Logic & Philosophy of Mathematics eJournal最新文献

{"title":"The Parable of the Prisoners","authors":"E. Guerra-Pujol, E. Guerra-Pujol","doi":"10.2139/ssrn.2281593","DOIUrl":"https://doi.org/10.2139/ssrn.2281593","url":null,"abstract":"Of the 78 possible strategic games in two-person game theory, one has acquired the most attention, and the most notoriety, from scholars and laymen alike. The so-called “Prisoner’s Dilemma,” or what we prefer to call the “Parable of the Prisoners,” is not only the most famous formal model of conflict and cooperation in the mathematical theory of games; it has also has generated extensive commentary in a wide variety of social sciences and other fields, including psychology, biology, politics, economics, law, and philosophy. In this paper, we shall revisit the origins of this popular parable and review a small but representative sample of this diverse literature, identifying common themes and ideas. We shall also present an opposing parable to show that the dilemma in the Prisoner’s Dilemma is unavoidable and inescapable in the one-shot version of the game, and we shall explain why this parable is more than just a story; it is an exemplar or mathematical “paradigm.”In summary, this paper is organized as follows: following this brief introduction, Part 2 reconstructs the origins of the Parable of the Prisoners. Part 3 then reviews various versions of the parable and the uses to which this parable has been put. By way of contrast, Part 4 presents a diametrically different model of behavior — the Altruist’s Dilemma — based on a suggestion by Schelling (1968), and Part 5 explains why the original Prisoner’s Dilemma is not just an instructive parable but also a scientific “paradigm.” Part 6 concludes.","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"171 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117293061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma - The Effect of Out-of-Equilibrium Play","authors":"K. Lindgren, V. Verendel","doi":"10.3390/g4010001","DOIUrl":"https://doi.org/10.3390/g4010001","url":null,"abstract":"The finitely repeated Prisoners Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained through most of the game. A game-theoretic reasoning based on backward induction eliminates strategies step by step until defection from the first round is the only remaining choice, reflecting the Nash equilibrium of the game. We investigate the Nash equilibrium solution for two different sets of strategies in an evolutionary context, using replicator-mutation dynamics. The first set consists of conditional cooperators, up to a certain round, while the second set in addition to these contains two strategy types that react differently on the first round action: The “Convincer strategies insist with two rounds of initial cooperation, trying to establish more cooperative play in the game, while the “Follower strategies, although being first round defectors, have the capability to respond to an invite in the first round. For both of these strategy sets, iterated elimination of strategies shows that the only Nash equilibria are given by defection from the first round. We show that the evolutionary dynamics of the first set is always characterised by a stable fixed point, corresponding to the Nash equilibrium, if the mutation rate is sufficiently small (but still positive). The second strategy set is numerically investigated, and we find that there are regions of parameter space where fixed points become unstable and the dynamics exhibits cycles of different strategy compositions. The results indicate that, even in the limit of very small mutation rate, the replicator-mutation dynamics does not necessarily bring the system with Convincers and Followers to the fixed point corresponding to the Nash equilibrium of the game. We also perform a detailed analysis of how the evolutionary behaviour depends on payoffs, game length, and mutation rate. Reference: Lindgren K, Verendel V. Evolutionary Exploration of the Finitely Repeated Prisoners Dilemma – The Effect of Out-of- Equilibrium Play. Games, 4(1):1-20, 2013.","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"189 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121838646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-Object Auctions with Resale: An Experimental Analysis","authors":"Marco Pagnozzi, Krista J. Saral","doi":"10.2139/ssrn.2198306","DOIUrl":"https://doi.org/10.2139/ssrn.2198306","url":null,"abstract":"We analyze the effects of resale through bargaining in multi-object uniform-price auctions with asymmetric bidders. The possibility of resale affects bidders' strategies, and hence the allocation of the objects on sale and the seller's revenue. Our experimental design consists of four treatments: one without resale and three resale treatments that vary both the bargaining mechanism and the amount of information available in the resale market. As predicted by theory: (i) without resale, asymmetry among bidders reduces demand reduction; (ii) resale increases demand reduction by high-value bidders; (iii) low-value bidders speculate by bidding more aggressively with resale. Therefore, resale induces speculation and demand reduction which reduce auction efficiency. In contrast to what is usually argued, resale does not necessarily increase final efficiency and may not reduce the seller's revenue. Features of the resale market that tend to increase its efficiency also reduce the seller's revenue.","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"763 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133319797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Logic of Forbidden Colours","authors":"E. Dragalina-Chernaya","doi":"10.2139/ssrn.2185926","DOIUrl":"https://doi.org/10.2139/ssrn.2185926","url":null,"abstract":"The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare