The aim of the paper is the construction of a distributional model which enables the study of the evolutionary dynamics that arise for symmetric games, and the equilibrium selection mechanisms that originate from such processes. The evolution of probability distributions over the state variables is studied using the Fokker-Planck diffusion equation. Equilibrium selection using the ’’basin of attraction’’ approach, and a selection process suggested by Pontryagin are contrasted. Examples are provided for all generic 2-person symmetric binary choice games. JEL (...) Classification: C78.. (shrink)

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained (...) in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999). (shrink)

Cooperation is the foundation of human social life, but it sometimes requires individuals to choose against their individual self-interest. How then is cooperation sustained? How do we decide when instead to follow our own goals? I develop a model that builds on Bacharach (in: Gold, Sugden (eds) Beyond individual choice: teams and frames in game theory, 2006) ‘circumspect we-reasoning’ to address these questions. The model produces a threshold cost/benefit ratio to describe when we-reasoning players should choose cooperatively. After (...) assumptions regarding player types and beliefs, we predict how the extent of cooperation varies across games. Results from two experiments offer strong support to the models and predictions herein. (shrink)

I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules.

We propose a two-step guessing game to measure the depth of thinking. We apply this method to the P beauty contest game. Using our method, we find that 81% of subjects do not make choice following best response reasoning while the classical method would suggest only 12%. The result suggests that the classical method has the fundamental problem that it cannot distinguish if a submitted number is due to best response reasoning or not. It also suggests that (...) traditional level k analysis falsely attributes some sophistication to random players, and that the degree of false attribution is large. Our procedure provides an alternative way to identify whether the individual has best response reasoning which is essential for any positive level of depth of thinking and differentiates between the depth of thinking and random choice, and hence provides a very different conclusion, which is suggestive of limitations of the classical method. (shrink)

Game theory is central to modern understandings of how people deal with problems of coordination and cooperation. Yet, ironically, it cannot give a straightforward explanation of some of the simplest forms of human coordination and cooperation--most famously, that people can use the apparently arbitrary features of "focal points" to solve coordination problems, and that people sometimes cooperate in "prisoner's dilemmas." Addressing a wide readership of economists, sociologists, psychologists, and philosophers, Michael Bacharach here proposes a revision of game theory (...) that resolves these long-standing problems. In the classical tradition of game theory, Bacharach models human beings as rational actors, but he revises the standard definition of rationality to incorporate two major new ideas. He enlarges the model of a game so that it includes the ways agents describe to themselves their decision problems. And he allows the possibility that people reason as members of groups, each taking herself to have reason to perform her component of the combination of actions that best achieves the group's common goal. Bacharach shows that certain tendencies for individuals to engage in team reasoning are consistent with recent findings in social psychology and evolutionary biology. As the culmination of Bacharach's long-standing program of pathbreaking work on the foundations of game theory, this book has been eagerly awaited. Following Bacharach's premature death, Natalie Gold and Robert Sugden edited the unfinished work and added two substantial chapters that allow the book to be read as a coherent whole. (shrink)

Impossibility theorems for 2-person and majority continuous games on the unit circle are presented. The emphasis is on simple methods, albeit generating new results, to offer insights into the sophisticated results of theorists in topological social choice.

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)

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

How do we prepare engineering students to make ethical and responsible decisions in their professional work? This paper presents an approach that enhances engineering students’ engagement with ethical reasoning by simulating decision-making in a complex scenario. The approach has two principal inspirations. The first is Anthony Weston’s scenario-based teaching. Weston’s concept of a scenario is a situation that changes in response to choices made by participants, according to an inner logic. Scenarios can dynamically explore open-ended complex problems without imposing predetermined (...) results, allowing students to apply their ethical reasoning in a more realistic fashion. The second inspiration is Thi Nguyen’s theory of games. According to Nguyen, games are the “art of agency,” meaning that they provide a structure under which some result is agreed to be valuable, along with prescribed ways of achieving that result, in a relatively low-stakes and temporary social arrangement. By playing many games, Nguyen argues, we can develop a “library of agency,” that is to say, a set of values and means to achieving them that can inform how we make high-stakes decisions in real life. Engaging with carefully designed game scenarios, then, can enable students to practice making ethical decisions within a structured framework, which unfolds in response to their choices, while their decisions are driven by some defined goal. This roleplaying game–based approach thus allows students to build their own ethical libraries of agency, in preparation for professional decision-making. The approach is illustrated using a specific example recently deployed in a seminar on engineered living materials (building materials that incorporate living tissues). The scenario uses techniques from tabletop roleplaying games (e.g. Dungeons & Dragons) for outcome resolution, adventure design, and character creation. Through the game, students practice making difficult decisions in a humanitarian context. (shrink)

