification of honest economic exchanges between self-interested agents in the Treatise foreshadows this contemporary literature. Hume analyzes the problem of explaining justice in self-interested economic exchange as a problem of agents coordinating on (...) a pattern of reciprocal cooperation, as opposed to some other behavioral pattern such as reciprocal exploitation, in exchanges repeated over time. Hume's arguments anticipate informally thecontemporary interpretation of just economic practices as forming part of an equilibrium of a repeated game. I close the paper by arguing that Hume does not provide a satisfactory explanation of how the mutual expectations that support justice in economic exchange arise in a community of self-interested agents. The problem Hume leaves unsolved is one of equilibrium selection, that is: Why do agents follow an equilibrium corresponding to just economic exchanges rather than some other equilibrium corresponding to unjust exchanges? I also argue that contemporary game theory still lacks a satisfactory theory of equilibrium selection, but that such a theory would lead us closer to a satisfactory Humean reconciliation of justice and self-interest in economic exchange. (shrink)

Game experiments designed to test the effectiveness of reward and/or punishment incentives in promoting cooperative behavior among their participants are quite common. Results from two such recent experiments conducted in Beijing, based on the Prisoner’s Dilemma (PD) game and Public Goods Game respectively, are summarized here. The unexpected empirical outcomes for the repeated PD game, that cooperation actually decreased when the participants had the option of using a costly punishment strategy and that participants who used (...) costly punishment in some round of the repeated game often did so in the first round, are discussed in terms of differences in attitudes toward reputation in Chinese culture compared to other locations (mostly in Western society) where similar experiments have been conducted. The second experiment models an institution providing incentives to increase contribution levels (i.e., cooperation) to the public good. The results show that combined institutional reward and punishment is the most effective means to increase cooperation, followed by a scheme using only punishment. It is shown how these empirical results are related to the theoretical predictions that assume players play rationally by optimizing their personal payoff given their opponents’ actions in these multi-player games. (shrink)

The Nash counterfactual considers the question: what would happen were I to change my behaviour assuming no one else does. By contrast, the Kantian counterfactual considers the question: what would happen were everyone to deviate from some behaviour. We present a model that endogenizes the decision to engage in this type of Kantian reasoning. Autonomous agents using this moral framework receive psychic payoffs equivalent to the cooperate-cooperate payoff in Prisoner’s Dilemma regardless of the other player’s action. Moreover, if both interacting (...) agents play Prisoner’s Dilemma using this moral framework, their material outcomes are a Pareto improvement over the Nash equilibrium. (shrink)

Universal social institutions, such as marriage, commons management and property, have emerged independently in radically different cultures. This requires explanation. As Boyer and Petersen point out ‘in a purely localist framework would have to constitute massively improbable coincidences’ . According to Boyer and Petersen, those institutions emerged naturally out of genetically wired behavioural dispositions, such as marriage out of mating strategies and borders out of territorial behaviour. While I agree with Boyer and Petersen that ‘unnatural’ institutions cannot thrive, this one-sided (...) explanation of universal social institutions in terms of genetic human nature is unsatisfactory. Drawing on the literature on multi-level selection and gene-culture coevolution, I argue that universal social institutions are first and foremost the products of cultural selection. They occupy fitness peaks in the landscape of cultural possibilities, much in the same way that biological adaptations occupy fitness peaks in the landscape of biological possibilities. To show this, I use game-theory. By modelling the domains of social interaction in which marriage, commons management, and property emerged as Prisoner’s dilemma situations, it becomes clear how an institutional framework allows the group to move to an interactive equilibrium with a larger payoff. Institutions do so by incentivising all parties to adopt a cooperative strategy. They are culturally selected ways of optimising genetically constrained domains of human social interaction. (shrink)

In the literature on logics of imperfect information it is often stated, incorrectly, that the Game-Theoretical Semantics of Independence-Friendly quantifiers captures the idea that the players of semantical games are forced to make some moves without knowledge of the moves of other players. We survey here the alternative semantics for IF logic that have been suggested in order to enforce this “epistemic reading” of sentences. We introduce some new proposals, and a more general logical language which distinguishes between “independence (...) from actions” and “independence from strategies”. New semantics for IF logic can be obtained by choosing embeddings of the set of IF sentences into this larger language. We compare all the semantics proposed and their purported game-theoretical justifications, and disprove a few claims that have been made in the literature. (shrink)

