Games

28 pages, 976 KiB

Open AccessArticle

Direct Reciprocity and Model-Predictive Strategy Update Explain the Network Reciprocity Observed in Socioeconomic Networks

by Fabio Della Rossa, Fabio Dercole and Anna Di Meglio

Games 2020, 11(1), 16; https://doi.org/10.3390/g11010016 - 16 Mar 2020

Cited by 3 | Viewed by 3671

Abstract

Network reciprocity has been successfully put forward (since M. A. Nowak and R. May’s, 1992, influential paper) as the simplest mechanism—requiring no strategical complexity—supporting the evolution of cooperation in biological and socioeconomic systems. The mechanism is actually the network, which makes agents’ interactions [...] Read more.

Network reciprocity has been successfully put forward (since M. A. Nowak and R. May’s, 1992, influential paper) as the simplest mechanism—requiring no strategical complexity—supporting the evolution of cooperation in biological and socioeconomic systems. The mechanism is actually the network, which makes agents’ interactions localized, while network reciprocity is the property of the underlying evolutionary process to favor cooperation in sparse rather than dense networks. In theoretical models, the property holds under imitative evolutionary processes, whereas cooperation disappears in any network if imitation is replaced by the more rational best-response rule of strategy update. In social experiments, network reciprocity has been observed, although the imitative behavior did not emerge. What did emerge is a form of conditional cooperation based on direct reciprocity—the propensity to cooperate with neighbors who previously cooperated. To resolve this inconsistency, network reciprocity has been recently shown in a model that rationally confronts the two main behaviors emerging in experiments—reciprocal cooperation and unconditional defection—with rationality introduced by extending the best-response rule to a multi-step predictive horizon. However, direct reciprocity was implemented in a non-standard way, by allowing cooperative agents to temporarily cut the interaction with defecting neighbors. Here, we make this result robust to the way cooperators reciprocate, by implementing direct reciprocity with the standard tit-for-tat strategy and deriving similar results. Full article

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

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21 pages, 392 KiB

Open AccessArticle

Perceptions of Farm Size Heterogeneity and Demand for Group Index Insurance

by Kathryn Vasilaky, Sofía Martínez Sáenz, Radost Stanimirova and Daniel Osgood

Games 2020, 11(1), 15; https://doi.org/10.3390/g11010015 - 11 Mar 2020

Cited by 1 | Viewed by 4895

Abstract

Weather insurance is a financial instrument proposed to increase coverage of unprotected weather shocks in developing countries. Structuring sales as group-based products has been argued as a strategy to increase the attractiveness of index insurance, raising the question as to what impacts farmer [...] Read more.

Weather insurance is a financial instrument proposed to increase coverage of unprotected weather shocks in developing countries. Structuring sales as group-based products has been argued as a strategy to increase the attractiveness of index insurance, raising the question as to what impacts farmer demand for group insurance choices. We test if farmers prefer to purchase real-world insurance products as groups, and if groups of more similar individuals are more likely to demand group over individual index insurance for the upcoming season. We exogenously assign farmers into groups of similar versus dissimilar perceived farm size. We find that farmers, when offered, prefer group over individual insurance contracts, and that groups of farmers who perceive each other to be more similar in farm size are more likely to purchase in a group, but purchase less insurance on average. Full article

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12 pages, 2036 KiB

Open AccessArticle

Dynamics of Strategy Distributions in a One-Dimensional Continuous Trait Space for Games with a Quadratic Payoff Function

by Georgiy Karev

Games 2020, 11(1), 14; https://doi.org/10.3390/g11010014 - 02 Mar 2020

Viewed by 3282

Abstract

Evolution of distribution of strategies in game theory is an interesting question that has been studied only for specific cases. Here I develop a general method to extend analysis of the evolution of continuous strategy distributions given a quadratic payoff function for any [...] Read more.

