Games

21 pages, 5251 KB

Open AccessArticle

Classifying Limited-Move Stability Cycles in 2 × 2 Games

by Leandro Chaves Rêgo, France Evellyn Gomes de Oliveira, Giannini Italino Alves Vieira and D. Marc Kilgour

Games 2025, 16(5), 54; https://doi.org/10.3390/g16050054 - 11 Oct 2025

Abstract

The

2 \times 2

game is the simplest non-trivial model of strategic interaction: there are two players, each has two strategies, and each has a strict preference ranking over the four possible outcomes. For models of play that depend only on the ranking [...] Read more.

The

2 \times 2

game is the simplest non-trivial model of strategic interaction: there are two players, each has two strategies, and each has a strict preference ranking over the four possible outcomes. For models of play that depend only on the ranking of the outcomes, the catalog of

2 \times 2

games permits many useful comparisons and contrasts. By interpreting a

2 \times 2

game as a graph model, we obtain new data on the properties of limited-move (

L_{h}

) stability. Specifically, for each

2 \times 2

strict ordinal game, we determine the

L_{h}

-stable outcomes; show how stability depends on the horizon, h; and find the lengths of cycles and the numbers of moves until cycling begins. We then compare our observations with other classifications of these games and with the values of the conflict and harmony indices. Full article

(This article belongs to the Section Non-Cooperative Game Theory)

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21 pages, 1631 KB

Open AccessArticle

Competition and Coordination of Regional Fresh Supply Chain Under Government Regulation

by Chao Zhao, Yongmei Chi, Nini Gao and Jixiang Song

Games 2025, 16(5), 53; https://doi.org/10.3390/g16050053 - 10 Oct 2025

Abstract

Fresh agricultural products have significant seasonality and perishability, and their cross-regional sales often face differences in market demand, price, and sales volume. In the context of government quality regulation, competition among retailers in different regions drives supply chain members to improve product quality, [...] Read more.

Fresh agricultural products have significant seasonality and perishability, and their cross-regional sales often face differences in market demand, price, and sales volume. In the context of government quality regulation, competition among retailers in different regions drives supply chain members to improve product quality, expand sales, and reduce losses. However, conflicts of interest under decentralized decision-making may lead to overall inefficiency. This article constructs a supply chain model consisting of a single Manufacturer and two regional Retailers to study the quality competition and coordination mechanism of cross-regional fresh food supply chains under government supervision. By comparing centralized and decentralized decision-making, it is found that although quality improvement in decentralized mode helps enhance competitiveness and sales performance, it is difficult to effectively increase profits and may even lead to a decline in profits. Therefore, this article proposes a cost-sharing contract to achieve supply chain coordination. Research has shown that this contract can effectively improve the overall profit of the supply chain and achieve Pareto improvement; under high market demand and strict regulatory penalties, the total profit of the supply chain increases, but the dominant Retailer benefits more, which can easily trigger the “Matthew effect”. The research results reveal the comprehensive impact of quality investment, contract coordination, market demand fluctuations, and regulatory intensity on supply chain performance, providing theoretical basis and management insights for improving the collaborative efficiency and policy design of cross-regional fresh food supply chains. Full article

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23 pages, 713 KB

Open AccessArticle

Non-Renewable Resource Extraction Model with Uncertainties

by Peichen Ye, Anna Tur and Yilun Wu

Games 2025, 16(5), 52; https://doi.org/10.3390/g16050052 - 9 Oct 2025

Abstract

This paper delves into a multi-player non-renewable resource extraction differential game model, where the duration of the game is a random variable with a composite distribution function. We first explore the conditions under which the cooperative solution also constitutes a Nash equilibrium, thereby [...] Read more.

