Open AccessArticle
Emotion at Stake—The Role of Stake Size and Emotions in a Power-to-Take Game Experiment in China with a Comparison to Europe
Games 2017, 8(1), 17; doi:10.3390/g8010017 -
Abstract
This paper experimentally investigates how monetary incentives and emotions influence behavior in a two-player power-to-take game (PTTG). In this game, one player can claim any part of the other's endowment (take rate), and the second player can respond by destroying any part of
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This paper experimentally investigates how monetary incentives and emotions influence behavior in a two-player power-to-take game (PTTG). In this game, one player can claim any part of the other's endowment (take rate), and the second player can respond by destroying any part of his or her own endowment. The experiment is run in China. We further compare our findings with the behavior of two European subject pools. Our results give new insights regarding emotion regulation. Even though stake size does not appear to matter for take rates and destruction rates, it does matter for the reaction function of the responder regarding the take rate. When stakes are high, there is less destruction for low and intermediate take rates, and more destruction for high take rates, compared to relatively low stakes. Under low incentives, ‘hot’ anger-type emotions are important for destruction, while ‘cool’ contempt becomes prominent under high monetary incentives. These results suggest emotion regulation in the high-stake condition. Moreover, emotions are found to fully mediate the impact of the take rate on destruction when stakes are low, whereas they only partially do so if stakes are high. Comparing the low-stakes data for China with existing European data, we find similarities in behavior, emotions and emotion intensities, as well as the full mediation of the take rate by emotions. We find some differences related to the type of emotions that are important for destruction. Whereas anger and joy are important in both, in addition, irritation and fear play a role in China, while this holds for contempt in the EU. Full article
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Open AccessArticle
The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm
Games 2017, 8(1), 16; doi:10.3390/g8010016 -
Abstract
We study the class of directed simple games, assuming that only integer solutions are admitted; i.e., the players share a resource that comes in discrete units. We show that the integer nucleolus—if nonempty—of such a game is composed of the images of a
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We study the class of directed simple games, assuming that only integer solutions are admitted; i.e., the players share a resource that comes in discrete units. We show that the integer nucleolus—if nonempty—of such a game is composed of the images of a particular payoff vector under all symmetries of the game. This payoff vector belongs to the set of integer imputations that weakly preserve the desirability relation between the players. We propose an algorithm for finding the integer nucleolus of any directed simple game with a nonempty integer imputation set. The algorithm supports the parallel execution of multiple threads in a computer application. We also consider the integer prenucleolus and the class of directed generalized simple games. Full article
Open AccessArticle
On Information Aggregation and Interim Efficiency in Networks
Games 2017, 8(1), 15; doi:10.3390/g8010015 -
Abstract
This paper considers a population of agents that are engaged in a listening network. The agents wish to match their actions to the true value of some uncertain (exogenous) parameter and to the actions of the other agents. Each agent begins with some
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This paper considers a population of agents that are engaged in a listening network. The agents wish to match their actions to the true value of some uncertain (exogenous) parameter and to the actions of the other agents. Each agent begins with some initial information about the parameter and, in addition, is able to receive further information from their neighbors in the network. I derive a closed expression for the (interim) social welfare loss that depends on the initial information structure and on the possible pieces of information that can be gathered under the network. Then, I explore how changes in the network may affect social welfare for extreme levels of complementarity in the agents’ actions. When the level of complementarity is very high, efficiency is achieved regardless of the network structure. For very low levels of complementarity in actions, efficiency can be either associated to more sparse or denser networks, depending on the size of the induced informative gains. The implications of this paper are relevant in security environments where agents are naturally interpreted as analysts who try to forecast the value of a parameter that describes a threat to security. Full article
Open AccessArticle
Swap Equilibria under Link and Vertex Destruction
Games 2017, 8(1), 14; doi:10.3390/g8010014 -
Abstract
We initiate the study of the destruction or adversary model (Kliemann 2010) using the swap equilibrium (SE) stability concept (Alon et al., 2010). The destruction model is a network formation game incorporating the robustness of a network under a more or less targeted