Evolution of distribution of strategies in game theory is an interesting question that has been studied only for specific cases. Here I develop a general method to extend analysis of the evolution of continuous strategy distributions given a quadratic payoff function for any initial distribution in order to answer the following question—given the initial distribution of strategies in a game, how will it evolve over time? I look at several specific examples, including normal distribution on the entire line, normal truncated distribution, as well as exponential and uniform distributions. I show that in the case of a negative quadratic term of the payoff function, regardless of the initial distribution, the current distribution of strategies becomes normal, full or truncated, and it tends to a distribution concentrated in a single point so that the limit state of the population is monomorphic. In the case of a positive quadratic term, the limit state of the population may be dimorphic. The developed method can now be applied to a broad class of questions pertaining to evolution of strategies in games with different payoff functions and different initial distributions. Full article

(This article belongs to the Special Issue Non-Imitative Dynamics in Evolutionary Game Theory)

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10 pages, 734 KiB

Open AccessArticle

Hybrid Assessment Scheme Based on the Stern- Judging Rule for Maintaining Cooperation under Indirect Reciprocity

by Isamu Okada, Hitoshi Yamamoto and Satoshi Uchida

Games 2020, 11(1), 13; https://doi.org/10.3390/g11010013 - 20 Feb 2020

Cited by 4 | Viewed by 5091

Abstract

Intensive studies on indirect reciprocity have explored rational assessment rules for maintaining cooperation and several have demonstrated the effects of the stern-judging rule. Uchida and Sasaki demonstrated that the stern-judging rule is not suitable for maintaining cooperative regimes in private assessment conditions while [...] Read more.

Intensive studies on indirect reciprocity have explored rational assessment rules for maintaining cooperation and several have demonstrated the effects of the stern-judging rule. Uchida and Sasaki demonstrated that the stern-judging rule is not suitable for maintaining cooperative regimes in private assessment conditions while a public assessment system has been assumed in most studies. Although both assessment systems are oversimplified and society is most accurately represented by a mixture of these systems, little analysis has been reported on their mixture. Here, we investigated how much weight on the use of information originating from a public source is needed to maintain cooperative regimes for players adopting the stern-judging rule when players get information from both public and private sources. We did this by considering a hybrid-assessment scheme in which players use both assessment systems and by using evolutionary game theory. We calculated replicator equations using the expected payoffs of three strategies: unconditional cooperation, unconditional defection, and stern-judging rule adoption. Our analysis shows that the use of the rule helps to maintain cooperation if reputation information from a unique public notice board is used with more than a threshold probability. This hybrid-assessment scheme can be applied to other rules, including the simple-standing rule and the staying rule. Full article

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18 pages, 5001 KiB

Open AccessArticle

Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ≤ 14 Players

by Hendrik Richter

Games 2020, 11(1), 12; https://doi.org/10.3390/g11010012 - 17 Feb 2020

Cited by 1 | Viewed by 3827

Abstract

We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. In a computational approach using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak [...] Read more.

We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. In a computational approach using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with

N \leq 14

vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of a certain length is a good predictor for the values of the structure coefficient, and thus a tendency to favor cooperation. Another property of particularly cooperation-promoting regular graphs with a low degree is that they are structured to have blocks with clusters of mutants that are connected by cut vertices and/or hinge vertices. Full article

(This article belongs to the Special Issue Non-Imitative Dynamics in Evolutionary Game Theory)

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13 pages, 254 KiB

Open AccessArticle

Subjective Homophily and the Fixtures Problem

by Joseph E. Duggan, Jr.

Games 2020, 11(1), 11; https://doi.org/10.3390/g11010011 - 13 Feb 2020

Cited by 2 | Viewed by 3126

Abstract

The Stable Fixtures problem (Irving and Scott (2007)) is a generalized matching model that nests the well-known Stable Roommates, Stable Marriage, and College Admissions problems as special cases. This paper extends a result of the Stable Roommates problem to demonstrate that a class [...] Read more.