This paper delves into a multi-player non-renewable resource extraction differential game model, where the duration of the game is a random variable with a composite distribution function. We first explore the conditions under which the cooperative solution also constitutes a Nash equilibrium, thereby extending the theoretical framework from a fixed duration to the more complex and realistic setting of random duration. Assuming that players are unaware of the switching moment of the distribution function, we derive optimal estimates in both time-dependent and state-dependent cases. The findings contribute to a deeper understanding of strategic decision-making in resource extraction under uncertainty and have implications for various fields where random durations and cooperative strategies are relevant. Full article

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9 pages, 221 KB

Open AccessArticle

Efficient Solutions to Multidimensional Claims Problem

by Sijia Xu and Peng Liu

Games 2025, 16(5), 51; https://doi.org/10.3390/g16050051 - 9 Oct 2025

Abstract

In this paper, we study the multidimensional claims problem and introduce the eating algorithm to this problem. It is shown that a solution is efficient if and only if it is the outcome of the eating algorithm with a profile of specific eating [...] Read more.

In this paper, we study the multidimensional claims problem and introduce the eating algorithm to this problem. It is shown that a solution is efficient if and only if it is the outcome of the eating algorithm with a profile of specific eating functions. Moreover, we adapt three classical solutions, i.e., the constrained equal awards rule, constrained equal losses rule, and proportional rule, to the current setting and show that they are special cases of the eating algorithm with specific eating functions. Full article

(This article belongs to the Section Applied Game Theory)

20 pages, 344 KB

Open AccessArticle

The “Value Principle” in Management Practices, Organizational Design, and Industrial Organization

by Patrick Legros and Andrew F. Newman

Games 2025, 16(5), 50; https://doi.org/10.3390/g16050050 - 12 Sep 2025

Abstract

The value principle in organizational economics states that the net market value of the goods that a firm sells is a key determinant of its organizational design. We survey and extend some recent developments in the theoretical literature at the nexus of organizational [...] Read more.

The value principle in organizational economics states that the net market value of the goods that a firm sells is a key determinant of its organizational design. We survey and extend some recent developments in the theoretical literature at the nexus of organizational and industrial economics, focusing on this precept as the unifying theme. Under perfect competition, we study how market price influences the use of scarce professional management and the degree of organizational heterogeneity in an industry. In a more general setting, we show how changes in demand influence not only the use of professional management, but also the size and the market power of firms. And we show how prices can affect the internal control structure of firms, sometimes in highly distorted ways. We discuss applications to comparative industrial organization and to technological diffusion. Full article

(This article belongs to the Special Issue Industrial Organization and Organizational Economics)

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15 pages, 467 KB

Open AccessArticle

Monopoly, Multi-Product Quality, Consumer Heterogeneity, and Market Segmentation

by Amit Gayer

Games 2025, 16(5), 49; https://doi.org/10.3390/g16050049 - 10 Sep 2025

Abstract

This paper introduces a novel ratio-based framework for analyzing how consumer heterogeneity translates into product differentiation in vertically structured monopoly markets. We consider a monopolist facing a continuum of consumers and a strictly convex production cost function and identify conditions under which the [...] Read more.

This paper introduces a novel ratio-based framework for analyzing how consumer heterogeneity translates into product differentiation in vertically structured monopoly markets. We consider a monopolist facing a continuum of consumers and a strictly convex production cost function and identify conditions under which the heterogeneity of preferences, measured by the length of the consumer type interval, maps into a corresponding range of offered qualities. The analysis shows that this mapping depends on the curvature of the marginal cost function: under linear costs, the relationship is proportional; under convex costs, heterogeneity expands faster than segmentation; and under concave costs, the reverse occurs. These findings offer a new lens for understanding endogenous market granularity in monopoly settings and have potential applicability in markets with vertically differentiated goods. We also show that under partial market coverage, this proportionality breaks down - even in the linear case - revealing a critical asymmetry in equilibrium structure. Full article

(This article belongs to the Special Issue Applications of Game Theory to Industrial Organization)

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11 pages, 260 KB

Open AccessOpinion

The Agentic Perspective in Experimental Economics

by Arturo Macías

Games 2025, 16(5), 48; https://doi.org/10.3390/g16050048 - 8 Sep 2025

Abstract

Mainstream experimental economics is characterized by its focus on theory testing and “treatment effects” on aggregate outcomes. The “agentic” alternative is concerned with the econometric specification of individual behavior. In this essay, first, a literature review of agentic experimental economics is provided, and [...] Read more.

