Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk

We present a new approach to studying equilibrium dynamics in a class of stochastic games with a continuum of players with private types and strategic complementarities. We introduce a suitable equilibrium concept, called Markov Stationary Nash Distributional Equilibrium (MSNDE), prove its existence, and determine comparative statics of equilibrium paths and the steady state invariant distributions to which they converge. Finally, we provide numerous applications of our results including: dynamic models of growth with status concerns, social distance, and paternalistic bequest with endogenous preference for consumption

Adaptive Algorithms and Collusion via Coupling

We develop a theoretical model to study strategic interactions between adaptive learning algorithms. Applying continuous-time techniques, we uncover the mechanism responsible for collusion between Artificial Intelligence algorithms documented by recent experimental evidence. We show that spontaneous coupling between the algorithms' estimates leads to periodic coordination on actions that are more profitable than static Nash equilibria. We provide a sufficient condition under which this coupling is guaranteed to disappear, and algorithms learn to play undominated strategies. We apply our results to interpret and complement experimental findings in the literature and to the design of learning-robust strategy-proof mechanisms. We show that ex-post feedback provision guarantees robustness to the presence of learning agents. We fully characterize the optimal learning-robust mechanisms: they are menu mechanisms.Comment: 57 pages, 13 figure

Learning for Cross-layer Resource Allocation in the Framework of Cognitive Wireless Networks

The framework of cognitive wireless networks is expected to endow wireless devices with a cognition-intelligence ability with which they can efficiently learn and respond to the dynamic wireless environment. In this dissertation, we focus on the problem of developing cognitive network control mechanisms without knowing in advance an accurate network model. We study a series of cross-layer resource allocation problems in cognitive wireless networks. Based on model-free learning, optimization and game theory, we propose a framework of self-organized, adaptive strategy learning for wireless devices to (implicitly) build the understanding of the network dynamics through trial-and-error. The work of this dissertation is divided into three parts. In the first part, we investigate a distributed, single-agent decision-making problem for real-time video streaming over a time-varying wireless channel between a single pair of transmitter and receiver. By modeling the joint source-channel resource allocation process for video streaming as a constrained Markov decision process, we propose a reinforcement learning scheme to search for the optimal transmission policy without the need to know in advance the details of network dynamics. In the second part of this work, we extend our study from the single-agent to a multi-agent decision-making scenario, and study the energy-efficient power allocation problems in a two-tier, underlay heterogeneous network and in a self-sustainable green network. For the heterogeneous network, we propose a stochastic learning algorithm based on repeated games to allow individual macro- or femto-users to find a Stackelberg equilibrium without flooding the network with local action information. For the self-sustainable green network, we propose a combinatorial auction mechanism that allows mobile stations to adaptively choose the optimal base station and sub-carrier group for transmission only from local payoff and transmission strategy information. In the third part of this work, we study a cross-layer routing problem in an interweaved Cognitive Radio Network (CRN), where an accurate network model is not available and the secondary users that are distributed within the CRN only have access to local action/utility information. In order to develop a spectrum-aware routing mechanism that is robust against potential insider attackers, we model the uncoordinated interaction between CRN nodes in the dynamic wireless environment as a stochastic game. Through decomposition of the stochastic routing game, we propose two stochastic learning algorithm based on a group of repeated stage games for the secondary users to learn the best-response strategies without the need of information flooding

Four Essays in Economic Theory

This thesis comprises four essays that belong to different strands of the theoretical economic literature. Chapter 1 and Chapter 2 study two-sided one-to-one matching markets with quasi-linear utility and multi-dimensional heterogeneity. Chapter 1 investigates the efficiency properties of two-sided investments and in particular the sources and limitations of potential investment coordination failures in large two-sided economies with competitive post-investment market. Chapter 2 scrutinizes a novel two-sided matching model with a finite number of agents and two-sided private information about exogenously given attributes. Chapter 3 is a note on the optimal size of fixed-prize research tournaments that seeks to fill two important gaps in an influential paper by Fullerton and McAfee (1999), and Chapter 4 studies the impact of incomplete information on the problem of maximizing revenue in a dynamic version of the knapsack problem, which is a classical combinatorial resource allocation problem with numerous economic applications