The Stable Fixtures problem (Irving and Scott (2007)) is a generalized matching model that nests the well-known Stable Roommates, Stable Marriage, and College Admissions problems as special cases. This paper extends a result of the Stable Roommates problem to demonstrate that a class of homophilic preferences with an appealing psychological interpretation is sufficient to ensure that starting from an arbitrary matching, a decentralized process of allowing the sequential matching of randomly chosen blocking pairs will converge to a pairwise-stable matching with probability one. Strategic implications of this class of preferences are examined and further possible generalizations and directions for future research are discussed. Full article

24 pages, 771 KiB

Open AccessArticle

Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story

by Papatya Duman

Games 2020, 11(1), 9; https://doi.org/10.3390/g11010009 - 07 Feb 2020

Cited by 1 | Viewed by 4195

Abstract

The purpose of this study is to experimentally test Trockel’s game, which is a modelling of the classical Chain Store Game (CSG), and determine whether one of the two theories of Equality and Deterrence may better account for the observed behavior. The CSG [...] Read more.

The purpose of this study is to experimentally test Trockel’s game, which is a modelling of the classical Chain Store Game (CSG), and determine whether one of the two theories of Equality and Deterrence may better account for the observed behavior. The CSG is an example of a simple game in extensive form where the actual behavior of well-informed players cannot be expected to agree with the clear results of game theoretical reasoning. To explain the disagreement between the theory and the expected behavior, Trockel’s game is proposed as an alternative modelling of the scenario. The existence of more than one equilibrium in Trockel’s game opens a door for reputation building. This study is the first attempt to experimentally test this alternative game with the same purpose. According to my data, there is some evidence in favor of both Equality and Deterrence Hypotheses. However, since the strategies compatible with the Equality Hypothesis are played more frequently, I observe some patterns which share the same intuition with the Deterrence Hypothesis. Full article

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

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2 pages, 153 KiB

Open AccessEditorial

Introduction to the Special Issue Political Games: Strategy, Persuasion, and Learning

by Gabriele Gratton and Galina Zudenkova

Games 2020, 11(1), 10; https://doi.org/10.3390/g11010010 - 07 Feb 2020

Cited by 2 | Viewed by 3971

Abstract

All political actors, from world leaders to common citizens, make choices based on information that is noisy, perhaps biased, and sometimes fake [...] Full article

(This article belongs to the Special Issue Political Games: Strategy, Persuasion, and Learning)

17 pages, 1422 KiB

Open AccessArticle

Fairness Preferences in a Bilateral Trade Experiment

by Alice Ciccone, Ole Rogeberg and Ragnhild Braaten

Games 2020, 11(1), 8; https://doi.org/10.3390/g11010008 - 31 Jan 2020

Cited by 1 | Viewed by 4065

Abstract

Is the willingness to make trades influenced by how the total gains from trade are split between the trading partners? We present results from a bilateral trade game (n = 128) where all participants were price-takers and trading pairs faced one of [...] Read more.

Is the willingness to make trades influenced by how the total gains from trade are split between the trading partners? We present results from a bilateral trade game (n = 128) where all participants were price-takers and trading pairs faced one of three exogenously imposed trading prices. The fixed prices divided the gains either symmetrically in the reference treatment or asymmetrically in treatments favoring either the buyer or seller. Price treatments generating asymmetric gains from trade reduced desired transaction levels on both sides of the market, but more strongly by the disfavored party. The data weakly indicated a larger reduction when the disfavored party was a seller. Full article

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3 pages, 290 KiB

Open AccessEditorial

Acknowledgment to Reviewers of Games in 2019

by Games Editorial Office

Games 2020, 11(1), 7; https://doi.org/10.3390/g11010007 - 26 Jan 2020

Viewed by 3098

Abstract

The editorial team greatly appreciates the reviewers who have dedicated their considerable time and expertise to the journal’s rigorous editorial process over the past 12 months, regardless of whether the papers are finally published or not [...] Full article

28 pages, 706 KiB

Open AccessArticle

Thankful or Thankless: Does the Past’s Altruism Increase the Present’s Public Good Contributions?

by Anna Lou Abatayo, Lea Skræp Svenningsen and Bo Jellesmark Thorsen

Games 2020, 11(1), 6; https://doi.org/10.3390/g11010006 - 21 Jan 2020

Cited by 3 | Viewed by 4011

Abstract

Two important aspects of global environmental problems are that (1) the actions of past generations affect the opportunities of the present, and (2) both in the past and the present generations, collaboration across different countries is needed to provide global public goods. In [...] Read more.