Mainstream experimental economics is characterized by its focus on theory testing and “treatment effects” on aggregate outcomes. The “agentic” alternative is concerned with the econometric specification of individual behavior. In this essay, first, a literature review of agentic experimental economics is provided, and a stylized workflow is proposed to produce and validate econometric models of individual behavior based on experimental data: (i) create a baseline (“optimal”) behavioral benchmark (by analytical means or reinforcement learning) for the considered multi-agent game, (ii) conduct experiments with human subjects, (iii) use the experimental results to characterize the structure of the deviations from the baseline behavior, and (iv) re-run the experiment with artificial agents calibrated in the previous step, and compare the outcomes with those of the human experiment. Two papers have been selected to illustrate the successful use of the proposed workflow. Finally, the relations between agent-based and experimental economics are discussed after deep learning has “tamed” the curse of dimensionality. Full article

(This article belongs to the Section Learning and Evolution in Games)

21 pages, 324 KB

Open AccessFeature PaperArticle

Asymptotic Thresholds for (a:b) Minimum-Degree Games

by Adnane Fouadi, Mourad El Ouali and Anand Srivastav

Games 2025, 16(5), 47; https://doi.org/10.3390/g16050047 - 8 Sep 2025

Abstract

We investigate the

(a : b)

Maker–Breaker subgraph game played on the edge set of the complete graph

K_{n}

, where

n, a, b \in N

, and Maker’s objective is to construct a member of a prescribed [...] Read more.

We investigate the

(a : b)

Maker–Breaker subgraph game played on the edge set of the complete graph

K_{n}

, where

n, a, b \in N

, and Maker’s objective is to construct a member of a prescribed family of graphs H, while Breaker aims to prevent this. In our study, Breaker moves first, and H is taken to be either the family of connected spanning subgraphs or the family of spanning subgraphs with minimum-degree at least

k = k (n)

. For the

(a : b)

minimum-degree-k game, we determine the asymptotically optimal threshold bias across a wide range of values for a. For the

(a : b)

connectivity game, we resolve an open problem posed by Hefetz et al. (2012) by identifying the exact leading term in the asymptotic behavior of the threshold bias when

a = c ln n

. Full article

(This article belongs to the Section Algorithmic and Computational Game Theory)

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17 pages, 415 KB

Open AccessArticle

Dividend Representations for Two Influence Assessments

by Yu-Hsien Liao

Games 2025, 16(5), 46; https://doi.org/10.3390/g16050046 - 4 Sep 2025

Abstract

This paper establishes dividend-based representations for two influence assessments. First, we define a system of min-dividends derived from the minimal-influence evaluation via a unique linear decomposition using unanimity-type spanning models. Building on this, we further construct a pair of internal and external min-dividends [...] Read more.

This paper establishes dividend-based representations for two influence assessments. First, we define a system of min-dividends derived from the minimal-influence evaluation via a unique linear decomposition using unanimity-type spanning models. Building on this, we further construct a pair of internal and external min-dividends satisfying Completeness and Balancedness conditions, through which we express the stable min-value as the net difference of internal gains and external losses. We then demonstrate that the minimal self-stable value can be represented as accumulated average min-dividends across all coalitions they have participated in. Furthermore, the proposed expression also is adopted to analyze the stability of the minimal self-stable value. These results extend the classical notion of dividends into a minimal-influence-based framework with potential applications in fair resource allocation and responsibility apportionment. Full article

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17 pages, 2567 KB

Open AccessArticle

Optimal Vaccination Strategies to Reduce Endemic Levels of Meningitis in Africa

by Alfredo Martinez, Jonathan Machado, Eric Sanchez and Igor V. Erovenko

Games 2025, 16(5), 45; https://doi.org/10.3390/g16050045 - 1 Sep 2025

Abstract

Meningococcal meningitis is a deadly acute bacterial infection caused by the Neisseria meningitidis bacterium that affects the membrane covering the brain and spinal cord. The World Health Organization launched the “Defeating bacterial meningitis by 2030” initiative in 2018, which relies on recent discoveries [...] Read more.

