Games

35 pages, 527 KB

Open AccessFeature PaperArticle

Strategy-Proof Mechanism Design with Boundedly Rational Agents: Theory and Experiment

by Katsuhiko Nishizaki

Games 2026, 17(1), 12; https://doi.org/10.3390/g17010012 - 14 Feb 2026

Viewed by 949

In a strategy-proof mechanism, implementation theory mostly assumes that each agent is rational in the sense that the agent reveals its true preference to induce its most preferred outcome. This assumption is sufficient to guarantee that the agent seeks such an outcome, but [...] Read more.

In a strategy-proof mechanism, implementation theory mostly assumes that each agent is rational in the sense that the agent reveals its true preference to induce its most preferred outcome. This assumption is sufficient to guarantee that the agent seeks such an outcome, but not necessary because the agent might be able to induce the outcome by revealing its other preference. On the basis of such an understanding, this paper considers an implementation problem with the bounded rationality of agents. The bounded rationality presented in this paper means that the agent might choose its best response which is different from its dominant strategy. To describe such behavior, this paper introduces a new notion of equilibrium, called

(n - k)

-dominant strategy Nash equilibrium at which at most

k \in {0, 1, \dots, n}

boundedly rational agents might choose their best responses which are different from their dominant strategies, and at least

(n - k)

rational agents choose their dominant strategies. In addition, to show what a socially optimal outcome is collectively chosen under the existence of boundedly rational agents, this paper introduces a new notion of implementation, called k-secure implementation, which is a double implementation in dominant strategy equilibria and

(n - k)

-dominant strategy Nash equilibria. In specific environments with

k \leq (n + 1) / 2

, this paper shows that majority rule satisfies k-secure implementability, but not secure implementability which is equivalent to n-secure implementability. In addition, this paper shows that majority rule realized the socially optimal outcome in the environments in laboratory experiments. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

16 pages, 319 KB

Open AccessArticle

A Structural Measure of Bargaining Fragility in Multi-Domain Agreements

by Robert Castro

Games 2026, 17(1), 11; https://doi.org/10.3390/g17010011 - 11 Feb 2026

Viewed by 660

Abstract

Negotiation outcomes are commonly analyzed through equilibrium concepts, yet many agreements fail during implementation for reasons not captured by incentive structure alone This paper introduces a pre-equilibrium screening criterion for bargaining fragility based on a small set of agreement-level quantities characterizing dependency architecture: [...] Read more.

Negotiation outcomes are commonly analyzed through equilibrium concepts, yet many agreements fail during implementation for reasons not captured by incentive structure alone This paper introduces a pre-equilibrium screening criterion for bargaining fragility based on a small set of agreement-level quantities characterizing dependency architecture: strain τ (the number of operative obligations requiring tracking), curvature κ (the density and strength of interdependencies among elements), compressibility σ (the extent to which complexity can be reduced through modularization without altering functional meaning), and the stability quotient Γ = κ/τ (average interdependence burden per element). We use the inequality Γ > σ as a classification rule; agreements with Γ > σ are classified as structurally fragile and, in the data, exhibit higher sensitivity to perturbations. Across 42 documented agreements, the diagnostic correctly classifies nearly all observed outcomes, with only a single false positive and no false negatives. The framework operates as a pre-equilibrium screen that complements (rather than replaces) Nash and bargaining equilibrium analyses by identifying agreement architectures that are structurally brittle under small shocks. Full article

(This article belongs to the Special Issue Recent Advances in Microeconomics and Game Theory)

14 pages, 1171 KB

Open AccessFeature PaperArticle

Equal Chances or Fewer Victims? Moral Judgments in Autonomous Vehicle Dilemmas

by Alexander Matros, Eren Bilen and Leonid Matros

Games 2026, 17(1), 10; https://doi.org/10.3390/g17010010 - 9 Feb 2026

Viewed by 899

Abstract

We examine the moral dilemma of how autonomous vehicles (AVs) should be programmed to act in unavoidable crash scenarios involving trade-offs between saving one life and saving many. We report results from three experimental studies that investigate individuals’ preferences over alternative AV decision [...] Read more.

