Games

4 pages, 159 KiB

Open AccessEditorial

Optimal Control Theory: Introduction to the Special Issue

by Ellina Grigorieva

Games 2021, 12(1), 29; https://doi.org/10.3390/g12010029 - 22 Mar 2021

Cited by 1 | Viewed by 3357

Abstract

Optimal control theory is a modern extension of the classical calculus of variations [...] Full article

(This article belongs to the Special Issue Optimal Control Theory)

22 pages, 337 KiB

Open AccessEditor’s ChoiceArticle

Optimal Incentives Schemes under Homo Moralis Preferences

by Roberto Sarkisian

Games 2021, 12(1), 28; https://doi.org/10.3390/g12010028 - 19 Mar 2021

Cited by 2 | Viewed by 2542

Abstract

This study focuses on the optimal incentive schemes in a multi-agent moral hazard model, where each agent has other-regarding preferences and an individual measure of output, with both being observable by the principal. In particular, the two agents display homo moralis preferences. I [...] Read more.

This study focuses on the optimal incentive schemes in a multi-agent moral hazard model, where each agent has other-regarding preferences and an individual measure of output, with both being observable by the principal. In particular, the two agents display homo moralis preferences. I find that, contrary to the case with purely selfish preferences, tournaments can never be optimal when agents are risk averse, and as the degree of morality increases, positive payments are made in a larger number of output realizations. Furthermore, I extend the analysis to a dynamic setting, in which a contract is initially offered to the agents, who then repeatedly choose which level of effort to provide in each period. I show that the optimal incentive schemes in this case are similar to the ones obtained in the static setting, but for the role of intertemporal discounting. Full article

11 pages, 844 KiB

Open AccessArticle

The Role of Cultural Capital on the Voluntary Contributions to Cultural Goods: A Differential Game Approach

by Massimo Finocchiaro Castro, Isidoro Mazza and Domenica Romeo

Games 2021, 12(1), 27; https://doi.org/10.3390/g12010027 - 18 Mar 2021

Cited by 2 | Viewed by 2332

Abstract

This study aims to offer a formal analysis which relates provision of cultural goods to the society’s level of cultural capital. Such a level is assumed to already exist in society and is increasable thanks to individual support for the offer of cultural [...] Read more.

This study aims to offer a formal analysis which relates provision of cultural goods to the society’s level of cultural capital. Such a level is assumed to already exist in society and is increasable thanks to individual support for the offer of cultural goods. The achievement of the highest levels of cultural capital increases satisfaction coming from cultural goods consumption, and then voluntary contributions. Social approval, deriving from donations, is positively related to society’s existing cultural capital and triggers a positive externality for donators, thus increasing contributions and generating a positive externality for the whole society. The dynamic analysis provided in this study requires the adoption of a differential game where individuals interact, making their choices on their voluntary contribution level. We find that, under certain conditions, the solution obtained for the Nash equilibrium with closed-loop strategies provides optimal level of cultural capital that exceed the Pareto efficient solution obtained through open-loop strategies. Full article

(This article belongs to the Special Issue Cooperation, Innovation and Safeguarding of the Environment)

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8 pages, 235 KiB

Open AccessArticle

The (Non) Economic Properties of the Law

by Leo Katz and Alvaro Sandroni

Games 2021, 12(1), 26; https://doi.org/10.3390/g12010026 - 16 Mar 2021

Viewed by 2026

Abstract

This paper shows that the logical properties of constraints imposed by law are fundamentally different from other constraints considered in economics such as budget constraints and bounded rationality constraints, such as the ones based on inattention or shortlisting. This suggests that to fully [...] Read more.