model-theoretical and game-theoretical approaches to the colour exclusion problem. What is gained, then, is a new game-theoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131724324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematics as Quasi-Matter to Build Models as Instruments","authors":"M. Boumans","doi":"10.1007/978-94-007-3030-4_22","DOIUrl":"https://doi.org/10.1007/978-94-007-3030-4_22","url":null,"abstract":"","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115578612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chaos, Artificial Life and Risk Mathematics","authors":"C. Gonçalves, Maria Odete Madeira","doi":"10.2139/ssrn.1659253","DOIUrl":"https://doi.org/10.2139/ssrn.1659253","url":null,"abstract":"The current work addresses the importance of chaos theory and artificial life as scientific bases for the development of a mathematical research of risk in the systems, within the framework of risk science and risk mathematics. It is argued, in particular, that a combination of chaos theory and artificial life may provide for a theoretical basis for the understanding of systemic situations of risk. It is presented, within the context of category computation theory, a notion of morphic incompressibility and it is addressed how statistical laws emerge in chaotic dynamics, which becomes morphically compressible at the statistical level, while being morphically incompressible at the individual orbits' level. The issue of the systemic origins of chaos is addressed in connection with this dual (orbit) incompressibility/(statistical) compressibility. Through the introduction of a one-dimensional game of life, that combines a coupled map lattice and a cellular automaton, in a model of an artificial ecosystem, it is, then, shown that artificial life can be effectively combined with chaos theory, in order to support the development of a mathematical theory of risk.","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126331246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Why Fallacies Appear to Be Better Arguments than They Are","authors":"D. Walton","doi":"10.22329/IL.V30I2.2868","DOIUrl":"https://doi.org/10.22329/IL.V30I2.2868","url":null,"abstract":"This paper explains how a fallacious argument can be deceptive by appearing to be a better argument of its kind than it really is. The explanation combines heuristics and argumentation schemes. Heuristics are fast and frugal shortcuts to a solution to a problem. They are reasonable to use, but sometimes jump to a conclusion that is not justified. In fallacious instances, according to the theory proposed, such a jump overlooks prerequisites of the defeasible argumentation scheme for the type of argument in question. Three informal fallacies, argumentum ad verecundiam, argumentum ad ignorantiam and fear appeal argument, are used to illustrate and explain the theory.","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125362984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pre-Funded and Internally Funded Pension Plans: The Potential for Improving Global Comparability","authors":"Mark LaMonte","doi":"10.2139/SSRN.978536","DOIUrl":"https://doi.org/10.2139/SSRN.978536","url":null,"abstract":"In this special comment, we discuss some of the analytical advantages and disadvantages of incorporating information about pension assets and liabilities for pre-funded and internally funded pension plans into key ratios. Moody's already has well-established methodologies in place for the analysis of both types of pension plans. These methodologies, which consider the debt-like nature of pension obligations regardless of how they are funded, introduce financial statement adjustments that result in broad comparability between companies with either type of pension plan. Moody's also seeks to improve comparability further by considering supplemental ratios that adjust for pension assets and obligations on a gross basis. The supplemental ratios are used as an enhancement to our existing methodologies and provide an alternative perspective in our analysis of pension obligations. They help us to identify outliers not evident under our existing practices and that may require further scrutiny. The purpose of this special comment is to present the supplemental ratios that we use in our analysis and to provide an overview of Moody's existing methodologies for pension plans.","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117242983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Моделирование Сложных Динамических Систем На Базе Расширений Сетей Петри (Modelling of Complex Dinamic Systems on the Basis of Expansions of Petri Nets)","authors":"Pavel Skorodumov","doi":"10.2139/SSRN.2509049","DOIUrl":"https://doi.org/10.2139/SSRN.2509049","url":null,"abstract":"Russian Abstract: В данной статье проведен краткий анализ сложных динамических систем. Рассмотрены основные преимущества методов имитационного моделирования. Выполнен краткий обзор дискретно-непрерывных и вложенных сетей Петри, их основных понятий и определений. Выдвигается идея их объединения, построения нового расширения сетей Петри и программного комплекса на его базе. English Abstract: In this article the brief analysis of complex dinamic systems is given. The main advanteges of imitating modeling are considered. The brief review of discrete-continuous and compound Petri nets, their main concepts and definitions is executed. The idea of their combination, creation new expansion of Petri nets and programm complex is given.","PeriodicalId":432647,"journal":{"name":"Logic & Philosophy of Mathematics eJournal","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116015207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}