Two important aspects of global environmental problems are that (1) the actions of past generations affect the opportunities of the present, and (2) both in the past and the present generations, collaboration across different countries is needed to provide global public goods. In this paper, we study how these two aspects influence public good provisions by running simultaneous intercountry laboratory experiments using a modified public goods game in Denmark, Spain and Ghana. While the theoretical predictions of the modified public goods game do not differ from that of the standard public goods game, our experimental results show otherwise. Pooling across results from our Danish, Spanish and Ghanaian participants, we find that present-generation individuals contribute a higher percentage of their endowments when they have better institutions and a lower percentage of their endowments when they have higher endowments. We also find that present-generation individuals contribute less to transnational public goods only when their initial conditions have not been affected by past-generation contributions. Full article

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21 pages, 2765 KiB

Open AccessArticle

Binding Contracts, Non-Binding Promises and Social Feedback in the Intertemporal Common-Pool Resource Game

by Wojtek Przepiorka and Andreas Diekmann

Games 2020, 11(1), 5; https://doi.org/10.3390/g11010005 - 13 Jan 2020

Cited by 4 | Viewed by 4741

Abstract

In the intertemporal common-pool resource game, non-cooperative behavior produces externalities reducing subjects’ payoffs in both the present and the future. In this paper, we investigate through two experiments whether binding contracts, non-binding promises and social feedback help to promote sustainable behavior. We find [...] Read more.

In the intertemporal common-pool resource game, non-cooperative behavior produces externalities reducing subjects’ payoffs in both the present and the future. In this paper, we investigate through two experiments whether binding contracts, non-binding promises and social feedback help to promote sustainable behavior. We find that cooperation is higher in groups where a contract can be signed or where subjects made a promise to cooperate throughout the experiment. However, not all groups sign the contract unanimously and subjects who made a promise adjust their cooperation downwards over time. We find no difference between the control condition without any regulation and the treatment condition in which subjects receive feedback on their past behavior in private. However, if received feedback can be learned by all group members, cooperation is significantly higher. Our findings show that non-binding promises and social feedback increase cooperation, but the former only in the short-run and the latter only if made public. Full article

(This article belongs to the Special Issue Social and Environmental Behavior and Game Theory)

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28 pages, 818 KiB

Open AccessArticle

Public Information: Relevance or Salience?

by Giovanna M. Invernizzi

Games 2020, 11(1), 4; https://doi.org/10.3390/g11010004 - 06 Jan 2020

Cited by 3 | Viewed by 5404

Abstract

How does salient public information affect voters’ behavior? In a majoritarian voting game with common preferences, rational voters could use public information as an information device (depending on accuracy) or as a coordination device (regardless of accuracy). A simple lab experiment contradicts both [...] Read more.

How does salient public information affect voters’ behavior? In a majoritarian voting game with common preferences, rational voters could use public information as an information device (depending on accuracy) or as a coordination device (regardless of accuracy). A simple lab experiment contradicts both hypotheses – subjects tend to follow public information when it is salient, regardless of the information’s accuracy, but fail to use it as a source of coordination. In particular, it matters whether the information is recent – subjects are more likely to follow public information when it is provided closer to the voting decision. These findings are important because the salience of public information is easily manipulable by political actors. Full article

(This article belongs to the Special Issue Political Games: Strategy, Persuasion, and Learning)

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31 pages, 446 KiB

Open AccessArticle

The Two-Stage Game Approach to Coalition Formation: Where We Stand and Ways to Go

by Achim Hagen, Pierre von Mouche and Hans-Peter Weikard

Games 2020, 11(1), 3; https://doi.org/10.3390/g11010003 - 01 Jan 2020

Cited by 9 | Viewed by 6182

Abstract

Coalition formation is often analysed in an almost non-cooperative way, as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalised this widely used [...] Read more.