This paper shows that the logical properties of constraints imposed by law are fundamentally different from other constraints considered in economics such as budget constraints and bounded rationality constraints, such as the ones based on inattention or shortlisting. This suggests that to fully incorporate law into economics may require a revision of economic theory. Full article

(This article belongs to the Special Issue Limited Attention)

19 pages, 8598 KiB

Open AccessArticle

Repeated Interaction and Its Impact on Cooperation and Surplus Allocation—An Experimental Analysis

by Sibilla Di Guida, The Anh Han, Georg Kirchsteiger, Tom Lenaerts and Ioannis Zisis

Games 2021, 12(1), 25; https://doi.org/10.3390/g12010025 - 4 Mar 2021

Cited by 2 | Viewed by 3916

Abstract

This paper investigates how the possibility of affecting group composition combined with the possibility of repeated interaction impacts cooperation within groups and surplus distribution. We developed and tested experimentally a Surplus Allocation Game where cooperation of four agents is needed to produce surplus, [...] Read more.

This paper investigates how the possibility of affecting group composition combined with the possibility of repeated interaction impacts cooperation within groups and surplus distribution. We developed and tested experimentally a Surplus Allocation Game where cooperation of four agents is needed to produce surplus, but only two have the power to allocate it among the group members. Three matching procedures (corresponding to three separate experimental treatments) were used to test the impact of the variables of interest. A total of 400 subjects participated in our research, which was computer-based and conducted in a laboratory. Our results show that allowing for repeated interaction with the same partners leads to a self-selection of agents into groups with different life spans, whose duration is correlated with the behavior of both distributors and receivers. While behavior at the group level is diverse for surplus allocation and amount of cooperation, aggregate behavior is instead similar when repeated interaction is allowed or not allowed. We developed a behavioral model that captures the dynamics observed in the experimental data and sheds light into the rationales that drive the agents’ individual behavior, suggesting that the most generous distributors are those acting for fear of rejection, not for true generosity, while the groups lasting the longest are those composed by this type of distributors and “undemanding” receivers. Full article

(This article belongs to the Special Issue Social Dilemmas and Other-Regarding Preferences)

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40 pages, 1023 KiB

Open AccessArticle

Political Mobilization in the Laboratory: The Role of Norms and Communication

by Pedro Robalo

Games 2021, 12(1), 24; https://doi.org/10.3390/g12010024 - 3 Mar 2021

Viewed by 3946

Abstract

Many field experiments have shown that political mobilization increases voter turnout, with personalized strategies considerably outperforming widely administered ones. Despite the abundant evidence, there is no systematic explanation of what drives citizens’ response to mobilization. In this paper, I propose and experimentally test [...] Read more.

Many field experiments have shown that political mobilization increases voter turnout, with personalized strategies considerably outperforming widely administered ones. Despite the abundant evidence, there is no systematic explanation of what drives citizens’ response to mobilization. In this paper, I propose and experimentally test in the laboratory a theoretical framework that investigates the psychological mechanisms underlying mobilization in both partisan and non-partisan settings. I conjecture that material mobilization efforts should increase participation because of reciprocity concerns. The transmission of normative appeals through interpersonal communication should have a similar effect by making a group norm salient. The results from two experiments show that the combination of a mobilization effort with a normative appeal leads to a significant and substantial increase in participation in both settings. Using content analysis, I show that this interaction effect is due to the way normative appeals are perceived when the sender is in charge of mobilization. Full article

(This article belongs to the Special Issue Laboratory Experiments: Cooperation, Sanctions and Norms)

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9 pages, 250 KiB

Open AccessArticle

An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

by Alexander Arguchintsev and Vasilisa Poplevko

Games 2021, 12(1), 23; https://doi.org/10.3390/g12010023 - 3 Mar 2021

Cited by 6 | Viewed by 2498

Abstract

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled [...] Read more.

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach. Full article

(This article belongs to the Special Issue Optimal Control Theory)

11 pages, 1100 KiB

Open AccessEditor’s ChoiceArticle

Teams Do Inflict Costly Third-Party Punishment as Individuals Do: Experimental Evidence

by Kenju Kamei

Games 2021, 12(1), 22; https://doi.org/10.3390/g12010022 - 3 Mar 2021

Cited by 1 | Viewed by 2981

Abstract

Initiated by the seminal work of Fehr and Fischbacher (Evolution and Human Behavior (2004)), a large body of research has shown that people often take punitive actions towards norm violators even when they are not directly involved in transactions. This paper shows in [...] Read more.