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We initiate the study of the destruction or adversary model (Kliemann 2010) using the swap equilibrium (SE) stability concept (Alon et al., 2010). The destruction model is a network formation game incorporating the robustness of a network under a more or less targeted attack. In addition to bringing in the SE concept, we extend the model from an attack on the edges to an attack on the vertices of the network. We prove structural results and linear upper bounds or super-linear lower bounds on the social cost of SE under different attack scenarios. For the case that the vertex to be destroyed is chosen uniformly at random from the set of max-sep vertices (i.e., where each causes a maximum number of separated player pairs), we show that there is no tree SE with only one max-sep vertex. We conjecture that there is no tree SE at all. On the other hand, we show that for the uniform measure, all SE are trees (unless two-connected). This opens a new research direction asking where the transition from “no cycle” to “at least one cycle” occurs when gradually concentrating the measure on the max-sep vertices. Full article
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Open AccessArticle
Interdependent Defense Games with Applications to Internet Security at the Level of Autonomous Systems
Games 2017, 8(1), 13; doi:10.3390/g8010013 -
Abstract
We propose interdependent defense (IDD) games, a computational game-theoretic framework to study aspects of the interdependence of risk and security in multi-agent systems under deliberate external attacks. Our model builds upon interdependent security (IDS) games, a model
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We propose interdependent defense (IDD) games, a computational game-theoretic framework to study aspects of the interdependence of risk and security in multi-agent systems under deliberate external attacks. Our model builds upon interdependent security (IDS) games, a model by Heal and Kunreuther that considers the source of the risk to be the result of a fixed randomized-strategy. We adapt IDS games to model the attacker’s deliberate behavior. We define the attacker’s pure-strategy space and utility function and derive appropriate cost functions for the defenders. We provide a complete characterization of mixed-strategy Nash equilibria (MSNE), and design a simple polynomial-time algorithm for computing all of them for an important subclass of IDD games. We also show that an efficient algorithm to determine whether some attacker’s strategy can be a part of an MSNE in an instance of IDD games is unlikely to exist. Yet, we provide a dynamic programming (DP) algorithm to compute an approximate MSNE when the graph/network structure of the game is a directed tree with a single source. We also show that the DP algorithm is a fully polynomial-time approximation scheme. In addition, we propose a generator of random instances of IDD games based on the real-world Internet-derived graph at the level of autonomous systems (≈27 K nodes and ≈100 K edges as measured in March 2010 by the DIMES project). We call such games Internet games. We introduce and empirically evaluate two heuristics from the literature on learning-in-games, best-response gradient dynamics (BRGD) and smooth best-response dynamics (SBRD), to compute an approximate MSNE in IDD games with arbitrary graph structures, such as randomly-generated instances of Internet games. In general, preliminary experiments applying our proposed heuristics are promising. Our experiments show that, while BRGD is a useful technique for the case of Internet games up to certain approximation level, SBRD is more efficient and provides better approximations than BRGD. Finally, we discuss several extensions, future work, and open problems. Full article
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Open AccessArticle
The Welfare Cost of Signaling
Games 2017, 8(1), 11; doi:10.3390/g8010011 -
Abstract
Might the resource costliness of making signals credible be low or negligible? Using a job market as an example, we build a signaling model to determine the extent to which a transfer from an applicant might replace a resource cost as an equilibrium
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Might the resource costliness of making signals credible be low or negligible? Using a job market as an example, we build a signaling model to determine the extent to which a transfer from an applicant might replace a resource cost as an equilibrium method of achieving signal credibility. Should a firm’s announcement of hiring for an open position be believed, the firm has an incentive to use a properly-calibrated fee to implement a separating equilibrium. The result is robust to institutional changes, outside options, many firms or many applicants and applicant risk aversion, though a sufficiently risk-averse applicant who is sufficiently likely to be a high type may lead to a preference for a pooling equilibrium. Full article
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Open AccessArticle
Topological Aspects of the Multi-Language Phases of the Naming Game on Community-Based Networks
Games 2017, 8(1), 12; doi:10.3390/g8010012 -
Abstract
The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents onverge on a globally shared name. Soon
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The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents onverge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also xamine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm. Full article
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Open AccessArticle
Cyclic Competition and Percolation in Grouping Predator-Prey Populations
