This paper presents a structural discrete choice model with social influence for large-scale social networks. The model is based on an incomplete information game and permits individual-specific parameters of consumers. It is challenging to apply this type of models to real-life scenarios for two reasons: (1) The computation of the Bayesian–Nash equilibrium is highly demanding; and (2) the identification of social influence requires the use of excluded variables that are oftentimes unavailable. To address these challenges, we derive the unique equilibrium conditions of the game, which allow us to employ a stochastic Bayesian estimation procedure that is scalable to large social networks. To facilitate the identification, we utilize community-detection algorithms to divide the network into different groups that, in turn, can be used to construct excluded variables. We validate the proposed structural model with the login decisions of more than 25,000 users of an online social game. Importantly, this data set also contains promotions that were exogenously determined and targeted to only a subgroup of consumers. This information allows us to perform exogeneity tests to validate our identification strategy using community-detection algorithms. Finally, we demonstrate the managerial usefulness of the proposed methodology for improving the strategies of targeting influential consumers in large social networks. This paper was accepted by Matthew Shum, marketing.

Integrating large language model (LLM) agents within game theory demonstrates their ability to replicate human-like behaviors through strategic decision making. In this paper, we introduce an augmented LLM agent, called the private agent, which engages in private deliberation and employs deception in repeated games. Utilizing the partially observable stochastic game (POSG) framework and incorporating in-context learning (ICL) and chain-of-thought (CoT) prompting, we investigated the private agent's proficiency in both competitive and cooperative scenarios. Our empirical analysis demonstrated that the private agent consistently achieved higher long-term payoffs than its baseline counterpart and performed similarly or better in various game settings. However, we also found inherent deficiencies of LLMs in certain algorithmic capabilities crucial for high-quality decision making in games. These findings highlight the potential for enhancing LLM agents' performance in multi-player games using information-theoretic approaches of deception and communication with complex environments.

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.

Biological systems, ranging from ant colonies to neural ecosystems, exhibit remarkable self-organizing intelligence. Inspired by these phenomena, this study investigates how bio-inspired computing principles can bridge game-theoretic rationality and multi-agent adaptability. This study systematically reviews the convergence of multi-agent reinforcement learning (MARL) and game theory, elucidating the innovative potential of this integrated paradigm for collective intelligent decision-making in dynamic open environments. Building upon stochastic game and extensive-form game-theoretic frameworks, we establish a methodological taxonomy across three dimensions: value function optimization, policy gradient learning, and online search planning, thereby clarifying the evolutionary logic and innovation trajectories of algorithmic advancements. Focusing on complex smart city scenarios-including intelligent transportation coordination and UAV swarm scheduling-we identify technical breakthroughs in MARL applications for policy space modeling and distributed decision optimization. By incorporating bio-inspired optimization approaches, the investigation particularly highlights evolutionary computation mechanisms for dynamic strategy generation in search planning, alongside population-based learning paradigms for enhancing exploration efficiency in policy refinement. The findings reveal core principles governing how groups make optimal choices in complex environments while mapping the technological development pathways created by blending cross-disciplinary methods to enhance multi-agent systems.

I consider a class of dynamic Bayesian games in which types evolve stochastically according to a first-order Markov process on a continuous type space. Types are privately informed, but they become public together with actions when payoffs are obtained, resulting in a delayed information revelation. In this environment, I show that there exists a stationary Bayesian–Markov equilibrium in which a player’s strategy maps a tuple of the previous type and action profiles and the player’s current type to a mixed action. The existence can be extended to K-periodic revelation. I also offer a computational algorithm to find an equilibrium.