Initiated by the seminal work of Fehr and Fischbacher (Evolution and Human Behavior (2004)), a large body of research has shown that people often take punitive actions towards norm violators even when they are not directly involved in transactions. This paper shows in an experimental setting that this behavioral finding extends to a situation where a pair of individuals jointly decides how strong a third-party punishment to impose. It also shows that this punishment behavior is robust to the size of social distance within pairs. These results lend useful insight since decisions in our everyday lives and also in courts are often made by teams. Full article

(This article belongs to the Special Issue Behavioral Coalition Formation: Theory and Experiments)

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10 pages, 244 KiB

Open AccessArticle

Path-Independent Consideration

by Juan Lleras, Yusufcan Masatlioglu, Daisuke Nakajima and Erkut Ozbay

Games 2021, 12(1), 21; https://doi.org/10.3390/g12010021 - 2 Mar 2021

Cited by 1 | Viewed by 2621

Abstract

In the context of choice with limited consideration, where the decision-maker may not pay attention to all available options, the consideration function of a decision maker is path-independent if her choice cannot be manipulated by the presentation of the choice set. This paper [...] Read more.

In the context of choice with limited consideration, where the decision-maker may not pay attention to all available options, the consideration function of a decision maker is path-independent if her choice cannot be manipulated by the presentation of the choice set. This paper characterizes a model of choice with limited consideration with path independence, which is equivalent to a consideration function that satisfies both the attention filter and consideration filter properties from Masatlioglu et al. (2012) and Lleras et al. (2017), respectively. Despite the equivalence of path-independent consideration with the consideration structures from these two papers, we show that, to have a choice with limited consideration that is path-independent, satisfying both axioms on the choice function that characterize choice limited consideration with attention and consideration filters unilaterally (from Masatlioglu et al. (2012) and Lleras et al. (2017)) is necessary but not sufficient. Full article

(This article belongs to the Special Issue Limited Attention)

16 pages, 455 KiB

Open AccessEditor’s ChoiceArticle

A Generalization of Quantal Response Equilibrium via Perturbed Utility

by Roy Allen and John Rehbeck

Games 2021, 12(1), 20; https://doi.org/10.3390/g12010020 - 1 Mar 2021

Cited by 6 | Viewed by 2907

Abstract

We present a tractable generalization of quantal response equilibrium via non-expected utility preferences. In particular, we introduce concave perturbed utility games in which an individual has strategy-specific utility indices that depend on the outcome of the game and an additively separable preference to [...] Read more.

We present a tractable generalization of quantal response equilibrium via non-expected utility preferences. In particular, we introduce concave perturbed utility games in which an individual has strategy-specific utility indices that depend on the outcome of the game and an additively separable preference to randomize. The preference to randomize can be viewed as a reduced form of limited attention. Using concave perturbed utility games, we show how to enrich models based on logit best response that are common from quantal response equilibrium. First, the desire to randomize can depend on opponents’ strategies. Second, we show how to derive a nested logit best response function. Lastly, we present tractable quadratic perturbed utility games that allow complementarity. Full article

(This article belongs to the Special Issue Limited Attention)

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2 pages, 152 KiB

Open AccessEditorial

Experiments on Communication in Games: Introduction to the Special Issue

by Caleb A. Cox and Brock Stoddard

Games 2021, 12(1), 19; https://doi.org/10.3390/g12010019 - 24 Feb 2021

Viewed by 2305

Abstract

Communication is an important topic in the experimental study of strategic behavior, both because of the vital role of communication in variety of strategic games, and because of the insights that can be gained through analyzing communication contents in experiments [...] Full article

(This article belongs to the Special Issue Experiments on Communication in Games)