Levels of trust and trustworthiness have important externalities for the society. But what exactly do these social concepts reflect? Building upon the argument that in typical real-life social exchanges people act simultaneously as both trustors and trustees, we study the impact of individuals’ social motives (or preferences) on their choices in a dual-role Trust Game (TG). We employ data from a large-scale representative experiment (N = 774), where all subjects played both roles of a binary TG with real monetary (...) incentives. Subjects’ social motives were inferred using their decisions in a Dictator Game and a dual-role Ultimatum Game. Next to self-interest and strategic motives we consider preferences for altruism, spitefulness, egalitarianism and efficiency. We demonstrate that there exists considerable heterogeneity in motives in the TG. Most importantly, among individuals who choose to trust as trustors, social motives can differ dramatically as there is a non-negligible proportion of them who seem to act out of (strategic) self-interest whereas others are driven more by efficiency considerations. Subjects’ elicited trustworthiness, however, can be used to infer such motivations: while the former are not trustworthy as trustees, the latter are. We discuss that research on trust can benefit from adding the second player’s choice in TG designs. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Difficult Road to Deciding on CircumcisionAnonymous TwoAnonymous TwoWhen I got my results back from my noninvasive prenatal testing, NIPT and found out I was going to have a little boy, one of my first thoughts was, "I don't want to circumcise him," which sounds silly because I just found out the gender of my baby and my first thought is about his genitalia. The idea of growing and (...) carrying this perfect little baby for nine months and then hurting him was unthinkable to me. I simply did not want to hurt him. The idea of it made me feel sick. Anytime the subject came up, I would protectively put my hand over my belly. And I do admit there were a lot of times I wished I was having a girl so I didn't have to deal with the circumcision debate.There was a lot of conversation between myself and my husband about it. My husband was adamant about getting it done. He referred to uncircumcised penises as "snake penises" and said our son will be made fun of for being different. He said it would be easier for him to clean and when he's old, he won't have to worry about infection. I would counter with, "well what if he falls in love with a girl from a culture that doesn't circumcise? She will think his penis is weird." The more we talked about it, the more ridiculous it felt thinking that far in advance and all these hypothetical situations he might get in over his penis. My parents wanted it done for religious reasons, but that wasn't a factor for me. My mom kept saying it's in the Bible and it needs to be done. My boss is Jewish and she joked that I could just convert to Judaism and the choice would be taken away from me so I didn't have to stress over it. Everything I read on my mommy groups and sites like Reddit called male circumcision child abuse and stated how barbaric it was. Terms like "genital mutilation" were thrown around a lot, and I didn't want to be part of a group that was seemingly looked down upon by so many.I spent my whole pregnancy saying how much I did not want to circumcise my baby. About a week after he was born and we were starting to get settled, my husband started to call around trying to get him an appointment for circumcision. It was unusual to do it this way, as typically it's done when babies are still in the hospital. But the hospital wasn't doing circumcisions because it was elective, and they weren't doing elective procedures because of COVID. At his first doctor's appointment, I talked to our pediatrician about it. She is Indian and told me she didn't circumcise her boys and said that it was very normal in many parts of the world to not do it. I would watch her pull back the skin to check it for fibers and think, "Is it really that bad to keep it? It's just skin." Our pediatrician didn't do it, as she doesn't perform procedures in the office, and she gave us some names of doctors that were supposed to be doing it. My husband called them all and none of them were doing circumcisions either. Finally, my husband found a doctor, but he was booked out for almost a month and a half. With no other option, we made the appointment. I was not thrilled about it, and made my husband do all the calls and arrange it because I did not agree with it.What made me change my mind about circumcising him was I didn't want him to be different. My husband assured me this was the best choice and he was very concerned our son would be bullied for being different. I have a good friend that is a nurse in a long term care facility currently. I called her and asked if it was really that bad for old men to care... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Advocates, Not Problem ParentsAnonymous TwoNothing could have prepared us for the shock of hearing that our son had a brain tumor.Rob* was 13½, an active, healthy eighth grader, when he developed a headache so bad he couldn’t get out of bed in the morning. We saw the pediatrician three times over the next ten days. On the third visit, after ruling out problems at home, stress at school, strep (...) throat and mono, he sent us for an MRI. When the radiology tech handed me the films and told us to drive back to the pediatrician’s office, I knew we were in trouble. Sure enough, after all the other patients had left, our long–time doctor called us into his tiny office, shut the door and fumbled with the films as he pointed to a white spot that he said was a brain tumor.So began the experience that would change the course of our lives. We remember the diagnosis in detail and relive it in slow motion. We recall packing suitcases, driving to the hospital, waiting to be seen in the emergency room, and walking through doors marked “Pediatric Hematology/Oncology” for the first time.We date everything “BC” (Before Cancer) or “AD” (After Diagnosis). We are grateful every day that [End Page 13] our son is alive, but we know he is forever changed. We are changed: Our nuclear family, our extended family, everyone who knew us and supported us at the time was affected. A pediatric cancer diagnosis is a bomb that shatters your world without warning. If you’re lucky, you can pick up a lot of the pieces, maybe even most of them, but the world you re–enter is never the one you inhabited before.Our doctor delivered the diagnosis to Rob and me at the same time. I’ve thought about this many times and perhaps one day will ask him: Why did he choose to do it that way? Was it a conscious decision or just happenstance? Was it kinder, in the long run—like pulling off a band–aid quickly—or terribly risky? What if I had collapsed at the news? I asked to step into the hall to use the phone. In a state of numbness, I called my husband. He knew we had had an MRI a few hours earlier. “Come quickly,” I said. “There’s a mass.”We chose to go to a top-ranked major medical center and were admitted that evening. A couple of days later, the discovery of tumor markers in Rob’s cerebrospinal fluid and blood confirmed a central nervous system mixed germ cell tumor. We were told he would require six cycles of chemotherapy, followed by six weeks of radiation, and possibly second–look surgery and high-dose chemo with stem cell rescue on top of that. We were given a consent form listing a catalogue of short–and long–term side effects, among them the likelihood of infertility. We were urged to start treatment as soon as possible.By sheer coincidence I had just completed a project for a small, nonprofit organization that existed to inform young adult cancer patients about their fertility rights and options. I knew that infertility concerns were usually pushed aside at diagnosis to make way for other priorities, namely the urgency of starting treatment. And that’s exactly the kind of pressure we were facing.But my husband and I were not ready to sign away our son’s fertility in what felt like a no–confidence vote, a capitulation. We needed to believe that he would survive and put this horror behind him, that he would look forward to marriage and starting a family. We were willing to cede nothing to the disease at this early stage of the game. Was this rational, naive or selfish on our part? I don’t know.The medical team seemed surprised when we asked for a delay in treatment in order to collect sperm samples. They warned that our son’s condition could decline suddenly—and that postponing treatment by even several days might be dangerous. However, at our insistence, they agreed to the delay... (shrink)

