We introduce two new iteration games: the game , which is a strengthening of the weak iteration game, and the game , which is somewhat stronger than but weaker than the full iteration game of length ω1. For a countable M elementarily embeddable in some Vη, with two players I and II, we can show that II wins and that I does not win.

How should deontologists approach decision-making under uncertainty, for an iterated decision problem? In this paper I explore the shortcomings of a simple expected value approach, using a novel example to raise questions about attitudes to risk, the moral significance of tiny probabilities, the independent moral reasons against imposing risks, the morality of sunk costs, and the role of agent-relativity in iterated decision problems.

I discuss how simulating another agent can be useful in some game-theoretical situations, particularly iterated games such as the centipede game.

The present study develops an artificial agent that plays the iterative chicken game based on a computational model that describes human behavior in competitive social interactions in terms of fairness. The computational model we adopted in this study, named as the self-concept fairness model, decides the agent’s action according to the evaluation of fairness of both opponent and self. We implemented the artificial agent in a computer program with a set of parameters adjustable by researchers. These parameters allow researchers to (...) determine the extent to which the agent behaves aggressively or cooperatively. To demonstrate the use of the proposed method for the investigation of human behavior, we performed an experiment in which human participants played the iterative chicken game against the artificial agent. Participants were divided into two groups, each being informed to play with either a person or the computer. The behavioral analysis results showed that the proposed method can induce changes in the behavioral pattern of human players by changing the agent’s behavioral pattern. Also, we found that participants tended to be more sensitive to fairness when they played with a human opponent than with a computer opponent. These results support that the artificial agent developed in this study will be useful to investigate human behavior in competitive social interactions. (shrink)

Many weaknesses of game theory are cured by new models that embody simple cognitive principles, while maintaining the formalism and generality that makes game theory useful. Social preference models can generate team reasoning by combining reciprocation and correlated equilibrium. Models of limited iterated thinking explain data better than equilibrium models do; and they self-repair problems of implausibility and multiplicity of equilibria.

In this paper, we investigate processes involving iterative information updating due to van Benthem (Int Game Theory Rev 9: 13—45, 2007), who characterized existent game-theoretic solution concepts by such processes in the framework of Plaza's public announcement logic. We refine this approach and clarify the relationship between stable strategies and information update processes. After extending Plaza's logic, we then derive the conditions under which a stable outcome is determined independently of the order of the iterative information updates. This result gives (...) an epistemic foundation for the order independence of iterated elimination of disadvantageous strategies. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (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)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for (...) L, that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)

Paul Grice has given an account of conversational implicatures that hinges on the hypothesis that communication is a cooperative activity performed by rational agents which pursue a common goal. The attempt to derive Grice’s principles from game theory is a natural step, since its aim is to predict the behaviour of rational agents in situations where the outcome of one agent’s choice depends also on the choices of others. Generalised conversational implicatures, and in particular scalar ones, offer an ideal test (...) bed for this working hypothesis, since with this kind of implicatures the alternative choices available to the agents are less dependent on context, and they can be derived from the meanings of the sentences employed. Some rival game-theoretic accounts of the same phenomena will be criticised. The present paper shows that scalar implicatures can be explained using iterated admissibility, but that some of these need an additional assumption in order to be accounted for. (shrink)

An important approach to game theory is to examine the consequences of beliefs that agents may have about each other. This paper investigates respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A assigns probability 1 to the choice of a given that B chooses a or b. Respect for public preferences requires that if it is common belief that B prefers a (...) to b, then it is common belief that all other agents respect that preference. Along the lines of Blume, Brandenburger and Dekel [3] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that given respect for public preferences and perfect recall, players choose in accordance with Iterated Backward Inference. Iterated Backward Inference is a procedure that generalizes standard backward induction reasoning for games of both perfect and imperfect information. From Asheim’s characterization of proper rationalizability [1] it follows that properly rationalizable strategies are consistent with respect for public preferences; hence strategies eliminated by Iterated Backward Inference are not properly rationalizable. (shrink)