14 pages, 3393 KiB

Open AccessArticle

Lab-Sophistication: Does Repeated Participation in Laboratory Experiments Affect Pro-Social Behaviour?

by Tiziana Medda, Vittorio Pelligra and Tommaso Reggiani

Games 2021, 12(1), 18; https://doi.org/10.3390/g12010018 - 22 Feb 2021

Cited by 3 | Viewed by 3565

Abstract

Experimental social scientists working at research-intensive institutions deal inevitably with subjects who have most likely participated in previous experiments. It is an important methodological question to know whether participants that have acquired a high level of lab-sophistication show altered pro-social behavioural patterns. In [...] Read more.

Experimental social scientists working at research-intensive institutions deal inevitably with subjects who have most likely participated in previous experiments. It is an important methodological question to know whether participants that have acquired a high level of lab-sophistication show altered pro-social behavioural patterns. In this paper, we focus both on the potential effect of the subjects’ lab-sophistication, and on the role of the knowledge about the level of lab-sophistication of the other participants. Our main findings show that while lab-sophistication per se does not significantly affect pro-social behaviour, for sophisticated subjects the knowledge about the counterpart’s level of (un)sophistication may systematically alter their choices. This result should induce caution among experimenters about whether, in their settings, information about lab-sophistication can be inferred by the participants, due to the characteristics of the recruitment mechanisms, the management of the experimental sessions or to other contextual clues. Full article

(This article belongs to the Special Issue Pro-sociality and Cooperation)

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21 pages, 599 KiB

Open AccessArticle

Fractional Punishment of Free Riders to Improve Cooperation in Optional Public Good Games

by Rocio Botta, Gerardo Blanco and Christian E. Schaerer

Games 2021, 12(1), 17; https://doi.org/10.3390/g12010017 - 5 Feb 2021

Cited by 2 | Viewed by 3835

Abstract

Improving and maintaining cooperation are fundamental issues for any project to be time-persistent, and sanctioning free riders may be the most applied method to achieve it. However, the application of sanctions differs from one group (project or institution) to another. We propose an [...] Read more.

Improving and maintaining cooperation are fundamental issues for any project to be time-persistent, and sanctioning free riders may be the most applied method to achieve it. However, the application of sanctions differs from one group (project or institution) to another. We propose an optional, public good game model where a randomly selected set of the free riders is punished. To this end, we introduce a parameter that establishes the portion of free riders sanctioned with the purpose to control the population state evolution in the game. This parameter modifies the phase portrait of the system, and we show that, when the parameter surpasses a threshold, the full cooperation equilibrium point becomes a stable global attractor. Hence, we demonstrate that the fractional approach improves cooperation while reducing the sanctioning cost. Full article

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26 pages, 1609 KiB

Open AccessArticle

Trust and Trustworthiness in Corrupted Economic Environments

by Leonardo Becchetti, Luca Corazzini and Vittorio Pelligra

Games 2021, 12(1), 16; https://doi.org/10.3390/g12010016 - 4 Feb 2021

Viewed by 3293

Abstract

We use an original variant of the standard trust game to study the effects of corruption on trust and trustworthiness. In this game, both the trustor and the trustee know that part of the surplus they can generate may be captured by a [...] Read more.

We use an original variant of the standard trust game to study the effects of corruption on trust and trustworthiness. In this game, both the trustor and the trustee know that part of the surplus they can generate may be captured by a third “corrupted” player under different expected costs of audit and prosecution. We find a slightly higher trustor’s giving in the presence of corruption, matched by a significant excess of reciprocity from the trustee. Both the trustor and the trustee expect, on average, corruption to act as a tax, inelastic to changes in the probability of corruption prosecution. Expectations are correct for the inelasticity assumption and for the actual value of the “corruption tax”. Our experimental findings lead to the rejection of four standard hypotheses based on purely self-regarding preferences. We discuss how the apparently paradoxical excess reciprocity effect is consistent with the cultural role of heroes in history, where examples of commendable giving have been used to stimulate emulation of ordinary people. Our results suggest that the excess reciprocity component of the trustee makes the trustor’s excess giving a rational and effective strategy. Full article