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move (...) simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

The paper presents a set of games of competition between two or three players in which reward is jointly determined by a stochastic biased mechanism and players’ choices. More specifically, a resource can be found with unequal probabilities in one of two locations. The first agent is rewarded only if it finds the resource and avoids being found by the next agent in line; the latter is rewarded only if it finds the former. Five benchmarks, based on different psychological and (...) game-theoretic assumptions are derived and their predictions compared to actual behavior of 120, 40, and 48 participants playing repeatedly. Of the five benchmarks—the unique (Nash) equilibrium, reinforcement learning, trust-based efficiency, maximum unpredictability, and regret-based (Impulse Balance) equilibrium—regret for missed opportunities best accounts for the qualitative aspect of participants’ behavior and regret attenuated by randomization best accounts for the quantitative aspect of behavior. (shrink)

Game theory based on rational choice is compared with game theory based on evolutionary, or other adaptive, dynamics. The Nash equilibrium concept has a central role to play in both theories, even though one makes extremely strong assumptions about cognitive capacities and common knowledge of the players, and the other does not. Nevertheless, there are also important differences between the two theories. These differences are illustrated in a number of games that model types of interaction that are (...) key ingredients for any theory of the social contract. (shrink)

We investigate Maker–Breaker games on graphs of size $\aleph _1$ in which Maker’s goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the game on the axiomatic framework. Relating to this, we prove that there is a winning strategy for Maker in the $K_{\omega,\omega _1}$ -game under ZFC+MA+ $\neg $ CH and a winning strategy for Breaker under ZFC+CH. We prove a similar result for the $K_{\omega _1}$ - (...) class='Hi'>game. Here, Maker has a winning strategy under ZF+DC+AD, while Breaker has one under ZFC+CH again. (shrink)