This paper provides a game-theoretic analysis of contrastive focus, extending insights from recent work on the role of noisy communication in prosodic accent placement to account for focus within sentences, sub-sentential phrases and words. The shared insight behind these models is that languages with prosodic focus marking assign prosodic prominence only within elements which constitute material critical for successful interpretation. We first take care to distinguish the information-structural notion of focus from an ontologically distinct notion of givenness marking, and then (...) outline the core properties of focus. We then introduce a signaling game between a speaker and hearer in which the goal is to transmit semantic content with the smallest signal possible. We apply the Iterated Best Response method of Franke to find equilibrium strategies in this game, where a unique equilibrium strategy in this case picks out the “critical information” of an utterance, which by hypothesis constitutes its focus. We show that iterating this game at different syntactic levels of a sentence makes correct predictions about the role of contrast in determining stress within words and phrases, and can be extended to account for association and second occurrence focus effects. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

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)

We isolate two abstract determinacy theorems for games of length $\omega_1$ from work of Neeman and use them to conclude, from large-cardinal assumptions and an iterability hypothesis in the region of measurable Woodin cardinals thatif the Continuum Hypothesis holds, then all games of length $\omega_1$ which are provably $\Delta_1$ -definable from a universally Baire parameter are determined;all games of length $\omega_1$ with payoff constructible relative to the play are determined; andif the Continuum Hypothesis holds, then there is (...) a model of ${\mathsf{ZFC}}$ containing all reals in which all games of length $\omega_1$ definable from real and ordinal parameters are determined. (shrink)

In referendum elections, voters are often required to register simultaneous votes on multiple proposals. The separability problem occurs when a voter’s preferred outcome on one proposal depends on the outcomes of other proposals. This type of interdependence can lead to unsatisfactory or even paradoxical election outcomes, such as a winning outcome that is the last choice of every voter. Here we propose an iterative voting scheme that allows voters to revise their voting strategies based on the outcomes of previous iterations. (...) Using a robust computer simulation, we investigate the potential of this approach to solve the separability problem. (shrink)

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

We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precisely capture the theory of the minimal model for this assumption.

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

This article argues that various deviations from the basic principles of the scientific ethos – primarily the appearance of pseudoscience in scientific communities – can be formulated and explained using specific models of game theory, such as the prisoner’s dilemma and the iterated prisoner’s dilemma. The article indirectly tackles the deontology of scientific work as well, in which it is assumed that there is no room for moral skepticism, let alone moral anti-realism, in the ethics of scientific communities. Namely, (...) on the basis of the generally accepted dictum of scientific endeavor as the pursuit of knowledge exclusively for knowledge’s sake, scientifically »right« behavior is seen to be clearly defined and distinguishable from scientifically »wrong« behavior. After elucidating the basic principles of game theory, the article illustrates – by using imaginary and real cases, as well as some views from the philosophyof biology (the units of selection debate) – how this sort of reasoning could be applied in an analysis of the functioning of science. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealisedexplanation gamein which players collaborate to find the best explanation(s) for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal patterns of (...) variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a (conditionally) optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

When does self-interest counsel cooperation? This question pertains both to the labile behaviors produced by rational deliberation and to the more instinctive and fixed behaviors produced by natural selection. In both cases, a standard starting point for the investigation is the one-shot prisoners' dilemma. In this game, each player has the option of producing one or the other of two behaviors. The pay-offs to the row player are as follows.

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in GL is carried over to CKL. Another important application is to obtain a Gentzen-style sequent calculus formulation of CKL and (...) its cut-elimination. The faithful embedding theorem is proved for the KD4-type propositional CKL and GL, but it holds for some variants of them. (shrink)

Let o(κ) denote the Mitchell order of κ. We show how to reduce long games which run to the first ordinal admissible in the play, to iteration games on models with a cardinal κ so that (1) κ is a limit of Woodin cardinals: and (2) o(κ) = κ⁺⁺. We use the reduction to derive several optimal determinacy results on games which run to the first admissible in the play.

We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation properties in countable support iterations in the so-called Case A that does not need a division into forcings that add reals and those who do not.

