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Games, Volume 9, Issue 1 (March 2018)

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Editorial

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Open AccessEditorial Acknowledgement to Reviewers of Games in 2017
Received: 12 January 2018 / Revised: 12 January 2018 / Accepted: 12 January 2018 / Published: 12 January 2018
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Research

Jump to: Editorial

Open AccessArticle The Effects of Excluding Coalitions
Received: 2 November 2017 / Revised: 13 December 2017 / Accepted: 18 December 2017 / Published: 1 January 2018
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Abstract
One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect
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One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value ( φ E value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent. Full article
Open AccessArticle On the Query Complexity of Black-Peg AB-Mastermind
Received: 8 November 2017 / Revised: 22 December 2017 / Accepted: 28 December 2017 / Published: 2 January 2018
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Abstract
Mastermind is a two players zero sum game of imperfect information. Starting with Erdős and Rényi (1963), its combinatorics have been studied to date by several authors, e.g., Knuth (1977), Chvátal (1983), Goodrich (2009). The first player, called “codemaker”, chooses a secret code
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Mastermind is a two players zero sum game of imperfect information. Starting with Erdős and Rényi (1963), its combinatorics have been studied to date by several authors, e.g., Knuth (1977), Chvátal (1983), Goodrich (2009). The first player, called “codemaker”, chooses a secret code and the second player, called “codebreaker”, tries to break the secret code by making as few guesses as possible, exploiting information that is given by the codemaker after each guess. For variants that allow color repetition, Doerr et al. (2016) showed optimal results. In this paper, we consider the so called Black-Peg variant of Mastermind, where the only information concerning a guess is the number of positions in which the guess coincides with the secret code. More precisely, we deal with a special version of the Black-Peg game with n holes and k n colors where no repetition of colors is allowed. We present upper and lower bounds on the number of guesses necessary to break the secret code. For the case k = n , the secret code can be algorithmically identified within less than ( n 3 ) log 2 n + 5 2 n 1 queries. This result improves the result of Ker-I Ko and Shia-Chung Teng (1985) by almost a factor of 2. For the case k > n , we prove an upper bound of ( n 2 ) log 2 n + k + 1 . Furthermore, we prove a new lower bound of n for the case k = n , which improves the recent n log log ( n ) bound of Berger et al. (2016). We then generalize this lower bound to k queries for the case k n . Full article
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Open AccessArticle Incentive Magnitude Effects in Experimental Games: Bigger is not Necessarily Better
Received: 10 November 2017 / Revised: 29 December 2017 / Accepted: 11 January 2018 / Published: 18 January 2018
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Abstract
In experimental games, task-related incentives are payments to experimental subjects that vary according to their strategy choices and the consequent outcomes of the games. Limited evidence exists regarding incentive magnitude effects in experimental games. We examined one-off strategy choices and self-reported reasons for
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In experimental games, task-related incentives are payments to experimental subjects that vary according to their strategy choices and the consequent outcomes of the games. Limited evidence exists regarding incentive magnitude effects in experimental games. We examined one-off strategy choices and self-reported reasons for choices in eight 3 × 3 and four 4 × 4 normal-form games under task-related incentives of conventional magnitude and compared them with choices and reasons in the same games under incentives five times as large. Both strategy choices and self-reported reasons for choices were almost indistinguishable between the two conditions. These results are in line with earlier findings on individual decision making and with a parametric model, in which the incentive elasticity of effort is very small when compared with other factors, such as the complexity of the decision problem. Full article
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Open AccessArticle Examining Spillovers between Long and Short Repeated Prisoner’s Dilemma Games Played in the Laboratory
Received: 27 November 2017 / Revised: 12 January 2018 / Accepted: 25 January 2018 / Published: 31 January 2018
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Abstract
We had participants play two sets of repeated Prisoner’s Dilemma (RPD) games, one with a large continuation probability and the other with a small continuation probability, as well as Dictator Games (DGs) before and after the RPDs. We find that, regardless of which
