Open AccessArticle
The Monty Hall Problem as a Bayesian Game
Games 2017, 8(3), 31; doi:10.3390/g8030031 -
Abstract
This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies
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This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty’s motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty and show that, under certain conditions on p, the unique equilibrium is one in which the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. In particular, we show that our formulation can explain the experimental results in Page (1998), that more people gradually choose switch as the number of doors in the problem increases. Full article
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Open AccessFeature PaperArticle
Game Theory of Pollution: National Policies and Their International Effects
Games 2017, 8(3), 30; doi:10.3390/g8030030 -
Abstract
In this paper we put forward a simple game-theoretical model of pollution control, where each country is in control of its own pollution, while the environmental effects of policies do not stop at country borders. In our noncooperative differential game, countries as players
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In this paper we put forward a simple game-theoretical model of pollution control, where each country is in control of its own pollution, while the environmental effects of policies do not stop at country borders. In our noncooperative differential game, countries as players minimize the present value of their own costs defined as a linear combination of pollution costs and costs of environmentally friendly policies, where the state vector of the system consists of the pollution stock per country. A player’s time-varying decision is her investment into clean policies, while her expected costs include also pollution caused by her neighbors. We analyze three variants of this game: (1) a Nash game in which each player chooses her investment into clean policies such that her expected costs are minimal, (2) a game in which the players imitate the investments into clean policies of their neighbors without taking the neighbor’s success concerning their costs into account and (3) a game in which each player imitates her neighbors’ investments into clean policies if this behavior seems to bring a profit. In each of these scenarios, we show under which conditions the countries have incentives to act environmentally friendly. We argue that the different results of these games can be used to understand and design effective environmental policies. Full article
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Open AccessArticle
Anticipated Communication in the Ultimatum Game
Games 2017, 8(3), 29; doi:10.3390/g8030029 -
Abstract
Anticipated verbal feedback in a dictator game has been shown to induce altruistic behavior. However, in the ultimatum game which, apart from generosity, entails a strategic component since a proposer may (rightly) fear that the responder will reject a low offer, it remains
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Anticipated verbal feedback in a dictator game has been shown to induce altruistic behavior. However, in the ultimatum game which, apart from generosity, entails a strategic component since a proposer may (rightly) fear that the responder will reject a low offer, it remains an open question whether anticipated verbal communication can be effective in increasing offers. We implement a between-subjects experimental design in the ultimatum game with strategy method manipulating the form of anticipated verbal communication (no communication, one-sided communication from proposers and two-sided communication) and find that offers are significantly higher in the presence of anticipated two-sided communication. However, anticipated one-sided communication from proposers has no effect on offers, suggesting, as found in previous studies, that it is the anticipation of feedback that is relevant. Full article
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Open AccessArticle
Reacting to Unfairness: Group Identity and Dishonest Behavior
Games 2017, 8(3), 28; doi:10.3390/g8030028 -
Abstract
We experimentally investigate whether individuals are more likely to engage in dishonest behavior after having experienced unfairness perpetrated by an individual with a salient group identity. Two individuals generate an endowment together, but only one can decide how to share it. They either
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We experimentally investigate whether individuals are more likely to engage in dishonest behavior after having experienced unfairness perpetrated by an individual with a salient group identity. Two individuals generate an endowment together, but only one can decide how to share it. They either share the same group identity or have distinct group identities. Then, they approach a task in which they can opportunistically engage in dishonest behavior. Our results show that when individuals share the same group identity, unfair distributive decisions do not trigger a dishonest reaction. In contrast, when different group identities coexist, dishonest behavior is observed as a reaction to unfairness. Full article
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Open AccessArticle
Cycles in Team Tennis and Other Paired-Element Contests
Games 2017, 8(3), 27; doi:10.3390/g8030027 -
Abstract
Team Tennis competitions produce aggregate scores for teams, and thus team rankings, based on head-to-head matchups of individual team members. Similar scoring rules can be used to rank any two groups that must be compared on the basis of paired elements. We explore