Game theory studies the choices of two or more agents strategically interacting under various conditions. This paper examines two applications of omniscience in game theory. The first has to do with the paradox of altruism. The paradox of altruism results when players, by seeking to maximize the outcomes of other players, bring about inferior outcomes for all the players. Not surprisingly, an omniscient player could not find herself ensnarled in an altruistic paradox. The second application is what Steven (...) Brams has called the “paradox of omniscience”. The paradox of omniscience is the surprising proposition that omniscience disadvantages a player in certain games if her opponent knows that she is omniscient. Contrary to Brams, I argue that there is no resolution of the paradox of omniscience with regard to normal games. Indeed, I show that omniscience is not the only divine property that is a strategic liability in normal games. Omniscience then has a mixed standing in game theory—in some cases a strategic asset; in others, a strategic liability. (shrink)

For decades, discrete choice modelling was practically dominated by only two models: multinomial probit and logit. This paper presents a novel alternative—harmonic choice model. It is qualitatively similar to multinomial probit and logit: if one choice alternative greatly exceeds all (falls below at least one of) other alternatives in terms of utility then it is chosen with probability close to one (zero). Compared to probit and logit, the new model has relatively flat tails and it is steeper (...) in the neighborhood of zero (when all alternatives yield the same utility and the decision maker chooses among them at random). (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)

Issues that arise in using game theory to model national security problems are discussed, including positing nation-states as players, assuming that their decision makers act rationally and possess complete information, and modeling certain conflicts as two-person games. A generic two-person game called the Conflict Game, which captures strategic features of such variable-sum games as Chicken and Prisoners'' Dilemma, is then analyzed. Unlike these classical games, however, the Conflict Game is a two-stage game in which each (...) player can threaten to retaliate — and carry out this threat in the second stage — if its opponent chose noncooperation in the first stage.Conditions for the existence of different pure-strategy Nash equilibria, or stable outcomes, are found, and these results are extended to situations in which the players can select mixed strategies (i.e., make probabilistic threats or choices). Although the Conflict Game sheds light on the rational foundations underlying arms races, nuclear deterrence, and other strategic situations, more detailed assumptions are required to tie this generic game to specific conflicts. (shrink)

Contemporary discussions of the positive relation between rational choice and moral theory are a special case of a much older tradition that seeks to show that mutual agreement upon certain moral rules works to the mutual advantage, or in the interests, of those who so agree. I make a few remarks about the history of discussions of the connection between morality and self-interest, after which I argue that the modern theory of rational choice can be naturally understood as (...) a continuation of this older tradition. I then go on to argue for a controversial three-fold thesis: (1) that grounding a theory of morality in terms of rational self-interest is the only epistemologically respectable way to proceed with the justification of moral principles; (2) that despite this, most of the contemporary explorations of rational choice foundations for moral principles do not work—that the models of rational choice to which they appeal yield less than the substantial results that they are intended to yield; but (3) that if one rethinks just what it means to be rational, one can find in fact a promising way to connect the two—specifically through the development of a theory of genuinely cooperative activity. (shrink)

It is widely believed that experimental results of behavioral game theory undermine standard economic and game theory. This paper suggests that experimental results present serious theoretical modeling challenges, but do not undermine two pillars of contemporary economic theory: the rational actor model, which holds that individual choice can be modeled as maximization of an objective function subject to informational and material constraints, and the incentive compatibility requirement, which holds that macroeconomic quantities must be derived from the interaction (...) and aggregation of individual choices. However, we must abandon the notion that rationality implies self-regarding behavior and the assumption that contracts are costlessly enforced by third parties. (shrink)

The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also from “residual” (...) consumption in the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one). (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 observe that in certain two-player repeated games of incomplete information, where information may be incomplete on both sides, it is possible for an informed player to signal his status as an informed player to the other without revealing any information about the choice of chance. The key to obtaining such a class of games is to relax the assumption that the players’ moves are observable. We show that in such cases players can achieve a kind of signaling that (...) is “zero-knowledge”, in the sense that the other player becomes convinced that her opponent is informed without ever learning the choice of chance. Moreover, such “zero-knowledge signaling” has all of the statistical properties associated with zero-knowledge proofs in intereactive protocols. In particular, under the general assumption that moves are unobservable, such signaling leads to a class of equilibria in repeated games that are separatingin regard to the status of player 1–informed or uninformed–but only for player 2; any other player in a network, being unable to observe the moves of player 2, remains uncertain as to the status of player 1. (shrink)

