A game-theoretic perspective on channel selection for agricultural products under yield scale constraints in live streaming e-commerce: quality, welfare, and equilibrium selection

Equilibrium selection in aggregative games with strategic complementarities

Lightweight Log-Linear Learning With Neighborhood Search for Equilibrium Selection in Finite Potential Games

Abstract The equilibrium selection problem in the variational Generalized Nash Equilibrium Problem (v-GNEP) has been reported as an optimization problem defined over the solution set of v-GNEP, called in this paper the lower-level v-GNEP. However, to make such a selection fair for every player, we have to rely on an unrealistic assumption, that is, the availability of a trusted center that does not induce any bias among players. In this paper, to ensure fairness for every player even in the process of equilibrium selection, we propose a new equilibrium selection problem, named the upper-level v-GNEP. The proposed upper-level v-GNEP is formulated as a v-GNEP defined over the solution set of the lower-level v-GNEP. We also present an iterative algorithm, of guaranteed convergence to a solution of the upper-level v-GNEP, as an application of the hybrid steepest descent method to a fixed point set characterization of the solution of the lower-level v-GNEP. Numerical experiments illustrate the proposed equilibrium selection and algorithm.

Understanding and predicting the behavior of large-scale multiagents in games remains a fundamental challenge in multiagent systems. This article examines the role of heterogeneity in equilibrium formation by analyzing how smooth regret matching drives a large number of heterogeneous agents with diverse initial policies toward unified behavior. By modeling the system state as a probability distribution of regrets and analyzing its evolution through the continuity equation, we uncover a key phenomenon in diverse multiagent settings: the variance of the regret distribution diminishes over time, leading to the disappearance of heterogeneity and the emergence of consensus among agents. This universal result enables us to prove convergence to quantal response equilibria in both competitive and cooperative multiagent settings. This work advances the theoretical understanding of multiagent learning and offers a novel perspective on equilibrium selection in diverse game-theoretic scenarios.

We introduce a new hypothesis testing-based learning dynamics in which players update their strategies by combining hypothesis testing with utility-driven exploration. In this dynamics, each player forms beliefs about opponents' strategies and episodically tests these beliefs using empirical observations. Beliefs are resampled either when the hypothesis test is rejected or through exploration, where the probability of exploration decreases with the player's (transformed) utility. In general finite normal-form games, we show that the learning process converges to a set of approximate Nash equilibria and, more importantly, to a refinement that selects equilibria maximizing the minimum (transformed) utility across all players. Our result establishes convergence to equilibrium in general finite games and reveals a novel mechanism for equilibrium selection induced by the structure of the learning dynamics.

Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control

Liquid-liquid equilibrium and solvent selection for efficient extraction of 2-methoxyphenol from aqueous solutions

Abstract Agreements are rarely fully enforceable, exposing trading parties to the risk of exploitation. In such cases, trust—defined as the belief in the trustworthiness of others—may be key to realizing gains from trade. This paper asks whether trust substitutes for or complements contract enforcement. While intuition may suggest trust matters more when enforcement is weak, our experiment, which exogenously varies both trust and enforcement, shows it can matter more when enforcement is strong. The mechanism is equilibrium selection: stronger enforcement allows more equilibria, and trust helps select efficient ones. This complementarity between trust and enforcement has important policy implications.

This paper addresses the challenge of fostering cooperation among virtual power plant (VPP) operators in competitive electricity markets, focusing on the application of evolutionary game theory (EGT) and static reward–punishment mechanisms. This investigation resolves four critical questions: the minimum reward–punishment thresholds triggering stable cooperation, the influence of initial market composition on equilibrium selection, the sufficiency of static versus dynamic mechanisms, and the quantitative mapping between regulatory parameters and market outcomes. The study establishes the mathematical conditions under which static reward–punishment mechanisms transform competitive VPP markets into stable cooperative systems, quantifying efficiency improvements of 15–23% and renewable integration gains of 18–31%. Through rigorous evolutionary game-theoretic analysis, we identify critical parameter thresholds that guarantee cooperation emergence, resolving longstanding market coordination failures documented across multiple jurisdictions. Numerical simulations and sensitivity analysis demonstrate that static reward–punishment systems enhance cooperation, optimize resources, and increase renewable energy utilization. Key findings include: (1) Reward–punishment mechanisms effectively promote cooperation and system performance; (2) A critical region exists where cooperation dominates, enhancing market outcomes; and (3) Parameter adjustments significantly impact VPP performance and market behavior. The theoretical contributions of this research address documented market failures observed across operational VPP implementations. Our findings provide quantitative foundations for regulatory frameworks currently under development in seven national energy markets, including the European Union’s proposed Digital Single Market for Energy and Japan’s emerging VPP aggregation standards. The model’s predictions align with successful cooperation rates achieved by established VPP operators, suggesting practical applicability for scaled implementations. Overall, through evolutionary game-theoretic analysis of 156 VPP implementations, we establish precise conditions under which static mechanisms achieve 85%+ cooperation rates. Based on this, future work could explore dynamic adjustments, uncertainty modeling, and technologies like blockchain to further improve VPP resilience.

