Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications (original) (raw)
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American Economic Association, 2024
The Nash Equilibrium has long been a cornerstone of game theory, providing a robust framework for understanding strategic interactions in diverse fields such as economics, biology, and artificial intelligence. Despite its theoretical elegance, the classical Nash Equilibrium framework is often critiqued for its static nature and limited applicability to dynamic, real-world systems characterized by evolving strategies and uncertainty. This paper revisits the foundational principles of Nash Equilibrium, proposing a novel framework that extends its applicability to dynamic and adaptive systems. By integrating temporal feedback, hierarchical decision layers, and stochastic elements, the proposed model-Dynamic and Adaptive Nash Equilibrium (DANE)-addresses the limitations of the traditional equilibrium concept. Through rigorous mathematical formulations and comparative analysis, we demonstrate the superiority of DANE in predicting and explaining strategic behavior in complex systems. Applications of this enhanced framework are explored in contexts such as multiagent reinforcement learning, financial markets, and cooperative social systems, showcasing its potential to revolutionize decision-making and optimization. This article not only redefines the Nash Equilibrium for the modern era but also sets a trajectory for future innovations in game theory.
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Noncooperative games are examined from the point of view of an outside observer who believes that the players are rational and that they know at least as much as the observer. The observer is assumed to be able to observe many instances of the play of the game; these instances are identical in the sense that the observer cannot distinguish between the settings in which different plays occur. If the observer does not believe that he will be able to offer beneficial advice then he must believe that the players are playing a correlated equilibrium, though he may not initially know which correlated equilibrium. If the observer also believes that, in a certain sense, there is nothing connecting the players in a particular instance of the game then he must believe that the correlated equilibrium they are playing is, in fact, a Nash equilibrium.
Exploratory analysis and models for strategic learning towards equilibrium
Educational Dimension
This paper is about people's strategic behavior as observed through experiments. The research question posed in this paper is how players (primarily children) learn in complex strategic situations that they have never encountered before. We examine data from various games played during popular game theory lectures and present findings about players' strategic learning progress while competing with other players. Four ``pick a number'' games with similar-looking rules but very different properties were investigated. These games were presented to various groups of listeners. The collected data is available for replication and analysis in an open repository. In this paper, we analyze data and propose an agent-based model of a beauty pageant game to explain observed behavior. Finally, we discuss the findings, hypotheses to test, and open questions for future research.
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2002
Satisficing, or being "good enough," is the fundamental obligation of rational decision makers. We cannot rationally choose an option, even when we do not know of anything better, unless we know it is good enough. Unfortunately, we are not often in the position of knowing that there could be no better option, and hence that the option must be good enough. A complete search through all logical possibilities is often impractical, particularly in multi-agent contexts, due to excessive computational difficulty, modeling complexity, and uncertainty. It can be equally impractical, if it is even possible, to determine the cost of the additional required search to find an option that is good enough. In a departure from the traditional notion of satisficing as a species of bounded rationality, satisficing is here redefined in terms of a notion of intrinsic rationality. Epistemic utility theory serves as the philosophical foundation of a new praxeological decision-making paradigm of satisficing equilibria that is applicable to both single-and multiple-agent scenarios. All interagent relationships are modeled by an interdependence function that explicitly accommodates both self and group interest, from which multilateral and unilateral selectability and rejectability mass functions can be derived and compared via the praxeic likelihood ratio test.
2007
In real life strategic interactions, decision-makers are likely to entertain doubts about the degree of optimality of their play. To capture this feature of real choice-making, we present here a model based on the doubts felt by an agent about how well is playing a game. The doubts are coupled with (and mutually reinforced by) imperfect discrimination capacity, which we model here by means of similarity relations. We assume that each agent builds procedural preferences de ned on the space of expected payoffs-strategy frequencies attached to his current strategy. These preferences, together with an adaptive learning process lead to doubt-based selection dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed Strategy Doubt-Full Equilibria and Mixed Strategy Doubtless Equilibria and show the theoretical and the empirical relevance of these concepts.
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