The insight of the BMS logical framework (proposed by Baltag, Moss and Solecki) is to represent how an event is perceived by several agents very similarly to the way one represents how a static situation is perceived by them: by means of a Kripke model. There are however some differences between the definitions of an epistemic model (representing the static situation) and an event model. In this paper we restore the symmetry. The resulting logical framework allows, unlike any other one, to express statements about ongoing events and to model the fact that our perception of events (and not only of the static situation) can also be updated due to other events. We axiomatize it and prove its decidability. Finally, we show that it embeds the BMS one if we add common belief operators.
{"title":"BMS revisited","authors":"Guillaume Aucher","doi":"10.1145/1562814.1562822","DOIUrl":"https://doi.org/10.1145/1562814.1562822","url":null,"abstract":"The insight of the BMS logical framework (proposed by Baltag, Moss and Solecki) is to represent how an event is perceived by several agents very similarly to the way one represents how a static situation is perceived by them: by means of a Kripke model. There are however some differences between the definitions of an epistemic model (representing the static situation) and an event model. In this paper we restore the symmetry. The resulting logical framework allows, unlike any other one, to express statements about ongoing events and to model the fact that our perception of events (and not only of the static situation) can also be updated due to other events. We axiomatize it and prove its decidability. Finally, we show that it embeds the BMS one if we add common belief operators.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115692089","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}
We study games in which the choices available to players are not fixed, and may change during the course of play. Specifically, we consider a model in which players may switch strategies, and a global (social) decision may remove some choices, based on the strategies being adopted by players. We propose a logical formalism in which such choices are specified, and a model of bounded memory strategies in which the eventual implications of such choices can be computed, and present preliminary results.
{"title":"Dynamic restriction of choices: a preliminary logical report","authors":"Soumya Paul, R. Ramanujam, Sunil Simon","doi":"10.1145/1562814.1562844","DOIUrl":"https://doi.org/10.1145/1562814.1562844","url":null,"abstract":"We study games in which the choices available to players are not fixed, and may change during the course of play. Specifically, we consider a model in which players may switch strategies, and a global (social) decision may remove some choices, based on the strategies being adopted by players. We propose a logical formalism in which such choices are specified, and a model of bounded memory strategies in which the eventual implications of such choices can be computed, and present preliminary results.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122523337","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}
The paper proposes Logic of Secrets in Collaboration Networks, a formal logical system for reasoning about a set of secrets established over a fixed configuration of communication channels. The system's key feature, a multi-channel relation called independence, is a generalization of a two-channel relation known in the literature as nondeducibility. The main result is the completeness of the proposed system with respect to a semantics of secrets.
{"title":"On interdependence of secrets in collaboration networks","authors":"Sara Miner More, Pavel Naumov","doi":"10.1145/1562814.1562843","DOIUrl":"https://doi.org/10.1145/1562814.1562843","url":null,"abstract":"The paper proposes Logic of Secrets in Collaboration Networks, a formal logical system for reasoning about a set of secrets established over a fixed configuration of communication channels. The system's key feature, a multi-channel relation called independence, is a generalization of a two-channel relation known in the literature as nondeducibility. The main result is the completeness of the proposed system with respect to a semantics of secrets.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"60 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116436003","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}
Epistemic game theory scrutinizes the relationship between knowledge, belief and choice of rational players. Here, the relationship between common knowledge and the limit of higher-order mutual knowledge is studied from a topological point of view. More precisely, the new epistemic operator limit knowledge defined as the topological limit of higher-order mutual knowledge is introduced. We then show that limit knowledge of the specific event rationality can be used for epistemic-topological characterizations of solution concepts in games. As a first step towards this scheme, we construct a game where limit knowledge of rationality appears to be a cogent strict refinement of common knowledge of rationality in terms of solution concepts. More generally, it is shown that for any given game and epistemic model of it satisfying some specific condition, every possible epistemic hypothesis as well as as every solution concept can be characterized by limit knowledge of rationality for some appropriate topology.
{"title":"Limit knowledge of rationality","authors":"C. Bach, Jérémie Cabessa","doi":"10.1145/1562814.1562823","DOIUrl":"https://doi.org/10.1145/1562814.1562823","url":null,"abstract":"Epistemic game theory scrutinizes the relationship between knowledge, belief and choice of rational players. Here, the relationship between common knowledge and the limit of higher-order mutual knowledge is studied from a topological point of view. More precisely, the new epistemic operator limit knowledge defined as the topological limit of higher-order mutual knowledge is introduced. We then show that limit knowledge of the specific event rationality can be used for epistemic-topological characterizations of solution concepts in games. As a first step towards this scheme, we construct a game where limit knowledge of rationality appears to be a cogent strict refinement of common knowledge of rationality in terms of solution concepts. More generally, it is shown that for any given game and epistemic model of it satisfying some specific condition, every possible epistemic hypothesis as well as as every solution concept can be characterized by limit knowledge of rationality for some appropriate topology.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"224 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116619447","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}
The Knower Paradox demonstrates that any theory T which 1) extends Robinson arithmetic Q, 2) includes a predicate K(x) intended to formalize "the formula with godel number x is known by agent i," and 3) contains certain elementary epistemic principles involving K(x) is inconsistent. The purpose of this paper is to show how this paradox may be redeveloped within a system of quantified explicit modal logic in the tradition of Artemov [4] and Fitting [10], [11] which we argue allows for a more faithful formulation of some of the epistemic principles on which it is based. Along the way, we isolate a principle -- the so-called Uniform Barcan Formula [UBF] -- which we show is required to derive an explicit counterpart of the axiom U (i.e. K(⌜K(⌝φ⌍) → φ⌍)) which was used in the original formulation of the Paradox. We argue that since there are independent epistemic reasons to be suspicious of UBF, the paradox may be resolved by abandoning this principle (and thereby U as well).