Over a quarter of the world’s population lives in countries that have undertaken transitions from central planning to some form of market-based coordination. These transitions entail far-reaching and complex economic and institutional changes and have had widely divergent trajectories. Important strands of literature have emphasised the many strategic complementarities that characterise the transition process. Contrary to a widespread assumption, new functioning economic institutions and a robust legal framework do not necessarily arise when property rights are reconfigured in a highly unstable and uncertain environment. Multiple equilibria emerge and expectations may play a key role in equilibrium selection. In this paper, we review the vast empirical literature on transition economies to provide comprehensive evidence about expectations at the beginning of transition, gathering and organising information from disparate studies across a wide set of countries. We thus provide the first comprehensive survey of the literature on agents’ subjective perceptions of transition paths.

The isolated effects of collateral reuse on financial stability are ambiguous and understudied. While greater collateral reuse can guarantee more payments with fewer assets, it can also increase the exposure to potential drops in collateral price. To analyze these tradeoffs, we develop a financial network model with endogenous asset pricing, multiple equilibria, and equilibrium selection. We find that more collateral reuse decreases the likelihood of the worst equilibrium (crisis), with varying effects depending on the network structure. Therefore, collateral reuse can unambiguously improve financial stability for a fixed degree of risk-taking behavior. However, with endogenous risk-taking, we show that a higher degree of collateral reuse can worsen financial stability through greater risk-taking. As a result, while crises may occur less frequently, their severity would increase, leading to a lower social surplus during crises.

Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium selection. We study the computational complexity of identifying and using symmetries. Using the classical framework of normal-form games, we consider game symmetries that can be across some or all players and/or actions. We find a strong connection between game symmetries and graph automorphisms, yielding graph automorphism and graph isomorphism completeness results for characterizing the symmetries present in a game. On the other hand, we also show that the problem becomes polynomial-time solvable when we restrict the consideration of actions in one of two ways. Next, we investigate when exactly game symmetries can be successfully leveraged for Nash equilibrium computation. We show that finding a Nash equilibrium that respects a given set of symmetries is PPAD- and CLS-complete in general-sum and team games respectively---that is, exactly as hard as Brouwer fixed point and gradient descent problems. Finally, we present polynomial-time methods for the special cases where we are aware of a vast number of symmetries, or where the game is two-player zero-sum and we do not even know the symmetries.

We study the exploration-exploitation trade-off for large multiplayer coordination games where players strategise via Q-Learning, a common learning framework in multi-agent reinforcement learning. Q-Learning is known to have two shortcomings, namely non-convergence and potential equilibrium selection problems, when there are multiple fixed points, called Quantal Response Equilibria (QRE). Furthermore, whilst QRE have full support for finite games, it is not clear how Q-Learning behaves as the game becomes large. In this paper, we characterise the critical exploration rate that guarantees convergence to a unique fixed point, addressing the two shortcomings above. Using a generating-functional method, we show that this rate increases with the number of players and the alignment of their payoffs. For many-player coordination games with perfectly aligned payoffs, this exploration rate is roughly twice that of p-player zero-sum games. As for large games, we provide a structural result for QRE, which suggests that as the game size increases, Q-Learning converges to a QRE near the boundary of the simplex of the action space, a phenomenon we term asymptotic extinction, where a constant fraction of the actions are played with zero probability at a rate o(1/N) for an N -action game.

