Open research questions in Game Theory and Applications

What the literature leaves open

• Prior work has focused on the existence and properties of Nash equilibria, but uniqueness is essential in many applications. The gap in prior work is addressed by proving necessary conditions for unique Nash equilibria.

  On the uniqueness of Nash equilibria in polymatrix games · 2026 · DOI

• The study of disjoint unions is less straightforward in Avoider-Enforcer games. The authors need to distinguish between two cases depending on parity.

  The Avoider-Enforcer Game in Hypergraphs of Rank 3 · 2026 · DOI

• The assumption that players can randomize arbitrarily is non-trivial. True randomness might be scarce or costly and humans are known to have difficulty generating truly random sequences.

  Playing repeated games with sublinear randomness · 2026 · DOI

• The paper identifies a gap in the literature regarding the characterization of normal-form games for which there exist Nash equilibria using O(1) randomness.

  Playing repeated games with sublinear randomness · 2026 · DOI

• The paper identifies the challenge of designing communication systems that take into account private anchors and costly reporting. The challenge is to balance the need for informative communication with the potential for noise and distortion in the reporting process. The paper also identifies the challenge of understanding how private anchors affect communication in various domains.

  Private Languages · 2026 · DOI

• Future research can focus on developing a direct method of calculus of variations for the Eulerian formulation. Future research can focus on applying the results to optimal transport problems.

  A variational formulation of a multi-population mean field games with non-local interactions · 2026 · DOI

• The gap in prior work is the lack of a variational formulation for non-local interactions. The gap in prior work is the lack of a direct method of calculus of variations for the Eulerian formulation.

  A variational formulation of a multi-population mean field games with non-local interactions · 2026 · DOI

• Further study of the performance of Tit For Tat in different contexts. Investigation of new strategies for the IPD. Analysis of the implications of the results for the design of cooperative systems.

  Reviving, reproducing, and revisiting Axelrod’s second tournament · 2026 · DOI

• The paper identifies a gap in the literature by providing a new interpretation of the regularized p-Laplacian. The gap is filled by using a tug-of-war game interpretation and proving existence, uniqueness, and Borel measurability of solutions.

  A projected tug-of-war game for the regularized p-Laplacian · 2026 · DOI

• Further study of the implications for learning algorithms and decentralized security decisions. Extension of the results to other types of games.

  On the uniqueness of Nash equilibria in polymatrix games · 2026 · DOI

• The paper identifies a gap in the proof of Dilmé's result. The gap is addressed by providing a simplified proof using Farkas' lemma.

  A simple proof of the sufficiency of Dilmé’s power-sequence test for Kreps-Wilson consistency · 2026 · DOI

• The lack of availability of the original tournament code. The need to update the surviving Fortran code to compile with modern compilers.

  Reviving, reproducing, and revisiting Axelrod’s second tournament · 2026 · DOI

• Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored.

  Microscopic dynamics of consensus formation in multi-agent LLM Naming Games · 2026

• Future research could further explore the application of game theory to social sciences. It could also investigate the use of mixed, or randomized, strategies in various games.

  Game theory for the social sciences · 1983 · DOI

• The paper identifies a gap in the application of game theory to social sciences. It notes that prior work has not fully explored the concept of perfect information in extended form games.

  Game theory for the social sciences · 1983 · DOI

• The gap in the literature is the lack of results for economies with externalities and non-convexities. The paper aims to fill this gap by providing a framework for analyzing approximate cores in these economies.

  Approximate cores of replica games and economies. Part I: Replica games, externalities, and approximate cores · 1983 · DOI

• The paper identifies a gap in the literature related to the analysis of entry, exit, and merger in economies. The paper suggests that existing models do not adequately capture the effects of setup costs and indivisibilities on the economy.

  Approximate cores of replica games and economies · 1983 · DOI

• To extend the model to more complex market structures. To analyze the robustness of the adaptive process. To apply the model to real-world markets.

  Low information nash equilibria for oligopolistic markets · 1983 · DOI

• Existing models assume complete information and high computation powers. The gap in existing models is the lack of a low information Nash equilibrium concept.

