博弈论中重复可允许算法的认知分析

博弈论中重复可允许(Iterated Admissibilty)算法对于快速约简博弈模型、寻找合理置信的纳什均衡具有重要意义,但该算法的认知基础存在悖论。本文构建一个完备的博弈认知逻辑系统EL_G,利用该系统语言描述博弈相关概念和性质,使得我们可以基于EL_G逻辑刻画重复可允许算法,从而达到为该算法提供合理的认知基础,解决算法背后的认知悖论的目的。     

说谎者悖论的一个新解决方案的纲要(英文)

首先,本文在第二节中提出了谎者悖论所包含的一些问题,比如加强的说谎者悖论,Curry悖论,Yablo悖论,偶然的说谎者悖论,以及塔尔斯基的真不可定义性定理。其次,在第三节简单介绍了塔尔斯基的分层理论,并且指出了他方案的一个最大不足之处就是把一个真谓词分成了很多个个真谓词,这和我们的直观很不符合。之后在第四节介绍了我的一个解悖方案,并讨论了它的一些性质,比如可靠性,完全性,以及我的方案和塔尔斯基方案的区别。第五节说明了第二节中提到的一些问题在我的这个方案下如何处理。     

不同博弈情境下社会排斥对社会决策的影响作用

本研究借助经典的最后通牒博弈范式(UG)和独裁者博弈范式(DG),将回应者/接受者作为研究对象,考察了不同公平条件、平等条件下社会排斥对社会决策的影响作用。实验结果发现:(1)在面对高不公平性的分配方案时,被排斥组比被接纳组更倾向于拒绝接受该分配方案;(2)被排斥组对高不公平性分配方案的满意度要显著低于被接纳组;(3)被排斥组在不平等的博弈(DG)条件下对分配方案的满意度显著低于平等博弈(UG)条件下对分配方案的满意度。本研究结果说明,社会排斥情境下的被试对公平与平等因素更加敏感:在高不公平条件下,被排斥的个体表现出更少的合作互惠行为,甚至不惜放弃自身经济利益,也要惩罚博弈对方的不公平行为;此外,在不平等的博弈条件下,被排斥的个体产生了更多的消极情绪体验。本文的研究结果提高了社会决策研究的生态效度和传统决策模型的预测效度,有利于更加完整透彻地了解社会决策的影响因素。     

“意外考试悖论”研究进展

意外考试悖论是对"知识"概念的直觉理解所提出的严峻挑战。克里普克在新近出版的文集中对该悖论提出了自己的解决方案,把产生该悖论的根源指向了所谓"知识的持久性"。该方案实际上是沿着蒯因的路线进行的。然而,索伦森所提出的该悖论的一个变体却巧妙地表明,即使不诉诸知识的持久性,仍然会产生悖论,也就是说知识的持久性并不是意外考试悖论产生的一个决定性因素。因此,索伦森提出的这一变体可以用来较为充分地反驳克里普克所提出的解悖方案。     

儿童公平行为的发展——来自博弈实验的证据

公平正义一直是人类不懈追求的目标,是心理学、经济学等多个学科共同关注的一个重要课题。发展心理学常采用故事法对儿童的公平认知进行研究,博弈范式的引入则为研究儿童的公平行为提供了新的方法和角度。该文主要介绍了独裁者博弈和最后通牒博弈中儿童公平行为的发展趋势,并对已有的矛盾性结论进行了原因分析,探讨了公平行为的内团体偏差效应、公平的本质是意图公平还是结果公平、以及心理理论与公平行为的关系等问题。最后,该文指出今后对儿童公平行为的研究应充分考虑社会情境与社会认知能力的影响。     

理性与有限理性-从经典博弈理论到进化博弈理论

博弈理论自产生起逐渐被广泛地用于生态学、杜会学、经济学等领域，越来越多的经济学家应用该理论来研究经济活动申经济主体的群体行为。与经典博弈理论不同，进化博弈理论并不要求经济主体是完全理性的，也不要求经济主体的行为满足预期一致性原则。因此进化博弈理论比经典博弈理论能够更准确地预测经济主体的行为。所以在短短的二十几年里进化博弈理论就获得了迅速的发展。     

心理理论发展研究的一种新范式——矩阵博弈

心理理论指对他人心理状态的理解,是一种毕生发展的能力。但之前的研究在研究对象和研究内容上存在一些缺陷。本文介绍了一种新范式——矩阵博弈(matrix game),对利用其研究心理理论进行了可行性分析,同时指出了两者相结合的理论基础和实证证据。未来研究可利用矩阵博弈来研究更广年龄范围人群心理理论的发展轨迹,并借助fMRI等技术来测查矩阵博弈中心理理论推理的脑机制。     

无差别悖论及其解决

无差别原则及其悖论由来己久。当代归纳逻辑的创始人凯恩斯曾为消除这些悖论付出巨大的努力。本文介绍了若干典型的无差别悖论和对它们的一些尝试性解决,还追溯到贝叶斯方法的创始人曾经受到的类似困扰。笔者提出一种新的解决方案,其核心是对古典无差别原则加以试验机制的限制和提出从参数θ到f（θ）的线性无差别条件。最后指出,古典无差别原则作为经验性的启发原则仍可保留,它同作为逻辑原则或准逻辑原则的试验机制无差别原则是并行不悖和相互补充的。     

确证悖论的相关变量法解决方案探微

确证悖论是科学哲学和逻辑哲学中的难题,自亨普尔1945年将之发表以来,许多人致力于解决它.目前较为流行的解悖方案是相干型解悖方案.本文也是沿着相干型方案,从相关变量法(RVM)理论的角度,提出了两种解悖方案.进一步地,分析RVM方案总的来讲是属于情境迟钝方案,并指出RVM的解悖方案是现有知识背景下的最佳归纳确证方案.     