Meningococcal meningitis is a deadly acute bacterial infection caused by the Neisseria meningitidis bacterium that affects the membrane covering the brain and spinal cord. The World Health Organization launched the “Defeating bacterial meningitis by 2030” initiative in 2018, which relies on recent discoveries of cheap and effective vaccines. Here, we consider one important factor—human behavior—which is often neglected by immunization campaigns. We constructed a game-theoretic model of meningitis in the meningitis belt, where individuals make selfish rational decisions whether to vaccinate based on the assumed costs and the vaccination decisions of the entire population. We identified conditions when individuals should vaccinate, and we found the optimal (equilibrium) population vaccination rate. We conclude that voluntary compliance significantly reduces the endemic levels of meningitis if the cost of vaccination relative to the cost of the disease is sufficiently low, but it does not eliminate the disease. We also performed uncertainty and sensitivity analysis on our model. Full article

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64 pages, 2160 KB

Open AccessFeature PaperArticle

Test Me If You Can—Providing Optimal Information for Consumers Through a Novel Certification Mechanism

by Ulrike Vollstädt, Patrick Imcke, Franziska Brendel and Christiane Ehses-Friedrich

Games 2025, 16(5), 44; https://doi.org/10.3390/g16050044 - 29 Aug 2025

Abstract

Certifiers such as Stiftung Warentest (Germany), Which? (UK), and Consumer Reports (US) reduce asymmetric information between buyers and sellers by providing credible information about product quality. However, due to their limited testing capacities, they face a set selection problem and test only a [...] Read more.

Certifiers such as Stiftung Warentest (Germany), Which? (UK), and Consumer Reports (US) reduce asymmetric information between buyers and sellers by providing credible information about product quality. However, due to their limited testing capacities, they face a set selection problem and test only a subset of all available product models. We show theoretically that, under any current mechanism to select product models for testing, buyers always end up buying suboptimal product models, unless all product models which would be sold under complete information (or all but the overall cheapest one) happen to be tested. Instead, we propose a novel mechanism based on voluntary disclosure, but with the same testing capacity, which always yields the maximum possible consumer surplus and thus weakly dominates any current mechanism. Furthermore, we confirm in a controlled laboratory experiment that our mechanism significantly increases consumer surplus. Full article

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20 pages, 593 KB

Open AccessArticle

The Power of Passivity in the Hirshleifer Contest Under Small Noise

by Guang-Zhen Sun

Games 2025, 16(5), 43; https://doi.org/10.3390/g16050043 - 29 Aug 2025

Abstract

Hirshleifer’s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective [...] Read more.

Hirshleifer’s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective choice in conflict even when the contest is highly deterministic (i.e., with small noise). For that purpose, we establish two propositions on the contest with

n \geq 2

risk-neutral contestants under small noise. The first proposition states that every contestant bids arbitrarily close to zero (if not bidding zero with positive probability at all) under sufficiently small noise. The second proposition, more strikingly, states that every contestant either bids arbitrarily close to the second-highest valuation (among all the contestants’ valuations), or simply remains passive with certainty under any sufficiently small noise. We further show that the first proposition holds for the contest between risk-averse individuals endowed with constant absolute risk aversion as well, and illustrate by an example how quickly polarization in bidding among contestants, as is predicted by the propositions, may emerge as the noise of the contest abates. These results help pave the way toward a complete characterization of the difference-form contest. Full article

(This article belongs to the Section Applied Game Theory)

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21 pages, 493 KB

Open AccessFeature PaperArticle

A Theoretical Analysis of Cooperation Incentives for Non-Mutually Dependent Sellers

by Lorenzo Ferrari, Werner Güth, Vittorio Larocca and Luca Panaccione

Games 2025, 16(5), 42; https://doi.org/10.3390/g16050042 - 27 Aug 2025

Abstract

This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. [...] Read more.