{"title":"Knowledge, proof and the Knower","authors":"Walter Dean, Hidenori Kurokawa","doi":"10.1145/1562814.1562828","DOIUrl":"https://doi.org/10.1145/1562814.1562828","url":null,"abstract":"The Knower Paradox demonstrates that any theory <i>T</i> which 1) extends Robinson arithmetic <i>Q</i>, 2) includes a predicate <i>K</i>(<i>x</i>) intended to formalize \"the formula with godel number <i>x</i> is known by agent <i>i</i>,\" and 3) contains certain elementary epistemic principles involving <i>K</i>(<i>x</i>) is inconsistent. The purpose of this paper is to show how this paradox may be redeveloped within a system of quantified explicit modal logic in the tradition of Artemov [4] and Fitting [10], [11] which we argue allows for a more faithful formulation of some of the epistemic principles on which it is based. Along the way, we isolate a principle -- the so-called Uniform Barcan Formula [UBF] -- which we show is required to derive an explicit counterpart of the axiom <b>U</b> (i.e. <i>K</i>(⌜<i>K</i>(⌝φ⌍) → φ⌍)) which was used in the original formulation of the Paradox. We argue that since there are independent epistemic reasons to be suspicious of UBF, the paradox may be resolved by abandoning this principle (and thereby <b>U</b> as well).","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126599559","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}
In this paper we address the issue which solution concept for strategic games is consistent to common belief that each player satisfies the sure-thing principle. Traditional epistemic analysis takes for granted that there is common belief that each player acts according to some expected utility function. Because our presumptions are milder than the traditional ones we are forced to modify the traditional epistemic approach and follow the idea of Morris (1996) to fasten the beliefs of the players to their preferences. One central finding of our paper is that common belief of sure-thing principle plus state-independence characterizes the solution concept proposed by Börgers (1993).
{"title":"Solutions of strategic games under common belief of sure-thing principle","authors":"Michael Trost","doi":"10.1145/1562814.1562847","DOIUrl":"https://doi.org/10.1145/1562814.1562847","url":null,"abstract":"In this paper we address the issue which solution concept for strategic games is consistent to common belief that each player satisfies the sure-thing principle. Traditional epistemic analysis takes for granted that there is common belief that each player acts according to some expected utility function. Because our presumptions are milder than the traditional ones we are forced to modify the traditional epistemic approach and follow the idea of Morris (1996) to fasten the beliefs of the players to their preferences. One central finding of our paper is that common belief of sure-thing principle plus state-independence characterizes the solution concept proposed by Börgers (1993).","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130185623","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}
This paper investigates a generalized version of inquisitive semantics (Groenendijk, 2008b; Mascarenhas, 2008). A complete axiomatization of the associated logic is established. The connection with intuitionistic logic is clarified and heavily exploited.
{"title":"Generalized inquisitive logic: completeness via intuitionistic Kripke models","authors":"Ivano Ciardelli, F. Roelofsen","doi":"10.1145/1562814.1562827","DOIUrl":"https://doi.org/10.1145/1562814.1562827","url":null,"abstract":"This paper investigates a generalized version of inquisitive semantics (Groenendijk, 2008b; Mascarenhas, 2008). A complete axiomatization of the associated logic is established. The connection with intuitionistic logic is clarified and heavily exploited.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128506573","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}
Tennenholtz (GEB 2004) developed Program Equilibrium to model play in a finite two-player game where each player can base their strategy on the other player's strategies. Tennenholtz's model allowed each player to produce a "loop-free" computer program that had access to the code for both players. He showed a folk theorem where the result of any mixed-strategy individually rational play could be an equilibrium payoff in this model even in a one-shot game. Kalai et al. gave a general folk theorem for correlated play in a more generic commitment model. We develop a new model of program equilibrium using general computational models and discounting the payoffs based on the computation time used. We give an even more general folk theorem giving correlated-strategy payoffs down to the pure minimax of each player. We also show the existence of equilibrium in other games not covered by the earlier work.