We examine the moral dilemma of how autonomous vehicles (AVs) should be programmed to act in unavoidable crash scenarios involving trade-offs between saving one life and saving many. We report results from three experimental studies that investigate individuals’ preferences over alternative AV decision rules in stylized crash scenarios. Across designs, we find robust support for a probabilistic decision rule that assigns passengers and pedestrians equal ex ante chances of survival (a 50:50 rule). This preference persists across different framings and remains salient even when additional probabilistic options are introduced. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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12 pages, 249 KB

Open AccessArticle

Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games

by Sam Ganzfried

Games 2026, 17(1), 9; https://doi.org/10.3390/g17010009 - 3 Feb 2026

Viewed by 681

Abstract

There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer normal-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have [...] Read more.

There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer normal-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have convergence guarantees in two-player zero-sum games, they do not guarantee convergence to Nash equilibrium in multiplayer games. We present an approach for exact computation of Nash equilibrium in multiplayer imperfect-information games that solves a quadratically-constrained program based on a nonlinear complementarity problem formulation from the sequence-form game representation. This approach capitalizes on recent advances for solving nonconvex quadratic programs. Our algorithm is able to quickly solve three-player Kuhn poker after removal of dominated actions. Of the available algorithms in the Gambit software suite, only the logit quantal response approach is successfully able to solve the game; however, the approach takes longer than our algorithm and also involves a degree of approximation. Our formulation also leads to a new approach for computing Nash equilibrium in multiplayer normal-form games which we demonstrate to outperform a previous quadratically-constrained program formulation. Full article

(This article belongs to the Special Issue New Advances in Computational Game Theory and Its Applications)

19 pages, 388 KB

Open AccessArticle

Exclusionary Contracts and Incentives to Innovate

by Simen Aardal Ulsaker

Games 2026, 17(1), 8; https://doi.org/10.3390/g17010008 - 3 Feb 2026

Viewed by 742

Abstract

This paper develops a game-theoretic model to study how exclusionary contracts affect firms’ incentives to invest in innovation. Several symmetric sellers compete to supply an identical product to a set of buyers, and each seller can invest in R&D to develop a higher-quality [...] Read more.

This paper develops a game-theoretic model to study how exclusionary contracts affect firms’ incentives to invest in innovation. Several symmetric sellers compete to supply an identical product to a set of buyers, and each seller can invest in R&D to develop a higher-quality version of the product. Prior to choosing their R&D investments, sellers may offer exclusionary contracts to buyers. In equilibrium, all buyers sign an exclusionary contract with the same seller, which eliminates rival sellers’ incentives to invest in R&D and concentrates innovative effort in a single firm. Banning exclusionary contracts increases the aggregate probability of innovation and the joint surplus of buyers and sellers only when the R&D technology exhibits sufficiently strong diseconomies of scale. Full article

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17 pages, 295 KB

Open AccessFeature PaperArticle

Communication and Standoff

by Catherine Hafer

Games 2026, 17(1), 7; https://doi.org/10.3390/g17010007 - 2 Feb 2026

Viewed by 532

Abstract

This paper examines the potential for pre-play communication to shorten the duration of two-player incomplete-information wars of attrition. If players’ types constitute costlessly verifiable information, then all types of players disclose their types, resulting in the war of attrition having duration zero. However, [...] Read more.