Evolutionary applications of game theory present one of the most pedagogically accessible varieties of genuine, contemporary theoretical biology. We present here Oyun (OY-oon, http://charlespence.net/oyun), a program designed to run iterated prisoner’s dilemma tournaments, competitions between prisoner’s dilemma strategies developed by the students themselves. Using this software, students are able to readily design and tweak their own strategies, and to see how they fare both in round-robin tournaments and in “evolutionary” tournaments, where the scores in a given “generation” directly determine (...) contribution to the population in the next generation. Oyun is freely available, runs on Windows, Mac, and Linux computers, and the process of creating new prisoner’s dilemma strategies is both easy to teach and easy for students to grasp. We illustrate with two interesting examples taken from actual use of Oyun in the classroom. (shrink)

This paper proposes a logical framework for representing static and dynamic properties of different kinds of individual and collective attitudes. A complete axiomatization as well as a decidability result for the logic are given. The logic is applied to game theory by providing a formal analysis of the epistemic conditions of iterated deletion of weakly dominated strategies (IDWDS), or iterated weak dominance for short. The main difference between the analysis of the epistemic conditions of iterated weak dominance (...) given in this paper and other analysis is that we use a semi-qualitative approach to uncertainty based on the notion of plausibility first introduced by Spohn, whereas other analysis are based on a quantitative representation of uncertainty in terms of probabilities. (shrink)

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

This paper forges links between early analytic philosophy and the posits of semiotics. I show that there are some striking and potentially quite important, but perhaps unrecognized, connections between three key concepts in Wittgenstein’s middle and later philosophy, namely, complex, rule-following, and language games. This reveals the existence of a conceptual continuity between Wittgenstein’s “early” and “later” philosophy that can be applied to the analysis of the iterability of representation in computer-generated images. Methodologically, this paper clarifies to at least (...) some degree, the nature, progress and promise of an approach to doing philosophy and semiotics from a modally modest perspective that sees in the intellectual products of humanities, and not in unreflective empiricism, the future of scientific development. This hybrid, non-reductionist approach shows, among other things, that semiotic processes are encoded by specific types of complexes in computer-generated images that display iterability in time and space. (shrink)

We introduce possibilistic beliefs into strategic games, describing a player’s belief about his opponents’ strategies as the set of their strategies he regards as possible. We formulate possibilistic strategic games where each player has preferences over his own strategies conditional on his possibilistic belief about his opponents’ strategies. We define several solution concepts for possibilistic strategic games such as (strict) equilibria, rationalizable sets, iterated elimination of never-best responses, and iterated elimination of strictly dominated strategies, and (...) we study their properties and relationships. We develop a class of possibilistic strategic games called possibilistic supermodular games to relate supermodular games to possibilistic strategic games. Lastly, we discuss a direction of extending our possibilistic framework to games with incomplete information. (shrink)

In a recent contribution in this journal, Sascia Pavan proposed a new game theoretic approach to explain generalized conversational implicatures in terms of general principles of rational behavior. His approach is based on refining Nash equilibrium by a procedure called iterated admissibility. I would like to strengthen Pavan’s case by sketching an epistemic interpretation of iterated admissibility, so as to further our understanding of why iterated admissibility might be a good approximation of pragmatic reasoning. But the explicit (...) epistemic view taken here also points to some shortcomings of his approach in comparison to rivaling accounts. (shrink)

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

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as (...) processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation. (shrink)

We show that for solvable games, the calculation of the strategies which survive iterative elimination of dominated strategies in normal games is equivalent to the calculation of the backward induction outcome of some extensive game. However, whereas the normal game form does not provide information on how to carry out the elimination, the corresponding extensive game does. As a by-product, we conclude that implementation using a subgame perfect equilibrium of an extensive game with perfect information is equivalent to (...) implementation through a solution concept which we call guided iteratively elimination of dominated strategies which requires a uniform order of elimination. Journal of Economic Literature Classifica-. (shrink)