  Low information nash equilibria for oligopolistic markets · 1983 · DOI

• There is a gap in understanding the systematic basis for turn-competitive hearings - Neither positioning nor thematic relation provides a systematic basis for these hearings

  Turn-competitive incomings · 1983 · DOI

• The analysis in Equations (24)–(28) establishes bounds with explicit dependence on ‖u‖∞, but does not provide guidance on how the payoff convergence rate scales with the utility function's modulus of continuity or Lipschitz properties, which would be essential for applications where payoff functions exhibit varying smoothness.

  On the Monotonicity and Rate of Convergence of the Markovian Persuasion Value · 2026 · DOI

• The framework in Section 5.5 assumes the adversary's memory erasure decisions are independent of past moves with a fixed probability (y − x)/(1 − x), but the paper does not extend analysis to strategic or history-dependent memory erasure policies, which would represent a more realistic adversarial model in persuasion games.

  On the Monotonicity and Rate of Convergence of the Markovian Persuasion Value · 2026 · DOI

• The paper identifies a gap in the existing literature on the existence of optimal policies for stochastic teams with decentralized mean-field information sharing. The paper identifies a need for a measure-valued MDP approach to derive the value iteration process for stochastic teams.

  Optimality of Symmetric Independent Policies Under Decentralized Mean-Field Information Sharing for Stochastic Teams and Equivalence with McKean−Vlasov Control of a Representative Agent · 2026 · DOI

• To study the evolution of payoff sensitivities in more complex strategic interactions. To explore the application of the results to various domains. To investigate the role of noisy learning in other contexts.

  Evolution of noisy learning in games · 2026 · DOI

• Most models treat the sensitivity of players to their strategies' performance as a fixed parameter. There is a lack of understanding of how strategies and sensitivities coevolve.

  Evolution of noisy learning in games · 2026 · DOI

Most-cited papers in Game Theory and Applications

• Implementation in Undominated Strategies: A Look at Bounded Mechanisms · The Review of Economic Studies · 1992 · 190 citations
• Game-Theoretic Statistics and Safe Anytime-Valid Inference · Statistical Science · 2023 · 80 citations
• The Role of Rivalry · Journal of Conflict Resolution · 2006 · 59 citations
• Payoff-based learning best explains the rate of decline in cooperation across 237 public-goods games · Nature Human Behaviour · 2021 · 53 citations
• An MCDM-based game-theoretic approach for strategy selection in higher education · Socio-Economic Planning Sciences · 2021 · 28 citations
• Algorithmic Fairness and Base Rate Tracking · Philosophy &amp Public Affairs · 2022 · 26 citations
• Shared Mental Models: Insights and Perspectives on Ideologies and Institutions · Kyklos · 2020 · 17 citations
• Evolutionary implementation in aggregative games · Mathematical Social Sciences · 2020 · 15 citations
• A Simple Logic of the Hide and Seek Game · Studia Logica · 2023 · 13 citations
• Collusive stability of cross-holding with cost asymmetry · Theory and Decision · 2021 · 11 citations

Most recent work

• Evolution of noisy learning in games · Proceedings of the National Academy of Sciences · 2026
• Maximizing Nash Social Welfare in Two-Value Instances: Delineating Tractability · Mathematics of Operations Research · 2026
• On the Monotonicity and Rate of Convergence of the Markovian Persuasion Value · Mathematics of Operations Research · 2026
• A survey of graphical models for decision-making: integrating causality and game theory · Artificial Intelligence Review · 2026
• Finding the Stable Point of Game: A Quick Solution to Nash Equilibrium · Science and Technology of Engineering, Chemistry and Environmental Protection · 2026
• Optimality of Symmetric Independent Policies Under Decentralized Mean-Field Information Sharing for Stochastic Teams and Equivalence with McKean−Vlasov Control of a Representative Agent · Mathematics of Operations Research · 2026
• Policy uncertainty and optimal provision of public information · Economic Modelling · 2026
• Markov Perfect Equilibria in Discrete Finite-Player and Mean-Field Games · SIAM Journal on Control and Optimization · 2026
• A Myerson value for multi-choice games with a communication network · Annals of Operations Research · 2026
• Sapio: From Distributed Intelligence to Collective Action · Zenodo (CERN European Organization for Nuclear Research) · 2026

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