This paper examines the potential for pre-play communication to shorten the duration of two-player incomplete-information wars of attrition. If players’ types constitute costlessly verifiable information, then all types of players disclose their types, resulting in the war of attrition having duration zero. However, if type constitutes unverifiable information, the results are less sanguine. Pre-play cheap-talk communication has no effect on the play of the subsequent war of attrition. Mediated cheap-talk communication is no better: No institution that relies on players’ cheap-talk reports can systematically allocate the prize to the player who values it more highly at a lower resource cost than is entailed in equilibrium play of the war of attrition. Costly signaling in the form of burning money can effectively supplant the war of attrition as a means of allocating the prize, but it requires the same expected equilibrium resource expenditures, with the same expected distribution across types, as does the war of attrition. Thus, in spite of players’ unanimous preference for a system in which types are made known, and in spite of their disclosing type in equilibrium when type is verifiable, they nonetheless expend resources to credibly communicate their types when type is not verifiable, and the resources expended are, on average, equivalent to those expended in a war of attrition. Full article

(This article belongs to the Special Issue Conflict and Communication: Applications of Game Theory to Political Economy)

23 pages, 367 KB

Open AccessArticle

Monetary Policy Committees, Independence, and Influence

by Esteban Colla-De-Robertis

Games 2026, 17(1), 6; https://doi.org/10.3390/g17010006 - 16 Jan 2026

Viewed by 952

Abstract

We develop a model of monetary policy committee decision-making, building on the framework of games played through agents (GPTA). Interest groups seek to influence policy by offering action-contingent contracts to committee members. The resulting equilibrium admits a simple characterization and shows how institutional [...] Read more.

We develop a model of monetary policy committee decision-making, building on the framework of games played through agents (GPTA). Interest groups seek to influence policy by offering action-contingent contracts to committee members. The resulting equilibrium admits a simple characterization and shows how institutional features—such as committee size—shape the extent of external influence. When political pressure pushes for expansive and inflationary policy, larger committees can enhance de facto independence by diluting this influence. We also show that when anti-inflationary pressures dominate, an appropriate choice of committee size can replicate the preference shift towards more conservativeness familiar from delegation frameworks, even when it is not feasible to appoint a conservative central banker in a systematic way. Full article

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9 pages, 575 KB

Open AccessArticle

On Collusion Sustainability and the Elasticity of Substitution

by Marc Escrihuela-Villar

Games 2026, 17(1), 5; https://doi.org/10.3390/g17010005 - 14 Jan 2026

Viewed by 619

Abstract

We analyze the relationship between collusion sustainability in an infinitely repeated game using trigger strategies and the elasticity of substitution. To this end, we adopt a demand function with constant elasticity of substitution between the differentiated goods. Since our model exhibits a one-to-one [...] Read more.

We analyze the relationship between collusion sustainability in an infinitely repeated game using trigger strategies and the elasticity of substitution. To this end, we adopt a demand function with constant elasticity of substitution between the differentiated goods. Since our model exhibits a one-to-one relationship between the elasticity of substitution and demand price elasticity, we demonstrate that a larger elasticity decreases the sustainability of collusion. Intuitively, a more elastic demand function causes the increase in deviation profits to compensate for the increase in collusive profits, making collusion less easily sustained. This result holds regardless of whether firms compete in quantities or prices. Full article

(This article belongs to the Section Applied Game Theory)

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10 pages, 272 KB

Open AccessArticle

Fair Division of Indivisible Items: Envy-Freeness vs. Efficiency Revisited

by Steven J. Brams, D. Marc Kilgour and Christian Klamler

Games 2026, 17(1), 4; https://doi.org/10.3390/g17010004 - 14 Jan 2026

Viewed by 873

Abstract

We study conflicts between envy-based fairness and efficiency for allocating indivisible items under additive utilities. We formalize several small, transparent instances showing that standard envy-freeness (EF) or its relaxations EFX and EFX₀—i.e., envy-freeness up to any item, where EFX restricts attention [...] Read more.

We study conflicts between envy-based fairness and efficiency for allocating indivisible items under additive utilities. We formalize several small, transparent instances showing that standard envy-freeness (EF) or its relaxations EFX and EFX₀—i.e., envy-freeness up to any item, where EFX restricts attention to positively valued items and EFX₀ allows removing zero-valued items as well—can conflict with Pareto-optimality (PO), maximin (MM), or maximum Nash welfare (MNW). Normatively, we argue that envy-freeness (even as EFX or EFX₀) is not a panacea for allocating indivisible items and should be weighed against efficiency and welfare criteria. Full article

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

23 pages, 1141 KB

Open AccessArticle

Randomized Algorithms and Neural Networks for Communication-Free Multiagent Singleton Set Cover

by Guanchu He, Colton Hill, Joshua H. Seaton and Philip N. Brown

Games 2026, 17(1), 3; https://doi.org/10.3390/g17010003 - 12 Jan 2026

Viewed by 867

Abstract

This paper considers how a system designer can program a team of autonomous agents to coordinate with one another such that each agent selects (or covers) an individual resource with the goal that all agents collectively cover the maximum number of resources. Specifically, [...] Read more.