Most definitions of cooperation provide sufficient but not necessary conditions. This paper describes a form of minimal cooperation, corresponding to mass actions implying many agents, such as demonstrations. It characterizes its intentional, epistemic, strategic, and teleological aspects, mostly obtained from weakening classical concepts. The rationality of minimal cooperation turns out to be part of its definition, whereas it is usually considered as an optional though desirable feature. Game-theoretic concepts thus play an important role in its (...) definition. The paper concludes by answering concrete questions about what should and should not be called cooperation. (shrink)

We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, (...) studies, and characterizes a natural method of associating coalitional interval games with strategic games. (shrink)

Cooperation admits of degrees. When factory workers stage a slowdown, they do not cease to cooperate with management in the production of goods altogether, but they are not fully cooperative either. Full cooperation implies that participants in a joint action are committed to rendering appropriate contributions as needed toward their joint end so as to bring it about, consistently with the type of action and the generally agreed upon constraints within which they work, as efficiently as they can, (...) where their contributions are sensitive to information (where available) about how others are contributing in the sense that they adjust as needed their contributions in light of information about how others are contributing to ensure effective pursuit of their joint end, where this includes rendering aid to other participants if needed, insofar as they are able. Full cooperation entails those cooperating are engaged in a joint intentional action. Some prominent studies of joint intentional action focus exclusively on cases of full cooperation (notably that of Michael Bratman (2014)). But not all joint intentional action is fully cooperative. One example is the work slowdown. Another example is provided by competitive games like chess and football, or sports like boxing and wrestling, where participants are clearly not intending to contribute to the pursuit of all of the goals of the others engaged in the activity, even when those goals are internal to the type of activity in question, but instead intend actively to frustrate some of them. In this paper, I provide a taxonomy of forms of non-cooperative behavior within the context of behavior that is still to some degree cooperative, and I argue that the minimal conditions of joint intentional action define minimal cooperative behavior, that is, that minimally joint intentional action is per se minimally cooperative behavior. I define in precise terms what that comes to, and how it is possible in cases in which it seems that one or more participants are in one or more ways acting so as to frustrate the contributions of other participants to their joint action. (shrink)

Steven Pinker proposes a game-theoretic framework to help explain the use of veiled speech in contexts where the ultimate aims of the speaker and hearer may diverge—such as cases of bribing a police officer to get out of a ticket and paying a maître d’ to get a table. This is presented as a response to what Pinker sees as the failure in H. P. Grice’s influential theory of meaning to recognize that speakers and hearers are not always (...) cooperating. In this paper I argue that Pinker mischaracterizes Grice’s views on cooperation, and use this to refine a positive picture of what sort of cooperation is demanded by Grice’s Cooperative Principle. This positive picture serves to insulate the Gricean framework from objectors—including Pinker—who overstate the obligations entailed by the adoption of the Cooperative Principle. I then argue that the cases Pinker presents are best treated by recognizing that in each instance the utterance is formulated with two intentions towards two different audiences and detail a resulting revision to Pinker’s game-theoretic framework that reflects this proposal. I conclude by demonstrating how this proposed game-theoretic framework of cooperation with multiple audiences can be used to model the costs and benefits of other types of discourse, including political speech. (shrink)

We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, (...) studies, and characterizes a natural method of associating coalitional interval games with strategic games. (shrink)

Fundamental problems of environmental sustainability, including climate change and fisheries management, require collective action on a scale that transcends the political and cultural boundaries of the nation-state. Rational, self-interested neoclassical economic theories of human behavior predict tragedy in the absence of third party enforcement of agreements and practical difficulties that prevent privatization. Evolutionary biology offers a theory of cooperation, but more often than not in a context of discrimination against other groups. That is, in-group boundaries are necessarily defined by (...) those excluded as members of out-groups. However, in some settings human’s exhibit behavior that is inconsistent with both rational economic and group driven cooperation of evolutionary biological theory. This paper reports the results of a non-cooperative game-theoretic exercise that models a tragedy of the commons problem in which groups of players may advance their own positions only at the expense of other groups. Students enrolled from multiple universities and assigned to different multi-university identity groups participated in experiments that repeatedly resulted in cooperative outcomes despite intergroup conflicts and expressions of group identity. We offer three possible explanations: students were cooperative because they were in an academic setting; students may have viewed their instructors as the out-group; or the emergence of a small number of influential, ethical leaders is sufficient to ensure cooperation amongst the larger groups. From our data and analysis, we draw out lessons that may help to inform approaches for institutional design and policy negotiations, particularly in climate change management. (shrink)