Bayesian Network Games

This thesis builds from the realization that Bayesian Nash equilibria are the natural definition of optimal behavior in a network of distributed autonomous agents. Game equilibria are often behavior models of competing rational agents that take actions that are strategic reactions to the predicted actions of other players. In autonomous systems however, equilibria are used as models of optimal behavior for a different reason: Agents are forced to play strategically against inherent uncertainty. While it may be that agents have conflicting intentions, more often than not, their goals are aligned. However, barring unreasonable accuracy of environmental information and unjustifiable levels of coordination, they still can\u27t be sure of what the actions of other agents will be. Agents have to focus their strategic reasoning on what they believe the information available to other agents is, how they think other agents will respond to this hypothetical information, and choose what they deem to be their best response to these uncertain estimates. If agents model the behavior of each other as equally strategic, the optimal response of the network as a whole is a Bayesian Nash equilibrium. We say that the agents are playing a Bayesian network game when they repeatedly act according to a stage Bayesian Nash equilibrium and receive information from their neighbors in the network. The first part of the thesis is concerned with the development and analysis of algorithms that agents can use to compute their equilibrium actions in a game of incomplete information with repeated interactions over a network. In this regard, the burden of computing a Bayesian Nash equilibrium in repeated games is, in general, overwhelming. This thesis shows that actions are computable in the particular case when the local information that agents receive follows a Gaussian distribution and the game\u27s payoff is represented by a utility function that is quadratic in the actions of all agents and an unknown parameter. This solution comes in the form of the Quadratic Network Game filter that agents can run locally, i.e., without access to all private signals, to compute their equilibrium actions. For the more generic payoff case of Bayesian potential games, i.e., payoffs represented by a potential function that depends on population actions and an unknown state of the world, distributed versions of fictitious play that converge to Nash equilibrium with identical beliefs on the state are derived. This algorithm highlights the fact that in order to determine optimal actions there are two problems that have to be solved: (i) Construction of a belief on the state of the world and the actions of other agents. (ii) Determination of optimal responses to the acquired beliefs. In the case of symmetric and strictly supermodular games, i.e., games with coordination incentives, the thesis also derives qualitative properties of Bayesian network games played in the time limit. In particular, we ask whether agents that play and observe equilibrium actions are able to coordinate on an action and learn about others\u27 behavior from only observing peers\u27 actions. The analysis described here shows that agents eventually coordinate on a consensus action. The second part of this thesis considers the application of the algorithms developed in the first part to the analysis of energy markets. Consumer demand profiles and fluctuating renewable power generation are two main sources of uncertainty in matching demand and supply in an energy market. We propose a model of the electricity market that captures the uncertainties on both, the operator and the user side. The system operator (SO) implements a temporal linear pricing strategy that depends on real-time demand and renewable generation in the considered period combining Real-Time Pricing with Time-of-Use Pricing. The announced pricing strategy sets up a noncooperative game of incomplete information among the users with heterogeneous but correlated consumption preferences. An explicit characterization of the optimal user behavior using the Bayesian Nash equilibrium solution concept is derived. This explicit characterization allows the SO to derive pricing policies that influence demand to serve practical objectives such as minimizing peak-to-average ratio or attaining a desired rate of return. Numerical experiments show that the pricing policies yield close to optimal welfare values while improving these practical objectives. We then analyze the sensitivity of the proposed pricing schemes to user behavior and information exchange models. Selfish, altruistic and welfare maximizing user behavior models are considered. Furthermore, information exchange models in which users only have private information, communicate or receive broadcasted information are considered. For each pair of behavior and information exchange models, rational price anticipating consumption strategy is characterized. In all of the information exchange models, equilibrium actions can be computed using the Quadratic Network Game filter. Further experiments reveal that communication model is beneficial for the expected aggregate payoff while it does not affect the expected net revenue of the system operator. Moreover, additional information to the users reduces the variance of total consumption among runs, increasing the accuracy of demand predictions

Investment Under Uncertainty, Market Evolution and Coalition Spillovers in a Game Theoretic Perspective.

The rationality assumption has been the center of neo-classical economics for more than half a century now. In recent years much research has focussed on models of bounded rationality. In this thesis it is argued that both full and bounded rationality can be used for different kind of problems. In the first part full rationality is assumed to analyse technology adoption by firms in a duopolistic and uncertain environment. In the second part, boundedly rational models are developed to study the evolution of market structure in oligopolistic markets as well as price formation on (possibly) incomplete financial markets. The third part of the thesis presents an alternative to the framework of Transferable Utility games in cooperative game theory. The model introduced here explicitly takes into account the outside options that players often have in real-life situations if they choose not to participate in a coalition.