短视玩家的理性:一种认知分析（英文）

本文中,我们对于"视域一致"型的逆向归纳法解进行了初步的认知分析。这种逆向归纳法解是文《扩展博弈中的短视》在研究一类具有视域受限型参与者的扩展博弈中所提出的。本文研究了在这类具有视域受限型参与者的博弈中,产生"视域一致"型的逆向归纳法解的认知前提条件。从技术层面上讲,本文是基于《保持理性的"希望":逆向归纳法悖论的一种解决方案》一文中所提出的方法,对于扩展博弈中逆向归纳法作出认知分析。文章的主要贡献在于明确了在短视博弈中"视域一致"型逆向归纳解的认知前提条件。     

Infinite "Backward" Induction Arguments

A large family of paradoxical arguments have been subsumed under the label "backward induction arguments". These include the iterated prisonerÕs dilemma, the centipede game, and the surprise test paradox. They are described as backward because they begin by considering a future hypothetical alternative, rule it out, and then rule out each predecessor. Thus they go backward in time ruling out finitely many alternatives. I present examples that go forward in time and eliminate infinitely many alternatives. These pose problems for solutions that focus on common knowledge assumptions.     

Conflict and Co-ordination in the Aftermath of Oracular Statements

Can victims of the oracle paradox, which is known primarily through its unexpected hanging and surprise examination versions, extricate themselves from their difficulties of reasoning? No. For they do not, contrary to recent opinion, commit errors of fallacious elimination. As I shall argue, the difficulties of reasoning faced by these victims do not originate in the domain of concepts, propositions and their entailment relations; nor do they result from misapprehensions about limitations on what can be known. The difficulties of reasoning flow, instead, from conflicts that arise in the practical dimension of life. The oracle paradox is in this way more evocative of problems faced in the theory of computation than it is like the celebrated Russell's paradox.     

PRACTICAL SOLUTIONS TO THE SURPRISE-EXAMINATION PARADOX*

In this paper I consider the surprise examination paradox from a practical perspective, paying special attention to the communicative role of the teacher's promise to the students. This perspective, which places the promise within a practice, rather than viewing it in the abstract, imposes constraints on adequate solutions to the paradox. In the light of these constraints. I examine various solutions which have been offered, and suggest two of my own.     

On the Epistemic Foundation for Iterated Weak Dominance: An Analysis in a Logic of Individual and Collective attitudes

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.     

Common knowledge of payoff uncertainty in games

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.’     

On Two Versions of ‘the Surprise Examination Paradox’

In this paper, I consider a popular version of the clever student’s reasoning in the surprise examination case, and demonstrate that a valid argument can be constructed. The valid argument is a reductio ad absurdum with the proposition that the student knows on the morning of the first day that the teacher’s announcement is fulfilled as its reductio. But it would not give rise to any paradox. In the process, I criticize Saul Kripke’s solution and Timothy Williamson’s attack on a key step of the student’s reasoning. I then consider the condemned prisoner case in W. V. Quine’s paper ‘On a So-Called Paradox’. I argue that the prisoner’s reasoning as conceived by Quine is more relevant and reasonable than the student’s argument in the popular version of the surprise examination case. I also argue that Quine’s criticism of the prisoner’s reasoning is correct, and therefore that the condemned prisoner case, and the surprise examination case as well, would not generate any paradox.     

Common reasoning about admissibility

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction.     

The Surprise Examination in Dynamic Epistemic Logic

We examine the paradox of the surprise examination using dynamic epistemic logic. This logic contains means of expressing epistemic facts as well as the effects of learning new facts, and is therefore a natural framework for representing the puzzle. We discuss a number of different interpretations of the puzzle in this context, and show how the failure of principle of success, that states that sentences, when learned, remain to be true and come to be believed, plays a central role in understanding the puzzle.     

On a so‐Called Solution to a Paradox

The mooronic solution to the surprise quiz paradox says students know there will be a surprise quiz one day this week but they lose this knowledge on the penultimate day. This is because ‘there will be a surprise quiz one day this week’ then becomes an instance of Moore's paradox. This view has surprising consequences. Furthermore, even though the surprise quiz announcement becomes an instance of Moore's paradox on the penultimate day, this does not prevent the students from knowing the quiz is coming. I conclude that the first stage of the paradoxical argument succeeds and the mooronic solution fails.     

Effects of financial incentives on the breakdown of mutual trust

Disagreements between psychologists and economists about the need for and size of financial incentives continue to be hotly discussed. We examine the effects of financial incentives in a class of interactive decision-making situations, called centipede games, in which mutual trust is essential for cooperation. Invoking backward induction, the Nash equilibrium solution for these games is counterintuitive. Our previous research showed that when the number of players in the centipede game is increased from two to three, the game is iterated in time, the players are rematched, and the stakes are unusually high, behavior approaches equilibrium play. Results from the present study show that reducing the size of the stakes elicits dramatically different patterns of behavior. We argue that when mutual trust is involved, the magnitude of financial incentives can induce a considerable difference.