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose a bargaining model based on the (...) benefit-equilibrating bargaining solution concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'. (shrink)

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of this thesis is to (...) enrich the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden, and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions. (shrink)

This article considers the political significance of game theoretical notions of cooperation by responding theologically to the writings of David Willetts, a minister in the UK government. The argument is that the forms of cooperative institutional life which societies require can be neither explained nor planned for solely by mathematical modelling of rational self-interest. What altruistic, civic cooperation depends upon is a complex web of affective trust, often theologically formed by open-handed faith rather than a self-protective pinch, (...) so that wise risks may be taken for the sake of future generations. (shrink)

This study aims to reveal the nature and motivation of human cooperation. By adopting the public goods game paradigm of competition and repetition, and introducing factors such as punishment and heterogeneous contributions, an experiment was conducted at Nanjing University in China, where 224 undergraduate students participated in seven games, including intragroup and intergroup competition. Meanwhile, participants’ social value orientation (SVO) was measured. The results indicated that cooperation (non-zero contribution) was the common choice for participants, but their contributions (...) varied across rounds and games. Individuals generally act as conditional free-riders in intragroup competition games, i.e., they use the “small for big” strategy. In contrast, individuals generally act as conditional cooperators in intergroup competitive games, i.e., they use the “tit for tat” strategy. Although SVO should theoretically be related to contribution, analysis revealed that participants’ contributions were not significantly dominated by SVO, but were primarily driven by self-interest. Specifically, individuals switch back and forth between conditional cooperators and conditional free-riders to seek maximum self-interest. Our results not only reveal the complexity and strategic nature of human behavior in competitive contexts but also highlight the central role of self-interest in driving individual decision-making, reflecting the balance between individuals’ pursuit of self-interest and adaptation to the environment in social interactions. (shrink)

Economists interpret global environmental quality to be a pure public good. Each country should contribute to its provision. However, this is hard to achieve because each government is tempted to take a free ride on the other governments' efforts. Not only has this dilemma been analysed with game theoretical methods but game theory has also been used to think about how to make amends. This paper reviews the game theoretical discussion on how international policy frameworks may be (...) designed to improve the chances for international cooperation. It is also shown that the evaluation of alternative environmental policy instruments deviates from the standard environmental economics model if applied to the international arena. For the benefit of an interdisciplinary readership, the evolution of the debate on global environmental policy is related to the recent history of economic thought. This history is taken to be materialised in the writings of economics' Nobel Prize laureates. (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)

In game-theoretic signaling models, evolution tends to favor perfectly precise signaling systems, but in the natural world communication is almost always imprecise. I argue that standard explanations for this discrepancy are only partially sufficient, and I show that communication is often ambiguous because signal senders take advantage of context sensitivity. As evidence, I make two additions to the signaling model: a cost for more complex signaling strategies and the ability to combine information in signals with independent information. Analysis (...) and simulation of the altered model shows that it leads to the predicted outcome of evolution favoring ambiguous signaling. (shrink)

The aim of this paper is to critically review the game-theoretic discussion of Hobbes and to develop a game-theoretic interpretation that gives due attention both to Hobbes's distinction between “moderates” and “dominators” and to what actually initiates conflict in the state of nature, namely, the competition for vital goods. As can be shown, Hobbes's state of nature contains differently structured situations of choice, the game-theoretic representation of which requires the prisoner's dilemma and the assurance (...) game and the so-called assurance dilemma. However, the “state of war” ultimately emerges from situations that cannot be described by any of these games because they represent zero-sum games in which the outcome of mutual cooperation does not exist. (shrink)

When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call (...) such games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically. (shrink)