Designing complex products involves working with uncertainties as the product, the requirements and the environment in which it is used co-evolve, and designers and external stakeholders make decisions that affect the evolving design. Rather than being held back by uncertainty, designers work, cooperate and communicate with each other notwithstanding these uncertainties by making assumptions to carry out their own tasks. To explain this, the paper proposes an adaptation of Kendall Walton’s make-believe theory to conceptualise designing as playing games of (...) make-believe by inferring what is required and imagining what is possible given the current set of assumptions and decisions, while knowing these are subject to change. What one is allowed and encouraged to imagine, conclude or propose is governed by socially agreed rules and constraints. The paper uses jet engine component design as an example to illustrate how different design teams make assumptions at the beginning of design activities and negotiate what can and cannot be done with the design. This often involves iteration – repeating activities under revised sets of assumptions. As assumptions are collectively revised, they become part of a new game of make-believe in the sense that there is social agreement that the decisions constitute part of the constraints that govern what can legitimately be inferred about the design or added to it. (shrink)

We show that for solvable games, the calculation of the strategies which survive iterative elimination of dominated strategies in normal games is equivalent to the calculation of the backward induction outcome of some extensive game. However, whereas the normal game form does not provide information on how to carry out the elimination, the corresponding extensive game does. As a by-product, we conclude that implementation using a subgame perfect equilibrium of an extensive game with perfect information is equivalent to (...) implementation through a solution concept which we call guided iteratively elimination of dominated strategies which requires a uniform order of elimination. Journal of Economic Literature Classification Number: C72. (shrink)

We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in J Semant 15(2):115–162, 1998 , J Semant 17(3):189–216, 2000 ) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217–242, 2000 ), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence (...) of bidirectional optimality and the former, and show based on numerical simulations that bidirectional optimization may be thought of as a process of reinforcement learning with lateral inhibition. (shrink)

An important approach to game theory is to examine the consequences of beliefs that rational agents may have about each other. This paper considers respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A considers the choice of a “infinitely more likely” than the choice of B; equivalently, if A assigns probability 1 to the choice of a given that B chooses a (...) or b. Respect for public preferences requires that if it is common belief that B prefers a to b, then it is common belief that all other agents respect that preference. Along the lines of Blume, Brandenburger and Dekel [4] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that if respect for public preferences and perfect recall obtains, then players choose in accordance with Iterated Backward Inference. Iterated Backward Inference is a procedure that generalizes standard backward induction reasoning for games of both perfect and imperfect information. From Asheim’s characterization of proper rationalizability [1] it follows that properly rationalizable strategies are consistent with respect for public preferences; hence strategies eliminated by Iterated Backward Inference are not properly rationalizable. (shrink)

Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition ‘strong rationalizability’), then the true (or actual) strategy profile is path equivalent to a (...) Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C8 , the set of profiles that survive the iterative deletion of inferior profiles. (shrink)

Weakly acyclic games form a natural generalization of the class of games that have the finite improvement property. In such games one stipulates that from any initial joint strategy some finite improvement path exists. We classify weakly acyclic games using the concept of a scheduler introduced in Simon and Apt. We also show that finite games that can be solved by the iterated elimination of never best response strategies are weakly acyclic. Finally, we explain (...) how the schedulers allow us to improve the bounds on finding a Nash equilibrium in a weakly acyclic game. (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 argues that various deviations from the basic principles of the scientific ethos – primarily the appearance of pseudoscience in scientific communities – can be formulated and explained using specific modelsof game theory, such as the prisoner’s dilemma and the iterated prisoner’s dilemma. The article indirectly tackles the deontology of scientific work as well, in which it is assumed that there is no room for moral skepticism, let alone moral anti-realism, in the ethics of scientific communities. Namely, on (...) the basis of the generally accepted dictum of scientific endeavor as the pursuit of knowledge exclusively for knowledge’s sake, scientifically »right« behavior is seen to be clearly defined and distinguishable from scientifically »wrong« behavior. After elucidating the basic principles of game theory, the article illustrates – by using imaginary and real cases, as well as some views from the philosophyof biology – how this sort of reasoning could be applied in an analysis of the functioning of science.U članku se tvrdi da se različite devijacije od osnovnih načela etosa znanosti – prije svega pojava pseudoznanosti u znanstvenim zajednicama – mogu formulirati i objasniti pomoću specifičnih modela teorije igara kao što su zatvorenikova dilema i ponovljena zatvorenikova dilema. Članak se, prema tome, neizravno bavi i deontologijom znanstvenoga rada, pri čemu je ključna pretpostavka da u etici znanstvenih zajednica nema mjesta moralnom skepticizmu, a kamoli moralnom antirealizmu: naime, znanstveno »ispravno« ponašanje smatra se jasno definiranim i razlučivim od znanstveno »pogrešnog« ponašanja na osnovi općeprihvaćene maksime znanstvenoga rada kao potrage za znanjem isključivo radi znanja. Nakon izlaganja osnovnih načela teorije igara, pokazuje se – koristeći se imaginarnim i zbiljskim slučajevima, kao i nekim stavovima iz filozofije biologije – kako bi se ovu vrstu razmišljanja moglo primijeniti u analizi funkcioniranja znanosti. (shrink)