As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a game. More precisely, dependency graphs play two roles. First, when we say that variable x depends on variable y, (...) then we mean that when a strategy assigns a value to variable x, it can be informed by the value that has been assigned to y. Second, and as a consequence of the first property, they capture a richer and more plausible model of concurrency than the simultaneous-action model implicit in conventional Boolean games. Dependency graphs implicitly define a partial ordering of the run-time events in a game: if x is dependent on y, then the assignment of a value to y must precede the assignment of a value to x; if x and y are independent, however, then we can say nothing about the ordering of assignments to these variables—the assignments may occur concurrently. We refer to Boolean games with dependency graphs as partial-order Boolean games. After motivating and presenting the partial-order Boolean games model, we explore its properties. We show that while some problems associated with our new games have the same complexity as in conventional Boolean games, for others the complexity blows up dramatically. We also show that the concurrency in partial-order Boolean games can be modelled using a closure-operator semantics, and conclude by considering the relationship of our model to Independence-Friendly logic. (shrink)

Nondeterministic models of collective choice posit convergence among the outcomes of simple-majority decisions. The object of this research is to estimate the extent of convergence of majority choice under different procedural conditions. The paper reports results from a computer simulation of simple-majority decision making by committees. Simulation experiments generate distributions of majority-adopted proposals in two-dimensional space. These represent nondeterministic outcomes of majority choice by committees. The proposal distributions provide data for a quantitative evaluation of committee-choice procedures (...) in respect to outcome convergence. Experiments were run under general conditions, and under conditions that restrict committee choice to several game-theoretic solution sets. The findings are that, compared to distributions of voter ideal points, majority-adopted proposals confined to the solution sets demonstrate different degrees of convergence. Second, endogenous agenda formation is a more important obstacle to convergence than the inherent instability of simple-majority rule. Third, if members maximize preferences in respect to agenda formation, a committee choice that approximates the central tendency of the distribution of voter preferences is unlikely. The conclusion is that the most effective way to increase the convergence of majority choice is to restrict the role of individual preferences in agenda formation: identification of proposals to be voted up or down by a committee. (shrink)

It is widely believed that experimental results of behavioral game theory undermine standard economic and game theory. This paper suggests that experimental results present serious theoretical modeling challenges, but do not undermine two pillars of contemporary economic theory: the rational actor model, which holds that individual choice can be modeled as maximization of an objective function subject to informational and material constraints, and the incentive compatibility requirement, which holds that macroeconomic quantities must be derived from the interaction (...) and aggregation of individual choices. However, we must abandon the notion that rationality implies self-regarding behavior and the assumption that contracts are costlessly enforced by third parties. (shrink)

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

This paper introduces a new Ehrenfeucht-Fraïssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating moves played in different models. The game allows Duplicator to delay her choices of the models till the very end of the game, making it easier for her to win. This adds on the toolkit of winning strategies (...) for Duplicator in Ehrenfeucht-Fraïssé type games and opens up new methods for tackling some open problems in descriptive complexity theory. As an application of the class game, it is shown that, if m is a power of a prime, then first order logic augmented with function quantifiers F1n of arity 1 and height n < m can not express that the size of the model is divisible by m. This, together with some new expressibility results for Henkin quantifiers H1n gives some new separation results on the class of finite models among various F1n on one hand and between F1n and H1n on the other. Since function quantifiers involve a bounded type of second order existential quantifiers, the class game solves an open problem raised by Fagin, which asks for some inexpressibility result using a winning strategy by Duplicator in a game that involves more than one coloring round. (shrink)

This paper reports the results of an experiment designed to uncover the stochastic structure of individual preferences over lotteries. Unlike previous experiments, which have presented subjects with pair-wise choices between lotteries, our design allowed subjects to choose between two lotteries or (virtually) any convex combination of the two lotteries. We interpret the mixtures of lotteries chosen by subjects as a measure of the stochastic structure of choice. We test between two alternative interpretations of stochastic choice: the random utility (...) interpretation and the deterministic preferences interpretation. The main findings of the experiment are that the typical subject prefers mixtures of lotteries rather than the extremes of a linear lottery choice set. The distribution of choices does not change between a first and second asking of the same question. We argue that this provides support for the deterministic preferences interpretation over the random utility interpretation of stochastic choice. As a subsidiary result, we find a small proportion of subjects make choices that violate transitivity, but the level of intransitive choice falls significantly over time. (shrink)

