Open AccessArticle
Security Investment, Hacking, and Information Sharing between Firms and between Hackers
Games 2017, 8(2), 23; doi:10.3390/g8020023 (registering DOI) -
Abstract
A four period game between two firms and two hackers is analyzed. The firms first defend and the hackers thereafter attack and share information. Each hacker seeks financial gain, beneficial information exchange, and reputation gain. The two hackers’ attacks and the firms’ defenses
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A four period game between two firms and two hackers is analyzed. The firms first defend and the hackers thereafter attack and share information. Each hacker seeks financial gain, beneficial information exchange, and reputation gain. The two hackers’ attacks and the firms’ defenses are inverse U-shaped in each other. A hacker shifts from attack to information sharing when attack is costly or the firm’s defense is cheap. The two hackers share information, but a second more disadvantaged hacker receives less information, and mixed motives may exist between information sharing and own reputation gain. The second hacker’s attack is deterred by the first hacker’s reputation gain. Increasing information sharing effectiveness causes firms to substitute from defense to information sharing, which also increases in the firms’ unit defense cost, decreases in each firm’s unit cost of own information leakage, and increases in the unit benefit of joint leakage. Increasing interdependence between firms causes more information sharing between hackers caused by larger aggregate attacks, which firms should be conscious about. We consider three corner solutions. First and second, the firms deter disadvantaged hackers. When the second hacker is deterred, the first hacker does not share information. Third, the first hacker shares a maximum amount of information when certain conditions are met. Policy and managerial implications are provided for how firms should defend against hackers with various characteristics. Full article
Open AccessFeature PaperArticle
Emotions and Behavior Regulation in Decision Dilemmas
Games 2017, 8(2), 22; doi:10.3390/g8020022 -
Abstract
We introduce a dynamic model of emotional behavior regulation that can generalize to a wide range of decision dilemmas. Dilemmas are characterized by availability of mutually exclusive goals that a decision maker is dually motivated to pursue. In our model, previous goal pursuant
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We introduce a dynamic model of emotional behavior regulation that can generalize to a wide range of decision dilemmas. Dilemmas are characterized by availability of mutually exclusive goals that a decision maker is dually motivated to pursue. In our model, previous goal pursuant decisions produce negative emotions that regulate an individual’s propensity to further pursue those goals at future times. This emotional regulation of behavior helps explain the non-stationarity and switching observed between so-called “preferences” revealed in repeated decision dilemmas (e.g., by choosing A over B at time 1, then choosing B over A at time 2). We also explain how behavior regulation under dilemma conditions is affected by the set of available options and how the strength and decay rate of emotions affect the tendency to choose behaviors pursuant of extremely (rather than moderately) different options over time. We discuss how emotional behavior regulation insights provided by our model can extend to a variety of topics including approach and avoidance, temptation and self-control, moral balancing, impulse buying and shopping momentum, dieting and exercise, work and leisure, sleep regulation, cooperation, and competition. Full article
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Open AccessFeature PaperArticle
A Study of the Triggers of Conflict and Emotional Reactions
Games 2017, 8(2), 21; doi:10.3390/g8020021 -
Abstract
We study three triggers of conflict and explore their resultant emotional reactions in a laboratory experiment. Economists suggest that the primary trigger of conflict is monetary incentives. Social psychologists suggest that conflicts are often triggered by fear. Finally, evolutionary biologists suggest that a
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We study three triggers of conflict and explore their resultant emotional reactions in a laboratory experiment. Economists suggest that the primary trigger of conflict is monetary incentives. Social psychologists suggest that conflicts are often triggered by fear. Finally, evolutionary biologists suggest that a third trigger is uncertainty about an opponent’s desire to cause harm. Consistent with the predictions from economics, social psychology, and evolutionary biology, we find that conflict originates from all three triggers. The three triggers differently impact the frequency of conflict, but not the intensity. Also, we find that the frequency and intensity of conflict decrease positive emotions and increase negative emotions and that conflict impacts negative emotions more than positive emotions. Full article
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Open AccessArticle
Watching Eyes and Living up to Expectations: Unkind, Not Kind, Eyes Increase First Mover Cooperation in a Sequential Prisoner’s Dilemma
Games 2017, 8(2), 20; doi:10.3390/g8020020 -
Abstract
(1) Background: Why and when images of watching eyes encourage prosocial behavior is still subject to discussion, and two recent meta-analyses show no effect of watching eyes on generosity. This study aims to discern the effect of watching eyes of different valence on
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(1) Background: Why and when images of watching eyes encourage prosocial behavior is still subject to discussion, and two recent meta-analyses show no effect of watching eyes on generosity. This study aims to discern the effect of watching eyes of different valence on two separate aspects of prosocial behavior, and additionally investigates whether individuals’ social value orientation moderates the effect of eyes. (2) Methods: Individuals take on the role of either a first or second mover in an incentivized, anonymous sequential prisoner’s dilemma (n = 247), a two-person game which separates the need to form expectations about the other player (first mover cooperation, trust) from the motive of greed (second mover cooperation, reciprocity). During decision-making, a picture of either kind eyes, unkind eyes, or a control picture is presented above each decision matrix. (3) Results: The results indicate that unkind eyes, and not kind eyes, significantly boost first mover cooperation. In contrast, neither type of eye cues increase second mover cooperation. Social value orientation does not moderate these effects. (4) Conclusions: Thus, the data suggest that the valence of eye cues matters, and we propose that unkind eyes urge first movers to live up to the interaction partner’s expectations. Full article
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Open AccessReview
The Emotional Moves of a Rational Actor: Smiles, Scowls, and Other Credible Messages
Games 2017, 8(2), 18; doi:10.3390/g8020018 -
Abstract
Many scholars turn to emotions to understand irrational behavior. We do the opposite: we turn to rationality and game theory to understand people’s emotions. We discuss a striking theory of emotions that began with the game theory of credible threats and promises, then
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Many scholars turn to emotions to understand irrational behavior. We do the opposite: we turn to rationality and game theory to understand people’s emotions. We discuss a striking theory of emotions that began with the game theory of credible threats and promises, then was enriched by evolutionary biology and psychology, and now is being tested in psychological experiments. We review some of these experiments which use economic games to set up strategic situations with real payoffs. The experiments test whether a player’s emotional expressions lend credibility to promises, threats, and claims of danger or hardship. The results offer insights into the hidden strategies behind a warm smile, an angry scowl, a look of terror, and eyes of despair. Full article
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Open AccessEditorial
Epistemic Game Theory and Logic: Introduction
Games 2017, 8(2), 19; doi:10.3390/g8020019 -
Abstract
Epistemic game theory and the systems of logic that support it are crucial for understanding rational behavior in interactive situations in which the outcome for an agent depends, not just on her own behavior, but also on the behavior of those with whom
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Epistemic game theory and the systems of logic that support it are crucial for understanding rational behavior in interactive situations in which the outcome for an agent depends, not just on her own behavior, but also on the behavior of those with whom she is interacting. Scholars in many fields study such interactive situations, that is, games of strategy. [...] Full article
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