Theory-of-mind (ToM) involves modeling an individual’s mental states to plan one’s action and to anticipate others’ actions through recursive reasoning that may be myopic (with limited recursion) or predictive (with full recursion). ToM recursion was examined using a series of two-player, sequential-move matrix games with a maximum of three steps. Participants were assigned the role of Player I, controlling the initial and the last step, or of Player II, controlling the second step. Appropriate for the assigned role, participants either (...) anticipated or planned Player II’s strategy at the second step, and then determined Player I’s optimal strategy at the first step. Participants more readily used predictive reasoning as Player II (i.e., planning one’s own move) than as Player I (i.e., anticipating an opponent’s move), although they did not differ when translating reasoning outcome about the second step to optimal action in the first step. Perspective-taking influenced likelihood of predictive reasoning, but it did not affect the rate at which participants acquired it during the experimental block. We conclude that the depth of ToM recursion (related to perspective-taking mechanisms) and rational application of belief–desire to action (instrumental rationality) constitute separate cognitive processes in ToM reasoning. (shrink)

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

Lars von Trier's movies can be seen as a series of iterations in an infinitely repeated prisoner's dilemma. After testing the logic of this game, at the core of which is the dilemma of cooperation or conflict, at the middle level at which an individual confronts a community up till Dogville, he has transposed the game to the level of social systems in Manderlay and the level of the minimal social unit, the couple in Anti-Christ. The story is the Oedipus (...) myth reversed and fit into the logic of the prisoner's dilemma which is, one could argue, the mathematical model of a Hobbesian world view. In that sense it could be called Von Trier's Anti-Oedipus. Moreover, this is the first film in which Von Trier fully embraces digital technologies. It is as if he as a filmmaker acts like the male protagonist in Anti-Christ, and assumes the role of the Anti-Christ in order to become a Savior, since digital technologies and special effects are aligned with 'evil' in this movie. (shrink)

The study explores the impact of robots’ emotional displays on people’s tendency to cooperate with a robot opponent in prisoner’s dilemma games. Participants played iterated prisoner’s dilemma games with a non-expressive robot (as a measure of cooperative baseline), followed by an angry, and a sad robot, in turn. Based on the Emotion as Social Information model, we expected participants with higher cooperative predispositions to cooperate less when a robot displayed anger, and cooperate more when the robot displayed (...) sadness. Contrarily, according to this model, participants with lower cooperative predispositions should cooperate more with an angry robot and less with a sad robot. The results of 60 participants failed to support the predictions. Only the participants’ cooperative predispositions significantly predicted their cooperative tendencies during gameplay. Participants who cooperated more in the baseline measure also cooperated more with the robots displaying sadness and anger. In exploratory analyses, we found that participants who accurately recognised the robots’ sad and angry displays tended to cooperate less with them overall. The study highlights the impact of personal factors in human–robot cooperation, and how these factors might surpass the influence of bottom-up emotional displays by the robots in the present experimental scenario. (shrink)