The analysis of the play "The Seagull" undertaken in the article is based on an unusual assumption. Chekhov's phrase is known that "after writing a story, you should cross out its beginning and end." What if we apply this "formula" to the dramatic works of Anton Pavlovich and assume that when finishing the plays, Chekhov "left out some part of the text"? The analysis of the "Seagull" is performed directly by the classic tool of directors – the method of effective (...) analysis. The work involved a wide range of facts about the social and everyday realities of the Russian Empire of the late XIX - early XX century. The choice of the play "The Seagull" is due to two reasons. Firstly, it is one of Chekhov's most famous and popular dramas. Interest in it has not waned for many decades, neither the audience nor the directors. Secondly, it is believed that the "Seagull" is read inside and out, and working with it is a challenge for the researcher. The analysis of "The Seagull" allows us to state that Chekhov's formula about "crossing out the beginning and the end" of the story is also applicable to his plays. Moreover, this "crossing out" is made taking into account the principles of classical drama. As a result, the reader is faced with the fact that the "Seagull" can be read in at least two – almost opposite in meaning – ways. The results obtained during the analysis, firstly, give grounds to assume that the case of the "Seagull" is not an isolated one, and Chekhov resorted to similar techniques in his other dramas. Secondly, to conclude that the "dramatic mechanism" of The Seagull is not just an attribute of the author's voice, but actually the path of evolution of classical drama proposed by Chekhov. (shrink)

This paper theoretically and experimentally investigates the behavior of asymmetric players in guessing games. The asymmetry is created by introducing r>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r>1$$\end{document} replicas of one of the players. Two-player and restricted N-player cases are examined in detail. Based on the model parameters, the equilibrium is either unique in which all players choose zero or mixed in which the weak player (r=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=1$$\end{document}) imitates the strong (...) player (r>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r>1$$\end{document}). A series of experiments involving two and three-player repeated guessing games with unique equilibrium is conducted. We find that equilibrium behavior is observed less frequently and overall choices are farther from the equilibrium in two-player asymmetric games in contrast to symmetric games, but this is not the case in three-player games. Convergence towards equilibrium exists in all cases but asymmetry slows down the speed of convergence to the equilibrium in two, but not in three-player games. Furthermore, the strong players have a slight earning advantage over the weak players, and asymmetry increases the discrepancy in choices (defined as the squared distance of choices from the winning number) in both games. (shrink)

Drawing from narratology and design studies, this article makes use of the notions of the ‘implied designer’ and ‘ludic unreliability’ to understand deceptive game design as a specific sub-set of transgressive game design. More specifically, in this text we present deceptive game design as the deliberate attempt to misguide players’ inferences about the designers’ intentions. Furthermore, we argue that deceptive design should not merely be taken as a set of design choices aimed at misleading players in their (...) efforts to understand the game, but also as decisions devised to give rise to experiential and emotional effects that are in the interest of players. Finally, we propose to introduce a distinction between two varieties of deceptive design approaches based on whether they operate in an overt or a covert fashion in relation to player experience. Our analysis casts light on expressive possibilities that are not customarily part of the dominant paradigm of user-centered design, and can inform game designers in their pursuit of wider and more nuanced creative aspirations. (shrink)

To describe simultaneous knowledge updates for different subgroups we propose anepistemic language with dynamic operators for actions. The language is interpreted onequivalence states (S5 states). The actions are interpreted as state transformers. Two crucial action constructors are learning and local choice. Learning isthe dynamic equivalent of common knowledge. Local choice aids in constraining theinterpretation of an action to a functional interpretation (state transformer).Bisimilarity is preserved under execution of actions. The language is applied todescribe various actions in card games.

According to cognitive psychologists, moral decision-making is a dual-process phenomenon involving two types of cognitive processes: explicit reasoning and implicit intuition. Moral development involves training and integrating both types of cognitive processes through a mix of instruction, practice, and reflection. Serious games are an ideal platform for this kind of moral training, as they provide safe spaces for exploring difficult moral problems and practicing the skills necessary to resolve them. In this article, we present Morality Play, a model for the (...) design of serious games for ethical expertise development based on the Integrative Ethical Education framework from moral psychology and the Lens of the Toy model for serious game design. (shrink)

Research showed that action real-time strategy gaming experience is related to cognitive and neural plasticity, including visual selective attention and working memory, executive control, and information processing. This study explored the relationship between ARSG experience and information transmission in the auditory channel. Using an auditory, two-choice, go/no-go task and lateralized readiness potential as the index to partial information transmission, this study examined information transmission patterns in ARSG experts and amateurs. Results showed that experts had a higher accuracy rate than (...) amateurs. More importantly, experts had a smaller stimulus-locked LRP component than amateurs on no-go trials, while the response-locked LRP component on go trials did not differ between groups. Thus, whereas amateurs used an asynchronous information transmission pattern, experts used a reduced asynchronous information transmission pattern or a synchronous pattern where most of processing occurred prior to response execution – an information transmission pattern that supports rapid, error-free performance. Thus, experts and amateurs may use different information transmission patterns in auditory processing. In addition, the information transmission pattern used by experts is typically observed only after long-term auditory training according to past research. This study supports the relationship between ARSG experience and the development of information processing patterns. (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)

The notion of perfect recall in extensive games was introduced by Kuhn (1953), who interpreted it as "equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves''. We provide a characterization and axiomatization of perfect recall based on two notions of memory: (1) memory of past knowledge and (2) memory of past actions.