(This article belongs to the Special Issue Laboratory Experiments: Cooperation, Sanctions and Norms)

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16 pages, 1242 KiB

Open AccessArticle

Coordinating Carbon Emissions via Production Quantities: A Differential Game Approach

by Gila E. Fruchter and Hussein Naseraldin

Games 2021, 12(1), 15; https://doi.org/10.3390/g12010015 - 3 Feb 2021

Viewed by 2110

Abstract

Production emissions in the industrial sector are a major source of environmental pollution. In this paper, we explore how emission considerations are integrated with production decisions. We develop a dynamic model consisting of two firms located in the same industrial park, which satisfies [...] Read more.

Production emissions in the industrial sector are a major source of environmental pollution. In this paper, we explore how emission considerations are integrated with production decisions. We develop a dynamic model consisting of two firms located in the same industrial park, which satisfies exogenously given demands in separate markets. The two firms can build up or rundown stocks (full backlogging), both of which are costly. The emission cost depends on the total output of the two firms. We develop Nash equilibrium feedback strategies, where each firm decides on its output based on its inventory or the inventories of both. We also develop a social planning solution where decisions are centralized. We present the analytic results for the total profits in these settings. The results show the benefits of a decentralized approach over a centralized one, provided there is a mechanism for coordination. Finally, emission costs are compared for the various solution concepts. Full article

(This article belongs to the Special Issue Cooperation, Innovation and Safeguarding of the Environment)

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16 pages, 376 KiB

Open AccessEditor’s ChoiceArticle

Cartel Formation in Cournot Competition with Asymmetric Costs: A Partition Function Approach

by Takaaki Abe

Games 2021, 12(1), 14; https://doi.org/10.3390/g12010014 - 1 Feb 2021

Cited by 1 | Viewed by 2974

Abstract

In this paper, we use a partition function form game to analyze cartel formation among firms in Cournot competition. We assume that a firm obtains a certain cost advantage that allows it to produce goods at a lower unit cost. We show that [...] Read more.

In this paper, we use a partition function form game to analyze cartel formation among firms in Cournot competition. We assume that a firm obtains a certain cost advantage that allows it to produce goods at a lower unit cost. We show that if the level of the cost advantage is “moderate”, then the firm with the cost advantage leads the cartel formation among the firms. Moreover, if the cost advantage is relatively high, then the formed cartel can also be stable in the sense of the core of a partition function form game. We also show that if the technology for the low-cost production can be copied, then the cost advantage may prevent a cartel from splitting. Full article

(This article belongs to the Special Issue Behavioral Coalition Formation: Theory and Experiments)

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18 pages, 353 KiB

Open AccessArticle

EU Demand for Defense, 1990–2019: A Strategic Spatial Approach

by Justin George and Todd Sandler

Games 2021, 12(1), 13; https://doi.org/10.3390/g12010013 - 1 Feb 2021

Cited by 17 | Viewed by 2902

Abstract

For 1990–2019, this study presents two-step GMM estimates of EU members’ demands for defense spending based on alternative spatial-weight matrices. In particular, EU spatial connectivity is tied to EU membership status, members’ contiguity, contiguity and power projection, inverse distance, and arms trade. At [...] Read more.

For 1990–2019, this study presents two-step GMM estimates of EU members’ demands for defense spending based on alternative spatial-weight matrices. In particular, EU spatial connectivity is tied to EU membership status, members’ contiguity, contiguity and power projection, inverse distance, and arms trade. At a Nash equilibrium, our EU demand equations are derived explicitly from a spatially based game-theoretical model of alliances. Myriad spatial linkages among EU members provide a robust free-riding finding, which differs from the spatial and non-spatial literature on EU defense spending. Even though the EU applies common trade policies and allows for unrestricted labor movement among members, members’ defense responses adhered to those of a defense alliance. Moreover, EU defense spending exhibits positive responses to GDP and transnational terrorist attacks, and a negative response to population. During the sample period, EU members did not view Russia as a military threat. Full article