Abstract This paper studies the replicator dynamics and the best-response dynamics of a signaling game with type-specific preferences over signals—a generalization of the beer-quiche game (Cho and Kreps in Q J Econ 102(2):179–221, 1987). When the prior probability of the high type is below the critical value at which player 2 is indifferent between accepting and not accepting, there is a unique, partially revealing equilibrium with partial pooling in the signal that the high type prefers. Under the replicator dynamics, this equilibrium is (Lyapunov) stable but not asymptotically stable. It is surrounded by periodic orbits each of which attracting a three-dimensional stable manifold from the interior of the state space. When the prior probability of the high type is above the critical value (the case usually considered), there are two equilibrium outcomes, each with pooling in one of the two signals. Under the replicator dynamics, the equilibrium outcome with pooling in the signal that the high type prefers is stable but not asymptotically stable. The equilibrium outcome with pooling in the signal that the low type prefers is unstable. Still, both components have basins of attraction with nonempty interior. The proofs use center manifold theory and chain recurrence. Throughout, results of the dynamic analysis are compared to equilibrium selection based on the intuitive criterion and index theory.

This paper introduces a common-interest communication game that generates pragmatics, where meaning emerges from the use of a preexisting language under equilibrium selection driven solely by efficiency. A key feature is that the sender describes the current state to the receiver by combining preexisting statements. This approach allows us to formalize two communication frictions: (i) longer descriptions incur higher costs, and (ii) with some probability, the receiver interprets only the conventional meaning. The absence of one friction leads to some efficient equilibria exhibiting pragmatics that disregards conventional meaning. However, when communication costs are sufficiently small, given the other friction, any efficient equilibrium exhibits natural pragmatics that refines conventional meaning, reflecting the context provided by the probability distribution of states. The resulting equilibrium pragmatics aligns with major linguistic theories, including Grice’s cooperative principle (1975) and Sperber and Wilson’s relevance theory (1986).

Abstract One‐shot public‐good situations are prominent in the public debate, and a prime example for behavior diverging from the standard Nash‐equilibrium. Could a Nash‐equilibrium predict one‐shot public‐good behavior in principle? A “revealed‐preference Nash‐equilibrium” (rpne) out‐of‐sample predicts behavior, outperforming other social‐preference models. The rpne is the set of “mutual conditional contributions,” interpreting elicited conditional contributions as best‐responses. Individual‐level analyses confirm the results and allow for studying equilibrium selection. While the Pareto‐dominant equilibrium is the modal choice, many participants use other criteria. Given the predictive positive‐contributions rpnes, many real‐life public‐good problems may be solvable if players could coordinate on an equilibrium‐selection criterion beforehand.

We study the problem of selecting, in a measurable manner, equilibria from each of a family of games. Typical equilibrium selection theorems assume continuity in, and compactness of, actions, while we merely assume equilibria exist for all games in the family, and payoffs are jointly Borel in parameter and actions. The existence of Lebesgue- or universally measurable selectors turns out to be independent of ZFC; the result is robust to restriction to zero-sum games, as well as to allowing mixed strategies. We show, however, that the existence of analytically measurable selections, well-known to exist for single decision makers, fails for families of two-player zero-sum games.

We develop a nonparametric and ordinal approach for testing pure strategy Nash equilibrium play in games with monotone best responses, such as those with strategic complements/substitutes. The approach makes minimal assumptions on unobserved heterogeneity, requires no parametric assumptions on payoff functions, and no restriction on equilibrium selection from multiple equilibria. The approach can also be extended in order to make inferences and predictions. Both model‐testing and inference can be implemented by a tractable computation procedure based on column generation. To illustrate how our approach works, we include an application to an IO entry game.

This paper studies a large class of multi‐agent contracting models with the property that agents' payoffs constitute a weighted potential game. Multiple equilibria arise due to agents' strategic interactions. I fully characterize a contracting scheme that is optimal for the principal for all equilibrium selection criteria that are more pessimistic than potential maximization. This scheme ranks agents in ascending order of their weights in the weighted potential game and then induces them to accept their offers in a dominance‐solvable way, starting from the first agent. I apply the general results to networks, public goods/“bads,” and a class of binary‐action applications.