Thomas Schelling, who wrote the foreword for this book, won the Nobel Prize in economics for "having enhanced our understanding of conflict and cooperation through game-theory analysis." This came after he had taught a course in game theory and rational choice to advanced students and government officials for 45 years. In this book, Robert Dodge provides in language for a broad audience, the concepts that Schelling taught. Armed with Schelling's understanding of game theory methods and his (...) approaches to problems, the general reader can improve daily decision making. Mathematics often make game theory challenging but was not a major part of Schelling's course and is even less of a factor in this book. Along with a summary of the material Schelling presented, included are problems from the course and similar less challenging questions. While considerable analysis is done with the basic game theory tool--the two-by-two matrix--much of the book is descriptive and rational decision-making is explained with stories. Chapter supplements are added to illuminate points presented by Schelling, including writings by Paul Krugman, Thomas Friedman, Steven Levitt, and others. (shrink)

Debreu (American Economic Review 50:186–188, 1960) famously criticized Luce (Individual choice behavior, Wiley, New York, 1959) choice model with what became known as the red-bus blue-bus example: if a choice set contains two distinct alternatives C (car) and B (blue bus) then adding a third alternative A (red bus) that is essentially identical to B does not affect the choice probability of C but reduces the choice probability of B by half. Debreu’s critique highlights the (...) existence of substitution effects violating the principle of independence from irrelevant alternatives—the cornerstone of Luce (Individual choice behavior, Wiley, New York, 1959) choice model. This paper weakens this principle to construct a model of probabilistic choice satisfying Debreu’s critique. (shrink)

Deliberation about what to do in any context requires reasoning about what will or would happen in various alternative situations, including situations that the agent knows will never in fact be realized. In contexts that involve two or more agents who have to take account of each others' deliberation, the counterfactual reasoning may become quite complex. When I deliberate, I have to consider not only what the causal effects would be of alternative choices that I might make, but also what (...) other agents might believe about the potential effects of my choices, and how their alternative possible actions might affect my beliefs. Counterfactual possibilities are implicit in the models that game theorists and decision theorists have developed – in the alternative branches in the trees that model extensive form games and the different cells of the matrices of strategic form representations – but much of the reasoning about those possibilities remains in the informal commentary on and motivation for the models developed. Puzzlement is sometimes expressed by game theorists about the relevance of what happens in a game ‘off the equilibrium path’: of what would happen if what is both true and known by the players to be true were instead false. (shrink)

The Belief Game is a two-person, nonzero-sum game in which both players can do well [e.g., at (3, 4)] or badly [e.g., at (1,1)] simultaneously. The problem that occurs in the play of this game is that its rational outcome of (2, 3) is not only unappealing to both players, especially God, but also, paradoxically, there is an outcome, (3, 4), preferred by both players that is unattainable. Moreover, because God has a dominant strategy, His omniscience does (...) not remedy the situation, though - less plausibly - if man possessed this quality, and God were aware of it, (3, 4) would be attainable.How reasonable is it to use the device of a simple game to argue that nonrevelation by God, and nonbelief by man, are rational strategies? Like any model of a complex reality, the Belief Game abstracts a great deal from the problem that confronts the thoughtful agnostic asking the most profound of existential questions. Yet, to the degree that belief in God is seen as a personal question, conceptualized in terms of a possible relationship one might have with one's Creator, it seems appropriate to try to model this relationship as a game. The most difficult question to answer, I suppose, is, if God exists, what are His preferences in such a game?I have argued that He would first like to be believed, but at the same time not reveal Himself. These goals, in my opinion, are consistent with the role He assumes in many biblical stories, although this is not to say that the Bible offers the final word on philosophical and theological matters in the modern world. Nevertheless, it seems to me to be a logical place from which to start, and the clues it offers on God's preferences seem not contradicted by contemporary events.Of course, the Belief Game supposes that God not only has preferences but makes choices as well. To many people today - myself included - these choices are not apparent. But if He does make them, and in particular chooses not to reveal Himself, I think the Belief Game helps us to understand why nonrevelation is rational. Furthermore, it gives us insight into why, given this choice by God, our own reasons for believing in Him - in a game-theoretic context - may be rendered tenuous. (shrink)