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We had participants play two sets of repeated Prisoner’s Dilemma (RPD) games, one with a large continuation probability and the other with a small continuation probability, as well as Dictator Games (DGs) before and after the RPDs. We find that, regardless of which is RPD set is played first, participants typically cooperate when the continuation probability is large and defect when the continuation probability is small. However, there is an asymmetry in behavior when transitioning from one continuation probability to the other. When switching from large to small, transient higher levels of cooperation are observed in the early games of the small continuation set. Conversely, when switching from small to large, cooperation is immediately high in the first game of the large continuation set. We also observe that response times increase when transitioning between sets of RPDs, except for altruistic participants transitioning into the set of RPDs with long continuation probabilities. These asymmetries suggest a bias in favor of cooperation. Finally, we examine the link between altruism and RPD play. We find that small continuation probability RPD play is correlated with giving in DGs played before and after the RPDs, whereas high continuation probability RPD play is not. Full article
(This article belongs to the Special Issue Economic Behavior and Game Theory)
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Open AccessArticle Optimal Incentives in a Principal–Agent Model with Endogenous Technology
Received: 2 November 2017 / Revised: 25 January 2018 / Accepted: 26 January 2018 / Published: 5 February 2018
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Abstract
One of the standard predictions of the agency theory is that more incentives can be given to agents with lower risk aversion. In this paper, we show that this relationship may be absent or reversed when the technology is endogenous and projects with
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One of the standard predictions of the agency theory is that more incentives can be given to agents with lower risk aversion. In this paper, we show that this relationship may be absent or reversed when the technology is endogenous and projects with a higher efficiency are also riskier. Using a modified version of the Holmstrom and Milgrom’s framework, we obtain that lower agent’s risk aversion unambiguously leads to higher incentives when the technology function linking efficiency and riskiness is elastic, while the risk aversion–incentive relationship can be positive when this function is rigid. Full article
Open AccessArticle Linear–Quadratic Mean-Field-Type Games: A Direct Method
Received: 4 January 2018 / Revised: 29 January 2018 / Accepted: 31 January 2018 / Published: 12 February 2018
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Abstract
In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control
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In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form. Full article
(This article belongs to the Special Issue Mean-Field-Type Game Theory)
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Open AccessArticle A Game-Theoretic Approach for Modeling Competitive Diffusion over Social Networks
Received: 26 October 2017 / Revised: 18 January 2018 / Accepted: 23 January 2018 / Published: 13 February 2018
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Abstract
In this paper, we consider a novel game theory model for the competitive influence maximization problem. We model this problem as a simultaneous non-cooperative game with complete information and rational players, where there are at least two players who are supposed to be
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In this paper, we consider a novel game theory model for the competitive influence maximization problem. We model this problem as a simultaneous non-cooperative game with complete information and rational players, where there are at least two players who are supposed to be out of the network and are trying to institutionalize their options in the social network; that is, the objective of players is to maximize the spread of a desired opinion rather than the number of infected nodes. In the proposed model, we extend both the Linear Threshold model and the Independent Cascade model. We study an influence maximization model in which users’ heterogeneity, information content, and network structure are considered. Contrary to previous studies, in the proposed game, players find not only the most influential initial nodes but also the best information content. The proposed novel game was implemented on a real data set where individuals have different tendencies toward the players’ options that change over time because of gaining influence from their neighbors and the information content they receive. This means that information content, the topology of the graph, and the individual’s initial tendency significantly affect the diffusion process. The proposed game is solved and the Nash equilibrium is determined for a real data set. Lastly, the numerical results obtained from the proposed model were compared with some well-known models previously reported in the literature. Full article
(This article belongs to the Special Issue Applications of Game Theory to Networks)
Open AccessArticle Game of Thrones: Accommodating Monetary Policies in a Monetary Union