Why do people stay together in monogamous relationships? Love? Fear? Habit? Ethics? Integrity? Desperation? In this paper I will consider a rather surprising answer that comes from mathematics. It turns out that cooperative behaviour, such as mutually-faithful marriages, can be given a firm basis in a mathematical theory known as game theory. I will suggest that faithfulness in relationships is fully accounted for by narrow self interest in the appropriate game theory setting. This is a surprising answer because (...) faithful behaviour is usually thought to involve love, ethics, and caring about the well being of your partner. It seems that the game-theory account of faithfulness has no need for such romantic notions. I will consider the philosophical upshot of the game-theoretic answer and see if it really does deliver what is required. Does the game-theoretic answer miss what is important about faithful relationships or does it help us get to the heart of the matter? Before we start looking at lasting, faithful relationships, though, let’s get a feel for how mathematics might be employed to help in matters of the heart. Let’s first consider how mathematics might shed light on dating to find a suitable partner. (shrink)

I discuss what learned and innate routines of self and other attribution agents need to possess if they are to enter into cooperative arrangements as described game theoretically. I conclude that these are not so different from belief desire psychology as described by philosophers of mind.

When game theory was introduced to biology, the components of classic game theory models were replaced with elements more befitting evolutionary phenomena. The actions of intelligent agents are replaced by phenotypic traits; utility is replaced by fitness; rational deliberation is replaced by natural selection. In this paper, I argue that this classic conception of comprehensive reapplication is misleading, for it overemphasizes the discontinuity between human behavior and evolved traits. Explicitly considering the representational roles of evolutionary game theory (...) brings to attention neglected areas of overlap, as well as a range of evolutionary possibilities that are often overlooked. The clarifications this analysis provides are well-illustrated by—and particularly valuable for—game theoretic treatments of the evolution of social behavior. (shrink)

Orbell and Dawes develop a non-game theoretic heuristic that yields a ‘cooperator's advantage’ by allowing players to project their own ‘cooperate-defect’ choices onto potential partners (1991, p. 515). With appropriate parameter values their heuristic yields a cooperative environment, but the cooperation depends, simply, on optimism about others' behavior (1991, p. 526). In earlier work, Dawes (1989) established a statistical foundation for such optimism. In this paper, I adapt some of the concerns of Dawes (1989) and develop a (...) game theoretic model based on a modification of the Harsanyi structure of games with incomplete information (1967–1968). I show that the commonly made conjecture that strategic play is incompatible with cooperation and the cooperator's advantage is false. (shrink)

Trusting in someone's cooperation is often connected with the danger of being exploited. So it is important that signals are exchanged which make it probable enough that the potential partner is reliable. Such signals must be too expensive for partners who are planning to abuse the trust they are given but cheap enough for those who wish to initiate a long-term cooperation. In a game theoretical model, it is shown that such signals could consist of presents given (...) before the partnership starts. (edited). (shrink)

How do people survive under extreme conditions? Will selfish, non-cooperating free-rider types – the solo players – have the best chances of surviving? Or would cooperating, hard-working types – the team players – have higher chances? All morale put aside, it is interesting to know whether non-cooperation or cooperation pays off in a game characterized by scarcity and hard competition for survival. A study of people in such a Hobbesian state of nature can also teach us important (...) lessons about social dynamics in contemporary, prosperous societies. An interesting case of ‘The survival game’ can be found in Solzhenitsyn’s (1963 [1962]) self-biographical book, One Day in the Life of Ivan Denisovich, depicting life in a Soviet Gulag prison camp in Siberia January 1951. We use Solzhenitsyn’s work as evidence of the interplay between five player types among prisoners: Cooperative blind-riders (BRs), hard-riders (HRs) and tough-riders (TRs), i.e. the so-called ‘toilers’; non-cooperative easy-riders (ERs), looked upon by the toilers as ‘bastards’, ‘screws’ and ‘errand boys’; and finally Low-riders (LRs), comprising ‘goners’ and ‘jackals’. The main research question addresses the successfulness of the survival strategies of the five player types. Apart from a Multiple Player Approach (MPA) that may be seen as a further development of second-generation theory of collective action (Ostrom & Ahn, 2009), we apply Goffman’s (1959) dramaturgical theory on our case. Hence, we argue that impression management at two different ‘stages’ – the Brigade stage and the Camp stage – is crucial for survival for hard-riding as well as for easy-riding players, in particular strategic masking. Seeking to unite Goffman and game-theoretic MPA, our overall purpose is to make a theoretical contribution to “game-related sociology” (Swedberg, 2001). (shrink)