Coalition formation is often analysed in an almost non-cooperative way, as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalised this widely used approach for the case where actions are simultaneous in each stage. Herein, we give special attention to the case of a symmetric physical game. Various theoretical results, in particular, for cartel games, are provided. As they are crucial, recent results on the uniqueness of coalitional equilibria of Cournot-like physical games are reconsidered. Various concrete examples are included. Finally, we discuss research strategies to obtain results about equilibrium coalition structures with abstract physical games in terms of qualitative properties of their primitives. Full article

(This article belongs to the Special Issue Game Theoretic Models in Natural Resource Economics)

12 pages, 753 KiB

Open AccessArticle

A Condorcet Jury Theorem for Large Poisson Elections with Multiple Alternatives

by Johanna M. M. Goertz

Games 2020, 11(1), 2; https://doi.org/10.3390/g11010002 - 23 Dec 2019

Viewed by 4200

Abstract

Herein, we prove a Condorcet jury theorem (CJT) for large elections with multiple alternatives. Voters have common interests that depend on an unknown state of nature. Each voter receives an imprecise private signal about the state of nature and then submits one vote [...] Read more.

Herein, we prove a Condorcet jury theorem (CJT) for large elections with multiple alternatives. Voters have common interests that depend on an unknown state of nature. Each voter receives an imprecise private signal about the state of nature and then submits one vote (simple plurality rule). We also assume that this is a Poisson voting game with population uncertainty. The question is whether the simple plurality rule aggregates information efficiently so that the correct alternative is elected with probability tending to one when the number of voters tends to infinity. The previous literature shows that the CJT holds for large elections with two alternatives, but there is also an example of a large election with three alternatives that has an inefficient equilibrium. We show that there always exists an efficient equilibrium, independent of the number of alternatives. Under certain circumstances (informative types), it is unique in elections with two alternatives. The existence of inefficient equilibria in elections with more than two alternatives is generic. Full article

(This article belongs to the Special Issue Political Economy, Social Choice and Game Theory)

27 pages, 904 KiB

Open AccessArticle

Measuring and Comparing Two Kinds of Rationalizable Opportunity Cost in Mixture Models

by James R. Bland

Games 2020, 11(1), 1; https://doi.org/10.3390/g11010001 - 19 Dec 2019

Viewed by 4695

Abstract

In experiments of decision-making under risk, structural mixture models allow us to take a menu of theories about decision-making to the data, estimating the fraction of people who behave according to each model. While studies using mixture models typically focus only on how [...] Read more.

In experiments of decision-making under risk, structural mixture models allow us to take a menu of theories about decision-making to the data, estimating the fraction of people who behave according to each model. While studies using mixture models typically focus only on how prevalent each of these theories is in people’s decisions, they can also be used to assess how much better this menu of theories organizes people’s utility than does just one theory on its own. I develop a framework for calculating and comparing two kinds of rationalizable opportunity cost from these mixture models. The first is associated with model mis-classification: How much worse off is a decision-maker if they are forced to behave according to model A, when they are in fact a model B type? The second relates to the mixture model’s probabilistic choice rule: How much worse off are subjects because they make probabilistic, rather than deterministic, choices? If the first quantity dominates, then one can conclude that model a constitutes an economically significant departure from model B in the utility domain. On the other hand, if the second cost dominates, then models a and B have similar utility implications. I demonstrate this framework on data from an existing experiment on decision-making under risk. Full article

(This article belongs to the Special Issue The Empirics of Behaviour under Risk and Ambiguity)

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