(This article belongs to the Special Issue Economics of Conflict and Terrorism)

13 pages, 3070 KiB

Open AccessArticle

Intention or Request: The Impact of Message Structures

by Siyu Wang and Timothy Flannery

Games 2021, 12(1), 12; https://doi.org/10.3390/g12010012 - 1 Feb 2021

Cited by 2 | Viewed by 3075

Abstract

This paper investigates how different message structures impact communication strategy as well as sender and receiver behavior. Specifically, we focus on comparing communication games with messages stating an intention versus a request. Our experimental results show that when a game includes self-signaling or [...] Read more.

This paper investigates how different message structures impact communication strategy as well as sender and receiver behavior. Specifically, we focus on comparing communication games with messages stating an intention versus a request. Our experimental results show that when a game includes self-signaling or self-committing messages, the two message structures yield negligibly different results. However, when the messages of the game are neither self-signaling nor self-committing, we find that more subjects send messages suggesting cooperation with request than intention. Interestingly, subjects also deviate from their suggested actions more frequently with request than intention. We surmise lying aversion plays a prominent role in contributing to the differences in games where messages lack the self-committing property. Full article

(This article belongs to the Special Issue Experiments on Communication in Games)

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12 pages, 1026 KiB

Open AccessArticle

Optimal Control and Positional Controllability in a One-Sector Economy

by Nikolai Grigorenko and Lilia Luk’yanova

Games 2021, 12(1), 11; https://doi.org/10.3390/g12010011 - 1 Feb 2021

Cited by 3 | Viewed by 1976

Abstract

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, [...] Read more.

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations. Full article

(This article belongs to the Special Issue Optimal Control Theory)

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3 pages, 162 KiB

Open AccessEditorial

Acknowledgment to Reviewers of Games in 2020

by Games Editorial Office

Games 2021, 12(1), 10; https://doi.org/10.3390/g12010010 - 27 Jan 2021

Cited by 1 | Viewed by 1972

Abstract

Peer review is the driving force of journal development, and reviewers are gatekeepers who ensure that Games maintains its standards for the high quality of its published papers [...] Full article

22 pages, 4037 KiB

Open AccessArticle

Necessary Optimality Conditions for a Class of Control Problems with State Constraint

by Adam Korytowski and Maciej Szymkat

Games 2021, 12(1), 9; https://doi.org/10.3390/g12010009 - 18 Jan 2021

Cited by 2 | Viewed by 3053

Abstract

An elementary approach to a class of optimal control problems with pathwise state constraint is proposed. Based on spike variations of control, it yields simple proofs and constructive necessary conditions, including some new characterizations of optimal control. Two examples are discussed. Full article

(This article belongs to the Special Issue Optimal Control Theory)

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18 pages, 1523 KiB

Open AccessArticle

Boltzmann Distributed Replicator Dynamics: Population Games in a Microgrid Context

by Gustavo Chica-Pedraza, Eduardo Mojica-Nava and Ernesto Cadena-Muñoz

Games 2021, 12(1), 8; https://doi.org/10.3390/g12010008 - 15 Jan 2021

Cited by 3 | Viewed by 2816

Abstract

Multi-Agent Systems (MAS) have been used to solve several optimization problems in control systems. MAS allow understanding the interactions between agents and the complexity of the system, thus generating functional models that are closer to reality. However, these approaches assume that information between [...] Read more.