What is a game? What are we doing when we play a game? What is the value of playing games? Several different philosophical subdisciplines have attempted to answer these questions using very distinctive frameworks. Some have approached games as something like a text, deploying theoretical frameworks from the study of narrative, fiction, and rhetoric to interrogate games for their representational content. Others have approached games as artworks and asked questions about the authorship of games, about the ontology of (...) the work and its performance. Yet others, from the philosophy of sport, have focused on normative issues of fairness, rule application, and competition. The primary purpose of this article is to provide an overview of several different philosophical approaches to games and, hopefully, demonstrate the relevance and value of the different approaches to each other. Early academic attempts to cope with games tried to treat games as a subtype of narrative and to interpret games exactly as one might interpret a static, linear narrative. A faction of game studies, self-described as “ludologists,” argued that games were a substantially novel form and could not be treated with traditional tools for narrative analysis. In traditional narrative, an audience is told and interprets the story, where in a game, the player enacts and creates the story. Since that early debate, theorists have attempted to offer more nuanced accounts of how games might achieve similar ends to more traditional texts. For example, games might be seen as a novel type of fiction, which uses interactive techniques to achieve immersion in a fictional world. Alternately, games might be seen as a new way to represent causal systems, and so a new way to criticize social and political entities. Work from contemporary analytic philosophy of art has, on the other hand, asked questions whether games could be artworks and, if so, what kind. Much of this debate has concerned the precise nature of the artwork, and the relationship between the artist and the audience. Some have claimed that the audience is a cocreator of the artwork, and so games are a uniquely unfinished and cooperative art form. Others have claimed that, instead, the audience does not help create the artwork; rather, interacting with the artwork is how an audience member appreciates the artist's finished production. Other streams of work have focused less on the game as a text or work, and more on game play as a kind of activity. One common view is that game play occurs in a “magic circle.” Inside the magic circle, players take on new roles, follow different rules, and actions have different meanings. Actions inside the magic circle do not have their usual consequences for the rest of life. Enemies of the magic circle view have claimed that the view ignores the deep integration of game life from ordinary life and point to gambling, gold farming, and the status effects of sports. Philosophers of sport, on the other hand, have approached games with an entirely different framework. This has lead into investigations about the normative nature of games—what guides the applications of rules and how those rules might be applied, interpreted, or even changed. Furthermore, they have investigated games as social practices and as forms of life. (shrink)

In Strategic Bargaining and Cooperation in Greenhouse Gas Mitigations, Zili Yang connects these two important approaches by incorporating various game theoretic solution concepts into a well-known integrated assessment model of climate ...

China’s E-commerce market is very active. Despite the impact of COVID-19, the market has ushered in major development opportunities. Alongside, the level of intellectual property protection in China is constantly improving. However, there are relatively few studies on intellectual property protection in the field of E-commerce. This study introduces the theory of social cogovernance and explores the construction of China’s E-commerce intellectual property protection system with the participation of collective organizations. Evolutionary game method is applied to model construction. Through (...) numerical simulation, the study analyzes the evolution of E-commerce platform and collective organization strategic choice. The results depict that improving the open space provided by E-commerce platforms for collective organizations and strengthening their public service capabilities can promote the construction of social cogovernance systems. The establishment of reasonable reward and punishment mechanisms can increase cooperation enthusiasm. We also discuss the theoretical and practical implications for governments, E-commerce platforms, and collective organizations, to improve the level of intellectual property protection in E-commerce. This study can provide suggestions for China’s E-commerce intellectual property protection, improve the overall level of intellectual property protection in China, and provide a reference for global E-commerce intellectual property protection. (shrink)

Two-player, zero-sum, non-cooperative, blindfold games in extensive form with incomplete information are considered in this paper. Any information about past moves which players played is stored in a database, and each player can access the database. A polynomial game is a game in which, at each step, all players withdraw at most a polynomial amount of previous information from the database. We show resource-bounded determinacy of some kinds of finite, zero-sum, polynomial games whose pay-off sets are computable by (...) non-deterministic polynomial-time function-oracle Turing machines. We call a pay-off set -determined if, for any polynomial game G associated with the given pay-off set, either player has a winning strategy which is in for any subgames of G. We show that there exists an FP-strongly-determined pay-off set which is computed by an exponential-time oracle Turing machine, where FP is the set of polynomial-time computable functions. We also discuss several relationships between the determinacy of polynomial games and recursion-theoretic properties for the classes co-NP and co-NEXP. We show that the polynomial version of the axiom of choice holds under some assumption of polynomial determinacy for a pay-off set which is polynomial-time computable with parallel queries. This principle of choice implies that co-NP has the separation property. (shrink)