How do people respond to others' accidental behaviors? Reward and punishment for accidents might be depend on the actor's intentions, or instead on the unintended outcomes she brings about. Yet, existing paradigms in experimental economics do not include the possibility of accidental monetary allocations. We explore the balance of outcomes and intentions in a two-player economic game where monetary allocations are made with a "trembling hand": that is, intentions and outcomes are sometimes mismatched. Player 1 allocates $10 between herself (...) and Player 2 by rolling one of three dice. One die has a high probability of a selfish outcome, another has a high probability of a fair outcome, and the third has a high probability of a generous outcome. Based on Player 1's choice of die, Player 2 can infer her intentions. However, any of the three die can yield any of the three possible outcomes. Player 2 is given the opportunity to respond to Player 1's allocation by adding to or subtracting from Player 1's payoff. We find that Player 2's responses are influenced substantially by the accidental outcome of Player 1's roll of the die. Comparison to control conditions suggests that in contexts where the allocation is at least partially under the control of Player 1, Player 2 will punish Player 1 accountable for unintentional negative outcomes. In addition, Player 2's responses are influenced by Player 1's intention. However, Player 2 tends to modulate his responses substantially more for selfish intentions than for generous intentions. This novel economic game provides new insight into the psychological mechanisms underlying social preferences for fairness and retribution. (shrink)

A recurring theme in discussions about the uncertainties of belief is their connection with the uncertainties of chance. Economists, broadly speaking, fall into two groups on this issue. One holds that beliefs can only be taken to correspond to point probabilities in situations that approximate games of chance. The other holds that beliefs should be treated as point probabilities, entering economics via decision theory and emerging as the parameters of consistent choice. I shall call these the traditional view and (...) the Bayesian view respectively. (shrink)

Economists are used to associate the rationality of individual choice behaviour with simple and unchanging individual preference patterns, typically predicting unique behavioural outcomes in a choice situation − leaving little room for probing apparent inconsistencies (except in situations of game-theoretic stratagems used by the choosers), and no provision for analysing genuine dilemmas. The paper comments on the (in this respect) richer contents of two recent extensions of the concept of rational choice: the first involved in Sen’s (...) theory of meta-ranking, and the second implied in Scitovsky’s distinction between “pleasure” and “comfort” as the two constituents of the state of individual welfare. The paper then proceeds to suggest a somewhat similar extension of rationality implied, it is argued, in the idea of “development” or “becoming” as part of a chosen, distinct, and articulated process involved, specifically, in education, or more vaguely, in “modernisation”. The emerging concept of rationality which permits of changes in individual preference patterns consistently, in steps, and in a direction initiated and chosen by the individual himself, is claimed in the paper to be more appropriate for the analysis of choice situations likely to be encountered by rational individuals in a complex developing society. The consistency conditions for individual behaviour permitted by such rich, “directional”, rationality have, however, yet to be specified. (shrink)

The concepts of omniscience and omnipotence are defined in 2 ? 2 ordinal games, and implications for the optimal play of these games, when one player is omniscient or omnipotent and the other player is aware of his omniscience or omnipotence, are derived. Intuitively, omniscience allows a player to predict the strategy choice of an opponent in advance of play, and omnipotence allows a player, after initial strategy choices are made, to continue to move after the other player is (...) forced to stop. Omniscience and its awareness by an opponent may hurt both players, but this problem can always be rectified if the other player is omniscient. This pathology can also be rectified if at least one of the two players is omnipotent, which can override the effects of omniscience. In some games, one player's omnipotence ? versus the other's ? helps him, whereas in other games the outcome induced does not depend on which player is omnipotent. Deducing whether a player is superior (omniscient or omnipotent) from the nature of his game playing alone raises several problems, however, suggesting the difficulty of devising tests for detecting superior ability in games. (shrink)

The interpretation of character motivations is a crucial part of the understanding of many narratives, including those found in video games. This interpretation can be complicated in video games by the player performing the role of a player-character within the game narrative. Such performance finds the player making choices for the character and also interpreting the resulting character actions and their effect on the game's narrative. This can lead to interpretative difficulties for game narratives and their players: (...) if a decision to act is made by the player, is it that the player's own imaginative reasons for acting warrant some narrative interpretations and exclude others? To answer this I argue that we need to investigate the interactive ontology of video game narratives, the notion of game playing as interpretative performance, and the player-character, an artifact through which performance is focused in narrative games. Doing so shows there to be at least two problems with the notion of the correct interpretation of narrative games. Neither of these problems entirely negates the normativity of game narratives, however, and so players are left with the problem of how they might decide which of the possible playings are warranted. I end by making some practical suggestions for the thoughtful and narratively interested game player. (shrink)