Multi-Agent Systems (MAS) have been used to solve several optimization problems in control systems. MAS allow understanding the interactions between agents and the complexity of the system, thus generating functional models that are closer to reality. However, these approaches assume that information between agents is always available, which means the employment of a full-information model. Some tendencies have been growing in importance to tackle scenarios where information constraints are relevant issues. In this sense, game theory approaches appear as a useful technique that use a strategy concept to analyze the interactions of the agents and achieve the maximization of agent outcomes. In this paper, we propose a distributed control method of learning that allows analyzing the effect of the exploration concept in MAS. The dynamics obtained use Q-learning from reinforcement learning as a way to include the concept of exploration into the classic exploration-less Replicator Dynamics equation. Then, the Boltzmann distribution is used to introduce the Boltzmann-Based Distributed Replicator Dynamics as a tool for controlling agents behaviors. This distributed approach can be used in several engineering applications, where communications constraints between agents are considered. The behavior of the proposed method is analyzed using a smart grid application for validation purposes. Results show that despite the lack of full information of the system, by controlling some parameters of the method, it has similar behavior to the traditional centralized approaches. Full article

(This article belongs to the Special Issue Optimal Control Theory)

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14 pages, 302 KiB

Open AccessArticle

Quantum Mean-Field Games with the Observations of Counting Type

by Vassili N. Kolokoltsov

Games 2021, 12(1), 7; https://doi.org/10.3390/g12010007 - 14 Jan 2021

Cited by 7 | Viewed by 2670

Abstract

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive [...] Read more.

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an

ϵ

-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem. Full article

29 pages, 767 KiB

Open AccessArticle

Parties’ Preferences for Office and Policy Goals

by Anna Bassi

Games 2021, 12(1), 6; https://doi.org/10.3390/g12010006 - 14 Jan 2021

Cited by 1 | Viewed by 2931

Abstract

Although parties’ preferences for office and policy goals have been featured by many rational choice models of party behavior and a majority of coalition theories, the literature still lacks a measure and a comprehensive analysis of how parties’ preferences vary among parties and [...] Read more.

Although parties’ preferences for office and policy goals have been featured by many rational choice models of party behavior and a majority of coalition theories, the literature still lacks a measure and a comprehensive analysis of how parties’ preferences vary among parties and across countries. This study aims to fill this gap by presenting the results of an original expert survey protocol, which finds that parties pursue both goals simultaneously as office is sought both as and an end and as a means to affect policy, and that the degree to which they prefer policy versus office objectives varies across parties and countries. I provide an application of the preference ratings for policy versus office in the context of government formation, by using the ratings to solve for and predict the equilibrium coalition that should have formed in Spain after the 2015 elections. The government predicted by the model matches the government that formed, providing evidence of the ability of the preference ratings to generate reliable predictions of the composition of government coalitions. Full article

(This article belongs to the Special Issue Government and Coalition Formation)

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12 pages, 271 KiB

Open AccessArticle

μ–σ Games

by Uwe Dulleck and Andreas Löffler

Games 2021, 12(1), 5; https://doi.org/10.3390/g12010005 - 12 Jan 2021

Viewed by 2441

Abstract

Risk aversion in game theory is usually modeled using expected utility, which was criticized early on, leading to an extensive literature on generalized expected utility. In this paper we are the first to apply

μ

–

σ

theory to the analysis of (static) [...] Read more.

Risk aversion in game theory is usually modeled using expected utility, which was criticized early on, leading to an extensive literature on generalized expected utility. In this paper we are the first to apply

μ

–

σ

theory to the analysis of (static) games.

μ

–

σ

theory is widely accepted in the finance literature; using it allows us to study the effect on uncertainty endogenous to the game, i.e., mixed equilibria. In particular, we look at the case of linear

μ

–

σ

utility functions and determine the best response strategy. In the case of 2 × 2 and N × M games, we are able to characterize all mixed equilibria. Full article

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17 pages, 340 KiB

Open AccessEditor’s ChoiceArticle

Social Pressure in Networks Induces Public Good Provision

by David Jimenez-Gomez

Games 2021, 12(1), 4; https://doi.org/10.3390/g12010004 - 12 Jan 2021

Cited by 2 | Viewed by 2725

Abstract

I develop a dynamic model with forward looking agents, and show that social pressure is effective in generating provision in a public good game: after a small group of agents start contributing to the public good, other agents decide to contribute as well [...] Read more.