In this article, I argue that if one closely follows Hobbes' line of reasoning in Leviathan, in particular his distinction between the second and the third law of nature, and the logic of his contractarian theory, then Hobbes' state of nature is best translated into the language of game theory by an assurance game, and not by a one-shot or iterated prisoner's dilemma game, nor by an assurance dilemma game. Further, I support Hobbes' conclusion that the (...) sovereign must always punish the Foole, and even exclude her from the cooperative framework or take her life, if she defects once society is established, which is best expressed in the language of game theory by a grim strategy. That is, compared to existing game-theoretic interpretations of Hobbes, I argue that the sovereign plays a grim strategy with the citizens once society is established, and not the individuals with one another in the state of nature. (shrink)

This article proposes ‘Recursive Consequentialism’: the moral theory which gives agents whatever advice will produce good consequences by being given. It can be thought of as a version of Donald Regan's ‘Cooperative Utilitarianism’ to which two additional elements have been added: allowing people with differing conceptions of ‘good consequences’, e.g., a Utilitarian and a non-Utilitarian, to cooperate with one another, and taking into account the full consequences of accepting, not just complying with, moral guidance. The theory is motivated by a (...) series of game-theoretic examples in which adherence to alternative Consequentialist moral theories produces bad consequences. (shrink)

David Buss’s Sexual Strategies Theory is one of the major evolutionary psychological research programmes, but, as I try to show in this paper, its theoretical and empirical foundations cannot yet be seen to be fully compelling. This lack of cogency comes about due to Buss’s failure to attend to the interactive nature of his subject matter, which leads him to overlook two classic and well known issues of game theoretic and evolutionary biological analysis. Firstly, Buss pays insufficient attention (...) to the fact that, since mate choice is a cooperative decision, what is adaptive for the two sexes individually is irrelevant to the evolutionary explanation of our sexual strategies; instead, all that matters is what is adaptive given the choices made by the other sex. Secondly, Buss does not pay enough attention to the difference between polymorphic and monomorphic evolutionarily stable states in his attempt to empirically confirm his theory. Because of this, the data he presents and analyses are unable to show that natural selection is the most important element in the explanation of the origins of our sexual strategies. In this way, I try to make clear that, at least as things stand now, Buss has failed to provide compelling grounds for thinking that Sexual Strategies Theory can make a major contribution to human psychology. (shrink)

This article reports a comparative test of the central-union theory vis-à-vis several other game-theoretic solution concepts in 3-person sidepayment games. Based on a laboratory experiment, this comparison utilizes nine games in characteristic function form. The solution concepts under test include the equal excess model, the Myerson–Shapley solution, the kernel, and two variants of the central-union theory. With regard to the player's payoffs, results show that the CU-1, CU-2, kernel, and equal excess theories have essentially equal predictive accuracy and (...) that all of these are more accurate than Myerson–Shapley. When the solution concepts are extended and coalition structure probability predictions are incorporated in the test, one version of the central-union theory is overall more accurate than the other solutions. (shrink)

This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow (...) between agents and their environment. The order of explanation is opposite in direction to that adopted in game-theoretic semantics, where sentence semantics (or a notion of valid inference) is derived from winning dialogue strategies. That approach and the current one may, however, be reconcilable, since we focus on cooperative dialogue, whereas the game-theoretic tradition concentrates on adversarial dialogue. (shrink)

Many of the problems we face can usefully be modeled as prisoners’ dilemmas. All the standard game-theoretic solutions to prisoners’ dilemmas lead, in the real world, to assurance games. But too often some aspects of our social interaction are as much obscured by, as illuminated by, game theory. Removing some of the epistemic constraints often accepted by game theorists will enable us to distinguish between productive and destructive prisoners’ dilemmas. Doing so is an important step in (...) understanding the nature of some of our social problems. (shrink)