Games 2017, 8(1), 10; doi:10.3390/g8010010 -
Abstract
We study, within the framework of game theory, the properties of a spatially distributed population of both predators and preys that may hunt or defend themselves either isolatedly or in group. Specifically, we show that the properties of the spatial Lett-Auger-Gaillard model, when
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We study, within the framework of game theory, the properties of a spatially distributed population of both predators and preys that may hunt or defend themselves either isolatedly or in group. Specifically, we show that the properties of the spatial Lett-Auger-Gaillard model, when different strategies coexist, can be understood through the geometric behavior of clusters involving four effective strategies competing cyclically,without neutral states. Moreover, the existence of strong finite-size effects, a form of the survival of the weakest effect, is related to a percolation crossover. These results may be generic and of relevance to other bimatrix games. Full article
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Open AccessArticle
Assessing Others’ Risk‐Taking Behavior from Their Affective States: Experimental Evidence Using a Stag Hunt Game
Games 2017, 8(1), 9; doi:10.3390/g8010009 -
Abstract
Researchers are increasingly exploring the role of emotions in interactive decision‐making. Recent theories have focused on the interpersonal effects of emotions—the influence of the decisionmaker’s expressed emotions on observers’ decisions and judgments. In this paper, we examine whether people assess others’ risk preferences
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Researchers are increasingly exploring the role of emotions in interactive decision‐making. Recent theories have focused on the interpersonal effects of emotions—the influence of the decisionmaker’s expressed emotions on observers’ decisions and judgments. In this paper, we examine whether people assess others’ risk preferences on the basis of their emotional states, whether this affects their own behavior, and how this assessment matches others’ actual behavior. To test these ideas, we used an experimental Stag Hunt game (n = 98), and included non‐trivial financial consequences. Participants were told (truthfully) that their counterparts’ previous task had left them happy, fearful, or emotionally neutral. People who were told their counterparts were fearful reported that they expected less risky decisions from these counterparts than people told their counterparts were neutral or happy. As a result, given that the Stag Hunt is a coordination game, these participants were themselves less risky. Interestingly, these participants’ expectations were not accurate; thus, coordination failed, and payoffs were low. This raises the possibility of a “curse of knowledge” whereby one player’s erroneous beliefs about the effects of the counterpart’s emotional state leads the first player to make poor action choices. Full article
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Open AccessArticle
Anger Management: Aggression and Punishment in the Provision of Public Goods
Games 2017, 8(1), 5; doi:10.3390/g8010005 -
Abstract
The ability to punish free-riders can increase the provision of public goods. However, sometimes, the benefit of increased public good provision is outweighed by the costs of punishments. One reason a group may punish to the point that net welfare is reduced is
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The ability to punish free-riders can increase the provision of public goods. However, sometimes, the benefit of increased public good provision is outweighed by the costs of punishments. One reason a group may punish to the point that net welfare is reduced is that punishment can express anger about free-riding. If this is the case, then tools that regulate emotions could decrease the use of punishments while keeping welfare high, possibly depending on pre-existing levels of aggression. In this lab experiment, we find that adopting an objective attitude (objective), through a form of emotion regulation called cognitive reappraisal, decreases the use of punishments and makes a statistically insignificant improvement to both net earnings and self-reported emotions compared to a control condition (natural). Although the interaction between the emotion regulation treatment and level of aggression is not significant, only low aggression types reduce their punishments; the results are of the same direction, but statistically insignificant for high aggression types. Overall, our findings suggest that pairing emotion regulation with punishments can decrease the use of punishments without harming monetary and mental welfare. Full article
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Open AccessArticle
The Evolution of Reputation-Based Cooperation in Regular Networks
Games 2017, 8(1), 8; doi:10.3390/g8010008 -
Abstract
Despite recent advances in reputation technologies, it is not clear how reputation systems can affect human cooperation in social networks. Although it is known that two of the major mechanisms in the evolution of cooperation are spatial selection and reputation-based reciprocity, theoretical study