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Team Tennis competitions produce aggregate scores for teams, and thus team rankings, based on head-to-head matchups of individual team members. Similar scoring rules can be used to rank any two groups that must be compared on the basis of paired elements. We explore such rules in terms of their strategic and social choice characteristics, with particular emphasis on the role of cycles. We first show that cycles play an important role in promoting competitive balance, and show that cycles allow for a maximum range of competitive balance within a league of competing teams. We also illustrate the impact that strategic behavior can have on the unpredictability of competition outcomes, and show for a general class of team tennis scoring rules that a rule is strategy-proof if and only if it is acyclic (dictatorial) and manipulable otherwise. Given the benefits of cycles and their relationship with manipulability, a league valuing competitive balance may invite such social choice violations when choosing a scoring rule. Full article
Open AccessArticle
Gender, Emotions, and Tournament Performance in the Laboratory
Games 2017, 8(3), 26; doi:10.3390/g8030026 -
Abstract
Individuals face competitive environments daily, and it is important to understand how emotions affect behavior in these environments and resulting economic consequences. Using a two-stage laboratory experiment, I analyze the role of reported emotions in tournament performance and assess how the behavioral response
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Individuals face competitive environments daily, and it is important to understand how emotions affect behavior in these environments and resulting economic consequences. Using a two-stage laboratory experiment, I analyze the role of reported emotions in tournament performance and assess how the behavioral response differs across genders. The first stage serves to induce emotions, while the second stage presents the subject with a one-on-one winner-take-all tournament with the individual who generated the feeling, using a real-effort task. Ultimately, I show that women respond to the negative feelings more strongly than men. I find that women increase performance when experiencing negative emotions, while male performance remains unaffected. Remarkably, there is no gender gap in tournament performance when there are negative emotions. Full article
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Open AccessArticle
Multi-Leader Multi-Follower Model with Aggregative Uncertainty
Games 2017, 8(3), 25; doi:10.3390/g8030025 -
Abstract
We study a non-cooperative game with aggregative structure, namely when the payoffs depend on the strategies of the opponent players through an aggregator function. We assume that a subset of players behave as leaders in a Stackelberg model. The leaders, as well the
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We study a non-cooperative game with aggregative structure, namely when the payoffs depend on the strategies of the opponent players through an aggregator function. We assume that a subset of players behave as leaders in a Stackelberg model. The leaders, as well the followers, act non-cooperatively between themselves and solve a Nash equilibrium problem. We assume an exogenous uncertainty affecting the aggregator and we obtain existence results for the stochastic resulting game. Some examples are illustrated. Full article
Open AccessArticle
Clusters with Minimum Transportation Cost to Centers: A Case Study in Corn Production Management
Games 2017, 8(2), 24; doi:10.3390/g8020024 -
Abstract
In Northern Thailand, the size and topographical structure of farmland makes it necessary for operators of small-scale waste management systems to be able to reach their clients in an effective manner. Over the past decades, corn contract farming has increased, and the chief
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In Northern Thailand, the size and topographical structure of farmland makes it necessary for operators of small-scale waste management systems to be able to reach their clients in an effective manner. Over the past decades, corn contract farming has increased, and the chief method for eliminating waste from these farms has chiefly been open burning on the fields, which produces enormous amounts of greenhouse gases (GHG) and Polycyclic Aromatic Hydrocarbons (PAHs). To find a way to reduce GHG emissions in the corn production system, this work focuses on finding clusters with minimum transportation time from waste disposal centers. To solve the clustering problems, four models are created and solved on AIMMS and MATLAB. Simulation results indicate that the number of clients essentially affects the performance of the procedure. The case studies are on corn production management in Chiang Mai, the region’s economic capital, as well as in 9 provinces in Northern Thailand, including Chiang Mai, whose combined corn production comprises 32.73 percent of the national production. With roughly 15% of the corn cobs and husks involved in the study, we found that by changing the waste elimination process, the total CO2 emissions can be reduced by up to 12,008.40 tons per year in Chiang Mai and up to 180,198.14 tons per year in the 9 provinces of Northern Thailand. Full article
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Open AccessArticle
Security Investment, Hacking, and Information Sharing between Firms and between Hackers
Games 2017, 8(2), 23; doi:10.3390/g8020023 -
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
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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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