This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. In each game of this class, both sellers simultaneously choose prices that determine their endogenous threats, i.e., conflict profits. The sellers are aware of the cooperation probability but cannot condition prices on whether or not there is cooperation. We characterize the equilibrium prices and the sellers’ expected profits. Our main result shows that the independent seller earns higher expected profits when cooperation is more likely. In contrast, the dependent seller earns lower expected profits when the likelihood of cooperation is below a threshold that we characterize explicitly, and higher profits are earned thereafter. These findings suggest that, within our framework, antitrust concerns may be mitigated. Since dependent sellers can incur losses from cooperation, collusion attempts become less viable in markets with one-sided dependency. Full article

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23 pages, 380 KB

Open AccessArticle

Power Indices with Threats in Precoalitions

by Jochen Staudacher

Games 2025, 16(5), 41; https://doi.org/10.3390/g16050041 - 25 Aug 2025

Abstract

We investigate power indices for simple games with precoalitions which distribute power among players in an external and an internal step. We extend an existing approach which uses the Public Good index both on the external level in the quotient game as well [...] Read more.

We investigate power indices for simple games with precoalitions which distribute power among players in an external and an internal step. We extend an existing approach which uses the Public Good index both on the external level in the quotient game as well as on the internal level for measuring the leverage of players to threaten their peers through departing the precoalition. We replace the Public Good index in that model by five other efficient power indices, i.e., the Shapley–Shubik index, the Deegan–Packel index, the Johnston index and two indices based on null player free winning coalitions. Axiomatizations of the novel power indices with threat partitions are presented. We also propose a slight modification to the existing framework for threat power indices which guarantees that null players are always assigned zero power. Numerical results for all power indices combined with different threat partitions are presented and discussed. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

10 pages, 526 KB

Open AccessArticle

Cooperative and Non-Cooperative Strategies in Product Warranty Pricing: A Hierarchical Game Approach

by Henrique Santos and Thyago Nepomuceno

Games 2025, 16(4), 40; https://doi.org/10.3390/g16040040 - 13 Aug 2025

Abstract

This paper analyzes the pricing dynamics of product warranties by developing a three-player hierarchical game model involving a manufacturer, an independent service agent, and a consumer. The model provides a scenario where the manufacturer and the agent form a coalition to coordinate pricing [...] Read more.

This paper analyzes the pricing dynamics of product warranties by developing a three-player hierarchical game model involving a manufacturer, an independent service agent, and a consumer. The model provides a scenario where the manufacturer and the agent form a coalition to coordinate pricing strategies, while interacting non-cooperatively with the consumer. In this framework, the manufacturer sets the product’s sale price, including the base warranty, while the agent determines the price of extended maintenance services. The key contribution is the application of the Shapley value to equitably distribute the coalition’s profits based on each member’s contribution—a novel approach in the warranty pricing literature. We detail the characteristic functions that define the coalition’s structure and present computer simulations to estimate the expected costs associated with maintenance services. A comprehensive sensitivity analysis is applied to report how changes in parameters influence equilibrium strategies and players’ payoffs. The results provide strategic insights into how manufacturers and agents can coordinate to optimize pricing, capture consumer surplus, and improve decision-making in warranty service markets. Full article

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14 pages, 784 KB

Open AccessArticle

Non-Cooperative Representations of Cooperative Games

by Justin Chan

Games 2025, 16(4), 39; https://doi.org/10.3390/g16040039 - 8 Aug 2025

Abstract

Non-cooperative games in normal form are specified by a player set, sets of player strategies, and payoff functions. Cooperative games, meanwhile, are specified by a player set and a worth function that maps coalitions of players to payoffs they can feasibly achieve. Although [...] Read more.