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Despite recent advances in reputation technologies, it is not clear how reputation systems can affect human cooperation in social networks. Although it is known that two of the major mechanisms in the evolution of cooperation are spatial selection and reputation-based reciprocity, theoretical study of the interplay between both mechanisms remains almost uncharted. Here, we present a new individual-based model for the evolution of reciprocal cooperation between reputation and networks. We comparatively analyze four of the leading moral assessment rules—shunning, image scoring, stern judging, and simple standing—and base the model on the giving game in regular networks for Cooperators, Defectors, and Discriminators. Discriminators rely on a proper moral assessment rule. By using individual-based models, we show that the four assessment rules are differently characterized in terms of how cooperation evolves, depending on the benefit-to-cost ratio, the network-node degree, and the observation and error conditions. Our findings show that the most tolerant rule—simple standing—is the most robust among the four assessment rules in promoting cooperation in regular networks. Full article
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Open AccessArticle
Social Pressure and Environmental Effects on Networks: A Path to Cooperation
Games 2017, 8(1), 7; doi:10.3390/g8010007 -
Abstract
In this paper, we study how the pro-social impact due to the vigilance by other individuals is conditioned by both environmental and evolutionary effects. To this aim, we consider a known model where agents play a Prisoner’s Dilemma Game (PDG) among themselves and
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In this paper, we study how the pro-social impact due to the vigilance by other individuals is conditioned by both environmental and evolutionary effects. To this aim, we consider a known model where agents play a Prisoner’s Dilemma Game (PDG) among themselves and the pay-off matrix of an individual changes according to the number of neighbors that are “vigilant”, i.e., how many neighbors watch out for her behavior. In particular, the temptation to defect decreases linearly with the number of vigilant neighbors. This model proved to support cooperation in specific conditions, and here we check its robustness with different topologies, microscopical update rules and initial conditions. By means of many numerical simulations and few theoretical considerations, we find in which situations the vigilance by the others is more effective in favoring cooperative behaviors and when its influence is weaker. Full article
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Open AccessEditorial
Acknowledgement to Reviewers of Games in 2016
Games 2017, 8(1), 6; doi:10.3390/g8010006 -
Open AccessEditorial
A Nobel Prize for Property Rights Theory
Games 2017, 8(1), 4; doi:10.3390/g8010004 -
Abstract This article provides a brief overview of the Property-Rights Theory of the firm, pioneered by Grossman and Hart (1986) and Hart and Moore (1990), and situates the theory in other literatures. Full article
Open AccessArticle
Economic Harmony: An Epistemic Theory of Economic Interactions
Games 2017, 8(1), 2; doi:10.3390/g8010002 -
Abstract
We propose an epistemic theory of micro-economic interactions, termed Economic Harmony. In the theory, we modify the standard utility, by changing its argument from the player’s actual payoff, to the ratio between the player’s actual payoff and his or her aspired payoff. We
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We propose an epistemic theory of micro-economic interactions, termed Economic Harmony. In the theory, we modify the standard utility, by changing its argument from the player’s actual payoff, to the ratio between the player’s actual payoff and his or her aspired payoff. We show that the aforementioned minor epistemic modification of the concept of utility is quite powerful in generating plausible and successful predictions of experimental results, obtained in the standard ultimatum game, and the sequential common pool resource dilemma (CPR) game. Notably, the cooperation and fairness observed in the studied games are accounted for without adding an other-regarding component in the players’ utility functions. For the standard ultimatum game, the theory predicts a division of φ and 1 − φ, for the proposer and responder, respectively, where φ is the famous Golden Ratio (≈0.618), most known for its aesthetically pleasing properties. We discuss possible extensions of the proposed theory to repeated and evolutionary ultimatum games. Full article
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Open AccessArticle
Cognitive Hierarchy Theory and Two-Person Games
Games 2017, 8(1), 1; doi:10.3390/g8010001 -
Abstract
The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven
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The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i) any snowdrift game can be characterized by only a parameter, its class; (ii) they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory. Full article
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Open AccessArticle
Strategy Constrained by Cognitive Limits, and the Rationality of Belief-Revision Policies
Games 2017, 8(1), 3; doi:10.3390/g8010003 -
Abstract
Strategy is formally defined as a complete plan of action for every contingency in a game. Ideal agents can evaluate every contingency. But real people cannot do so, and require a belief-revision policy to guide their choices in unforeseen contingencies. The objects of