This paper considers how a system designer can program a team of autonomous agents to coordinate with one another such that each agent selects (or covers) an individual resource with the goal that all agents collectively cover the maximum number of resources. Specifically, we study how agents can formulate strategies without information about other agents’ actions so that system-level performance remains robust in the presence of communication failures. First, we use an algorithmic approach to study the scenario in which all agents lose the ability to communicate with one another, have a symmetric set of resources to choose from, and select actions independently according to a probability distribution over the resources. We show that the distribution that maximizes the expected system-level objective under this approach can be computed by solving a convex optimization problem, and we introduce a novel polynomial-time heuristic based on subset selection. Further, both of the methods are guaranteed to be within

1 - 1 / e

of the system’s optimal in expectation. Second, we use a learning-based approach to study how a system designer can employ neural networks to approximate optimal agent strategies in the presence of communication failures. The neural network, trained on system-level optimal outcomes obtained through brute-force enumeration, generates utility functions that enable agents to make decisions in a distributed manner. Empirical results indicate the neural network often outperforms greedy and randomized baseline algorithms. Collectively, these findings provide a broad study of optimal agent behavior and its impact on system-level performance when the information available to agents is extremely limited. Full article

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

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14 pages, 305 KB

Open AccessArticle

All-Pay Auctions with Different Forfeits

by Benjamin Kang and James Unwin

Games 2026, 17(1), 2; https://doi.org/10.3390/g17010002 - 9 Jan 2026

Viewed by 600

Abstract

In an auction, each party bids a certain amount, and the one who bids the highest is the winner. Interestingly, auctions can also be used as models for other real-world systems. In an all-pay auction all parties must pay a forfeit for bidding. [...] Read more.

In an auction, each party bids a certain amount, and the one who bids the highest is the winner. Interestingly, auctions can also be used as models for other real-world systems. In an all-pay auction all parties must pay a forfeit for bidding. In the most commonly studied all-pay auction, parties forfeit their entire bid, and this has been considered as a model for expenditure on political campaigns. Here, we consider a number of alternative forfeits that might be used as models for different real-world competitions, such as preparing bids for defense or infrastructure contracts. Full article

(This article belongs to the Special Issue Game-Theoretical Analysis of the Division of Labor and Trade Conflict)

21 pages, 1386 KB

Open AccessFeature PaperArticle

Endowment Inequality in Common Pool Resource Games: An Experimental Analysis

by Garrett Milam and Andrew Monaco

Games 2026, 17(1), 1; https://doi.org/10.3390/g17010001 - 4 Jan 2026

Viewed by 901

Abstract

This work addresses whether heterogeneity in player endowments influences investment decisions in common pool resource (CPR) games, shedding light on the relationship between inequality and economic decision making. We explore two theoretical avenues from behavioral economics—linear other-regarding preferences and inequity aversion—and examine the [...] Read more.

This work addresses whether heterogeneity in player endowments influences investment decisions in common pool resource (CPR) games, shedding light on the relationship between inequality and economic decision making. We explore two theoretical avenues from behavioral economics—linear other-regarding preferences and inequity aversion—and examine the predictions of each with a laboratory experiment. Our experimental results roundly reject the majority of these explanations: in treatments with endowment inequality, high endowment individuals invest more in the common pool resource than low endowment individuals. We discuss these results in the context of the literature on psychological entitlement and positional preferences. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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Games, Volume 17, Issue 1 (February 2026) – 12 articles

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