I develop a dynamic model with forward looking agents, and show that social pressure is effective in generating provision in a public good game: after a small group of agents start contributing to the public good, other agents decide to contribute as well due to a fear of being punished, and this generates contagion in the network. In contrast to earlier models in the literature, contagion happens fast, as part of the best response of fully rational individuals. The network topology has implications for whether contagion starts and the extent to which it spreads. I find conditions under which an agent decides to be the first to contribute in order to generate contagion in the network, as well as conditions for contribution due to a self-fulfilling fear of social pressure. Full article

(This article belongs to the Special Issue Pro-sociality and Cooperation)

22 pages, 383 KiB

Open AccessEditor’s ChoiceArticle

Constrained versus Unconstrained Rational Inattention

by Yaron Azrieli

Games 2021, 12(1), 3; https://doi.org/10.3390/g12010003 - 5 Jan 2021

Cited by 1 | Viewed by 2617

Abstract

The rational inattention literature is split between two versions of the model: in one, mutual information of states and signals are bounded by a hard constraint, while, in the other, it appears as an additive term in the decision maker’s utility function. The [...] Read more.

The rational inattention literature is split between two versions of the model: in one, mutual information of states and signals are bounded by a hard constraint, while, in the other, it appears as an additive term in the decision maker’s utility function. The resulting constrained and unconstrained maximization problems are closely related, but, nevertheless, their solutions differ in certain aspects. In particular, movements in the decision maker’s prior belief and utility function lead to opposite comparative statics conclusions. Full article

(This article belongs to the Special Issue Limited Attention)

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19 pages, 1774 KiB

Open AccessArticle

Nudge the Lunch: A Field Experiment Testing Menu-Primacy Effects on Lunch Choices

by Ola Andersson and Lif Nelander

Games 2021, 12(1), 2; https://doi.org/10.3390/g12010002 - 5 Jan 2021

Cited by 9 | Viewed by 6744

Abstract

By way of a field experiment conducted at a university cafeteria this paper finds that placing a vegetarian option instead of a meat option at the top of a menu decreases the share of meat dishes sold by 11%. This translates to a [...] Read more.

By way of a field experiment conducted at a university cafeteria this paper finds that placing a vegetarian option instead of a meat option at the top of a menu decreases the share of meat dishes sold by 11%. This translates to a 6% decrease of daily emissions due to food sales. Using data on payment method, we find that the result is most likely driven by non-students responding to the nudge. Full article

(This article belongs to the Special Issue Limited Attention)

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23 pages, 692 KiB

Open AccessArticle

Are People Willing to Tell Pareto White Lies? A Review and New Experimental Evidence

by Edward Cartwright, Lian Xue and Charlotte Brown

Games 2021, 12(1), 1; https://doi.org/10.3390/g12010001 - 23 Dec 2020

Cited by 5 | Viewed by 4573

Abstract

We explore whether individuals are averse to telling a Pareto white lie—a lie that benefits both themselves and another. We first review and summarize the existing evidence on Pareto white lies. We find that the evidence is relatively limited and varied in its [...] Read more.

We explore whether individuals are averse to telling a Pareto white lie—a lie that benefits both themselves and another. We first review and summarize the existing evidence on Pareto white lies. We find that the evidence is relatively limited and varied in its conclusions. We then present new experimental results obtained using a coin-tossing experiment. Results are provided for both the UK and China. We find evidence of willingness to tell a partial lie (i.e., inflating reports slightly) and high levels of aversion to telling a Pareto white lie that would maximize payoffs. We also find no significant difference between willingness to tell a Pareto white lie and a selfish black lie—a lie that harms another. We find marginal evidence of more lying in China than the UK, but the overall results in the UK and China are very similar. Full article

(This article belongs to the Special Issue Experiments on Dishonesty in Strategic Interactions)

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Games, Volume 12, Issue 1 (March 2021) – 29 articles

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