{"title":"Program equilibria and discounted computation time","authors":"L. Fortnow","doi":"10.1145/1562814.1562833","DOIUrl":"https://doi.org/10.1145/1562814.1562833","url":null,"abstract":"Tennenholtz (GEB 2004) developed Program Equilibrium to model play in a finite two-player game where each player can base their strategy on the other player's strategies. Tennenholtz's model allowed each player to produce a \"loop-free\" computer program that had access to the code for both players. He showed a folk theorem where the result of any mixed-strategy individually rational play could be an equilibrium payoff in this model even in a one-shot game. Kalai et al. gave a general folk theorem for correlated play in a more generic commitment model.\u0000 We develop a new model of program equilibrium using general computational models and discounting the payoffs based on the computation time used. We give an even more general folk theorem giving correlated-strategy payoffs down to the pure minimax of each player. We also show the existence of equilibrium in other games not covered by the earlier work.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"8 Pt 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126272374","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}
In numerous economic scenarios, contracting parties may not have a clear picture of all the relevant aspects. While confronted with these unawareness issues, the strategic decisions of the contracting parties critically depend on their sophistication. A contracting party may be unaware of what she is entitled to determine. Therefore, she can only infer some missing pieces via the contract offered by other parties and determine whether to accept the contract based on her own evaluation of how reasonable the contract is. Further, a contracting party may actively gather information and collect evidence about all possible contingencies to avoid to be trapped into the contractual agreement. In this paper, we propose a general framework to investigate these strategic interactions with unawareness, reasoning, and cognition. We build our conceptual framework upon the classical principal-agent relationship and compare the equilibrium behaviors under various degrees of the unaware agent's sophistication. Several implications regarding optimal contract design, possible exploitation, and cognitive thinking are also presented.
{"title":"Contractual traps","authors":"Ying-Ju Chen, Xiao-Qiang Zhao","doi":"10.1145/1562814.1562825","DOIUrl":"https://doi.org/10.1145/1562814.1562825","url":null,"abstract":"In numerous economic scenarios, contracting parties may not have a clear picture of all the relevant aspects. While confronted with these unawareness issues, the strategic decisions of the contracting parties critically depend on their sophistication. A contracting party may be unaware of what she is entitled to determine. Therefore, she can only infer some missing pieces via the contract offered by other parties and determine whether to accept the contract based on her own evaluation of how reasonable the contract is. Further, a contracting party may actively gather information and collect evidence about all possible contingencies to avoid to be trapped into the contractual agreement. In this paper, we propose a general framework to investigate these strategic interactions with unawareness, reasoning, and cognition. We build our conceptual framework upon the classical principal-agent relationship and compare the equilibrium behaviors under various degrees of the unaware agent's sophistication. Several implications regarding optimal contract design, possible exploitation, and cognitive thinking are also presented.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133463665","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}
The recent explosion of electronic commerce has frequently brought together economists, computer scientists, and businesses in the pursuit of new designs for markets that succeed in attracting participants and becoming viable businesses. Real-world design has been guided by theoretical insights, empirical evidence and practical experience. This talk explores where new theory and evidence are needed to answer questions of practical importance, as well as what kinds of conceptual frameworks, insights and approaches have the most influence and relevance in practice. One key insight from the economics of market design is that the effect of the rules of a market, such as auction rules, on participation and division of surplus within a marketplace is often much more important than the impact of the rules on behavior for a fixed set of participants. The talk will also consider how to map between stylized models and practice, focusing on identifying the assumptions from theory that most often fail in practice and the new questions that this implies for theory; for example, in a realistic application there is typically no mechanism that yields efficient allocation in a prior-free, incentive-compatible model, and so the market designer needs a framework for evaluating tradeoffs between alternative mechanisms, and must consider the relative importance of different types of robustness and features of a mechanism. Finally, in online marketplaces with rapidly evolving market designs, theory can be used to guide real-world experiments and empirical analysis, and empirical evidence can in turn inform us about what theoretical issues are most important.
{"title":"Designing markets: economics, computer science and the real world","authors":"S. Athey","doi":"10.1145/1562814.1562816","DOIUrl":"https://doi.org/10.1145/1562814.1562816","url":null,"abstract":"The recent explosion of electronic commerce has frequently brought together economists, computer scientists, and businesses in the pursuit of new designs for markets that succeed in attracting participants and becoming viable businesses. Real-world design has been guided by theoretical insights, empirical evidence and practical experience. This talk explores where new theory and evidence are needed to answer questions of practical importance, as well as what kinds of conceptual frameworks, insights and approaches have the most influence and relevance in practice. One key insight from the economics of market design is that the effect of the rules of a market, such as auction rules, on participation and division of surplus within a marketplace is often much more important than the impact of the rules on behavior for a fixed set of participants. The talk will also consider how to map between stylized models and practice, focusing on identifying the assumptions from theory that most often fail in practice and the new questions that this implies for theory; for example, in a realistic application there is typically no mechanism that yields efficient allocation in a prior-free, incentive-compatible model, and so the market designer needs a framework for evaluating tradeoffs between alternative mechanisms, and must consider the relative importance of different types of robustness and features of a mechanism. Finally, in online marketplaces with rapidly evolving market designs, theory can be used to guide real-world experiments and empirical analysis, and empirical evidence can in turn inform us about what theoretical issues are most important.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127830328","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}
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