Non-cooperative games in normal form are specified by a player set, sets of player strategies, and payoff functions. Cooperative games, meanwhile, are specified by a player set and a worth function that maps coalitions of players to payoffs they can feasibly achieve. Although these games study distinct aspects of social behavior, this paper proposes a novel attempt at relating the two models. In particular, cooperative games may be represented by a non-cooperative game in which players can freely sign binding agreements to form coalitions. These coalitions inherit a joint strategy set and seek to maximize collective payoffs. When these coalitions play against one another, the equilibrium payoffs for each coalition coincide with what is predicted by the worth function. This paper proves sufficient conditions under which cooperative games can be represented by non-cooperative games. This paper finds that all strictly superadditive partition function form (PFF) games can be represented under Nash equilibrium (NE) and rationalizability; that all weakly superadditive characteristic function form (CFF) games can be represented under NE; and that all weakly superadditive PFF games can be represented under trembling hand perfect equilibrium (THPE). Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

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24 pages, 526 KB

Open AccessArticle

Responsibility Hoarding by Overconfident Managers

by Petra Nieken, Abdolkarim Sadrieh and Nannan Zhou

Games 2025, 16(4), 38; https://doi.org/10.3390/g16040038 - 26 Jul 2025

Abstract

Overconfidence is a well-established behavioral bias that involves the overestimation of one’s own capabilities. We introduce a model in which managers and agents exert effort in a joint production, after the manager decides on the allocation of the tasks. A rational manager tends [...] Read more.

Overconfidence is a well-established behavioral bias that involves the overestimation of one’s own capabilities. We introduce a model in which managers and agents exert effort in a joint production, after the manager decides on the allocation of the tasks. A rational manager tends to reduce their own effort by delegating the critical task to the agent more often than in an efficient task allocation. In contrast, an overconfident manager engages in responsibility hoarding, i.e., is likely to delegate a critical task less often to the agent than a rational manager. In fact, a manager with a sufficiently high ability and a moderate degree of overconfidence increases the total welfare by refusing to delegate critical tasks and by exerting more effort than a rational manager. Finally, we derive the conditions under which the responsibility hoarding can persist in an organization, showing that the bias survives as long as the overconfident manager can rationalize the observed output by underestimating the ability of the agent. Full article

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31 pages, 883 KB

Open AccessArticle

Pure Bayesian Nash Equilibria for Bayesian Games with Multidimensional Vector Types and Linear Payoffs

by Sébastien Huot and Abbas Edalat

Games 2025, 16(4), 37; https://doi.org/10.3390/g16040037 - 14 Jul 2025

Abstract

In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a [...] Read more.

In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash equilibriums for such games and efficient algorithms to find them. For continuous priors, we suggest a methodology to perform Nash equilibrium searches in simple cases. For discrete priors, we present algorithms that can handle two-action and two-player games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash equilibrium. We illustrate our results with several examples like the double-game prisoner’s dilemma (DGPD), the game of chicken, and the sustainable adoption decision problem (SADP). Full article

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33 pages, 3140 KB

Open AccessArticle

“Anything Goes” in an Ultimatum Game?

by Peter Paul Vanderschraaf

Games 2025, 16(4), 36; https://doi.org/10.3390/g16040036 - 9 Jul 2025

Abstract

I consider an underexplored possible explainer of the “surprising” results of Ultimatum Game experiments, namely, that Proposers and Recipients consider following only some of all the logically possible strategies of their Ultimatum Game. I present an evolutionary analysis of different games having the [...] Read more.

I consider an underexplored possible explainer of the “surprising” results of Ultimatum Game experiments, namely, that Proposers and Recipients consider following only some of all the logically possible strategies of their Ultimatum Game. I present an evolutionary analysis of different games having the same set of allowable Proposer offers and functions that determine Proposer and Recipient payoffs. For Unrestricted Ultimatum Games, where Recipients may choose from among any of the logically possible pure strategies, populations tend to evolve most often to Nash equilibria where Proposers make the lowest allowable offer. However, for Threshold Reduced Ultimatum Games, where Recipients must choose from among minimum acceptable offer strategies, and for Range Reduced Ultimatum Games, where Recipients must choose from among pure strategies that spurn offers that are “too high” as well as “too low”, populations tend to evolve most often to Nash equilibria where Proposers offer substantially more than the lowest possible offer, a result that is consistent with existing Ultimatum Game experimental results. Finally, I argue that, practically speaking, actual Proposers and Recipients will likely regard some reduction of the Unrestricted Ultimatum Game as their game because, for them, the strategies of this reduction are salient. Full article

(This article belongs to the Special Issue Evolution of Cooperation and Evolutionary Game Theory)

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