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Strategy is formally defined as a complete plan of action for every contingency in a game. Ideal agents can evaluate every contingency. But real people cannot do so, and require a belief-revision policy to guide their choices in unforeseen contingencies. The objects of belief-revision policies are beliefs, not strategies and acts. Thus, the rationality of belief-revision policies is subject to Bayesian epistemology. The components of any belief-revision policy are credences constrained by the probability axioms, by conditionalization, and by the principles of indifference and of regularity. The principle of indifference states that an agent updates his credences proportionally to the evidence, and no more. The principle of regularity states that an agent assigns contingent propositions a positive (but uncertain) credence. The result is rational constraints on real people’s credences that account for their uncertainty. Nonetheless, there is the open problem of non-evidential components that affect people’s credence distributions, despite the rational constraint on those credences. One non-evidential component is people’s temperaments, which affect people’s evaluation of evidence. The result is there might not be a proper recommendation of a strategy profile for a game (in terms of a solution concept), despite agents’ beliefs and corresponding acts being rational. Full article
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Open AccessArticle
Network Formation with Endogenous Link Strength and Decreasing Returns to Investment
Games 2016, 7(4), 40; doi:10.3390/g7040040 -
Abstract
We study the formation of networks where agents choose how much to invest in each relationship. The benefit that an agent can derive from a network depends on the strength of the direct links between agents. We assume that the strength of the
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We study the formation of networks where agents choose how much to invest in each relationship. The benefit that an agent can derive from a network depends on the strength of the direct links between agents. We assume that the strength of the direct link between any pair of agents is a concave function of their investments towards each other. In comparison with some existing models of network formation where the strength technology is a convex function of investment, we find that (i) the symmetric complete network can dominate the star architecture in terms of total utility; (ii) a dominating symmetric complete network needs not be stable; and, (iii) star and complete networks can be dominated by small-world networks. Full article
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Open AccessArticle
Modeling Poker Challenges by Evolutionary Game Theory
Games 2016, 7(4), 39; doi:10.3390/g7040039 -
Abstract
We introduce a model for studying the evolutionary dynamics of Poker. Notably, despite its wide diffusion and the raised scientific interest around it, Poker still represents an open challenge. Recent attempts for uncovering its real nature, based on statistical physics, showed that Poker
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We introduce a model for studying the evolutionary dynamics of Poker. Notably, despite its wide diffusion and the raised scientific interest around it, Poker still represents an open challenge. Recent attempts for uncovering its real nature, based on statistical physics, showed that Poker in some conditions can be considered as a skill game. In addition, preliminary investigations reported a neat difference between tournaments and ‘cash game’ challenges, i.e., between the two main configurations for playing Poker. Notably, these previous models analyzed populations composed of rational and irrational agents, identifying in the former those that play Poker by using a mathematical strategy, while in the latter those playing randomly. Remarkably, tournaments require very few rational agents to make Poker a skill game, while ‘cash game’ may require several rational agents for not being classified as gambling. In addition, when the agent interactions are based on the ‘cash game’ configuration, the population shows an interesting bistable behavior that deserves further attention. In the proposed model, we aim to study the evolutionary dynamics of Poker by using the framework of Evolutionary Game Theory, in order to get further insights on its nature, and for better clarifying those points that remained open in the previous works (as the mentioned bistable behavior). In particular, we analyze the dynamics of an agent population composed of rational and irrational agents, that modify their behavior driven by two possible mechanisms: self-evaluation of the gained payoff, and social imitation. Results allow to identify a relation between the mechanisms for updating the agents’ behavior and the final equilibrium of the population. Moreover, the proposed model provides further details on the bistable behavior observed in the ‘cash game’ configuration. Full article
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Open AccessArticle
Probabilistic Unawareness
Games 2016, 7(4), 38; doi:10.3390/g7040038 -
Abstract
The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the
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The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level, and then axiomatized by Heifetz and Mongin (2001). The paper embodies in this framework those properties of unawareness that have been highlighted in the seminal paper by Modica and Rustichini (1999). Their paper deals with full belief, but we argue that the properties in question also apply to partial belief. Our main result is a (soundness and) completeness theorem that reunites the two strands—modal and probabilistic—of doxastic logic. Full article
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