Received: 24 December 2017 / Revised: 26 January 2018 / Accepted: 31 January 2018 / Published: 19 February 2018
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Abstract
In this paper, we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyze the interactions between fiscal (governments) and monetary (common central bank) policy
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In this paper, we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyze the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm, we calculate solutions for several games: a noncooperative solution where each government and the central bank play against each other (a feedback Nash equilibrium solution), a fully-cooperative solution with all players following a joint course of action (a Pareto optimal solution) and three solutions where various coalitions (subsets of the players) play against coalitions of the other players in a noncooperative way. It turns out that the fully-cooperative solution yields the best results, the noncooperative solution fares worst and the coalition games lie in between, with a broad coalition of the fiscally more responsible countries and the central bank against the less thrifty countries coming closest to the Pareto optimum. Full article
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Open AccessFeature PaperArticle Dynamic Pricing Decisions and Seller-Buyer Interactions under Capacity Constraints
Games 2018, 9(1), 10; https://doi.org/10.3390/g9010010
Received: 26 December 2017 / Revised: 13 February 2018 / Accepted: 18 February 2018 / Published: 22 February 2018
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Abstract
Focusing on sellers’ pricing decisions and the ensuing seller-buyer interactions, we report an experiment on dynamic pricing with scarcity in the form of capacity constraints. Rational expectations equilibrium solutions are constructed and then tested experimentally with subjects assigned the roles of sellers and
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Focusing on sellers’ pricing decisions and the ensuing seller-buyer interactions, we report an experiment on dynamic pricing with scarcity in the form of capacity constraints. Rational expectations equilibrium solutions are constructed and then tested experimentally with subjects assigned the roles of sellers and buyers. We investigate behavior in two between-subject conditions with high and moderate levels of capacity. Our laboratory market exhibits strategic sophistication: the price offers of sellers and the buyers’ aggregate responses largely approximate equilibrium predictions. We also observe systematic deviations from equilibrium benchmarks on both sides of the market. Specifically, in our experiment the sellers are boundedly strategic: their prices often exhibit strategic adjustments to profit from buyers with limited strategic sophistication, but they are also often biased towards equilibrium pricing even when that would not be ex-post optimal. Full article
(This article belongs to the Special Issue Logistic Games)
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Open AccessArticle Imitation of Peers in Children and Adults
Games 2018, 9(1), 11; https://doi.org/10.3390/g9010011
Received: 17 January 2018 / Revised: 12 February 2018 / Accepted: 22 February 2018 / Published: 1 March 2018
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Abstract
Imitation of the successful choices of others is a simple and superficially attractive learning rule. It has been shown to be an important driving force for the strategic behavior of (young) adults. In this study we examine whether imitation is prevalent in the
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Imitation of the successful choices of others is a simple and superficially attractive learning rule. It has been shown to be an important driving force for the strategic behavior of (young) adults. In this study we examine whether imitation is prevalent in the behavior of children aged between 8 and 10. Surprisingly, we find that imitation seems to be cognitively demanding. Most children in this age group ignore information about others, foregoing substantial learning opportunities. While this seems to contradict much of the literature in the field of psychology, we argue that success-based imitation of peers may be harder for children to perform than non-success-based imitation of adults. Full article
(This article belongs to the Special Issue Choice and Decision Making)
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Open AccessArticle The Optimal Contract under Adverse Selection in a Moral-Hazard Model with a Risk-Averse Agent
Games 2018, 9(1), 12; https://doi.org/10.3390/g9010012
Received: 13 November 2017 / Revised: 14 February 2018 / Accepted: 21 February 2018 / Published: 1 March 2018
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Abstract
This paper studies the optimal contract offered by a risk-neutral principal to a risk-averse agent when the agent’s hidden ability and action both improve the probability of the project being successful. We show that if the agent is sufficiently prudent and able, the
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This paper studies the optimal contract offered by a risk-neutral principal to a risk-averse agent when the agent’s hidden ability and action both improve the probability of the project being successful. We show that if the agent is sufficiently prudent and able, the principal induces a higher probability of success than under moral hazard, despite the costly informational rent given up. Moreover, there is distortion at the top. Finally, the conditions to avoid pooling are difficult to satisfy because of the different kinds of incentives to be managed and the overall trade-off between rent extraction, insurance, and efficiency involved. Full article
(This article belongs to the Special Issue Contracts, Incentives and Information: Theory and Evidence)
Open AccessArticle Creating a Domain of Losses in the Laboratory: Effects of Endowment Size
Games 2018, 9(1), 13; https://doi.org/10.3390/g9010013
Received: 7 December 2017 / Revised: 11 February 2018 / Accepted: 18 February 2018 / Published: 2 March 2018
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Abstract
This study examines the effects of initial endowment size on individual behavior in a binary choice game with no dominant strategy. Subjects make decisions in two, theoretically identical sequences, differing in initial endowment levels only. Each decision involves a choice between an option
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This study examines the effects of initial endowment size on individual behavior in a binary choice game with no dominant strategy. Subjects make decisions in two, theoretically identical sequences, differing in initial endowment levels only. Each decision involves a choice between an option with a certain loss and an option with a loss that is increasing in the number of individuals who choose it. For the higher endowment level, all subjects are guaranteed a positive payoff. For the lower endowment level, subjects who choose the uncertain loss option could receive a negative payoff. The results indicate that in the first round of play, subjects with the higher endowment level choose the certain loss option significantly more often than subjects with the lower endowment level. There are, however, no significant differences in behavior beyond the first few rounds of play. Full article
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Open AccessArticle Does Imperfect Data Privacy Stop People from Collecting Personal Data?
Games 2018, 9(1), 14; https://doi.org/10.3390/g9010014
Received: 15 February 2018 / Revised: 26 February 2018 / Accepted: 28 February 2018 / Published: 5 March 2018
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Abstract
Many companies try to access personal information to discriminate among consumers. We analyse how privacy regulations affect the acquisition and disclosure of information in a simple game of persuasion. Theory predicts that no data will be acquired with Disclosure Duty of collected data
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Many companies try to access personal information to discriminate among consumers. We analyse how privacy regulations affect the acquisition and disclosure of information in a simple game of persuasion. Theory predicts that no data will be acquired with Disclosure Duty of collected data whereas Consent Law with perfect privacy results in complete information acquisition. Imperfect privacy, i.e., an environment in which leaks of collected data are possible, gives rise to multiple equilibria. Results from a laboratory experiment confirm the qualitative differences between Consent Law and Disclosure Duty and show that imperfect privacy does not stop people from collecting personal information. Full article
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Open AccessArticle Sequential Auctions with Capacity Constraints: An Experimental Investigation
Games 2018, 9(1), 15; https://doi.org/10.3390/g9010015
Received: 13 November 2017 / Revised: 19 February 2018 / Accepted: 28 February 2018 / Published: 12 March 2018
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Abstract
We conduct a laboratory experiment where groups of 4 subjects constrained to obtain at most one good each, sequentially bid for three goods in first and second price auctions. Subjects learn at the beginning of each auction their valuation for the good and
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We conduct a laboratory experiment where groups of 4 subjects constrained to obtain at most one good each, sequentially bid for three goods in first and second price auctions. Subjects learn at the beginning of each auction their valuation for the good and exit the auction once they have obtained one good. We show that, contrary to equilibrium predictions, subjects’ bidding behavior is excessively similar across units and across mechanisms at the aggregate level. We provide two (complementary) explanations for these departures. One is bounded rationality. Subjects do not fully comprehend subtle differences between mechanisms. The other is self-selection. Subjects are very heterogeneous and some of them deviate more from equilibrium than others. Since deviations take mostly the form of overbidding, these subjects win the first or second good and exit the auction, leaving those who play closer to theoretical predictions to bid for the third good. Support for this hypothesis comes from the documented higher bidding, lower efficiency and lower profits associated with the first and second unit compared to the third one. Full article
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