(Mechanical) Reasoning on Infinite Extensive Games

In order to better understand reasoning involved in analyzing infinite games in extensive form, we performed experiments in the proof assistant Coq that are reported here.Comment: 11

Mean-Field-Type Games in Engineering

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201

Intrinsic Motivation versus Signaling in Open Source Software Development

This papers sheds light on the puzzling fact that even though open source software (OSS) is a public good, it is developed for free by highly qualified, young, motivated individuals, and evolves at a rapid pace. We show that when OSS development is understood as the private provision of a public good, these features emerge quite naturally. We adapt a dynamic private-provision-of-public-goods model to reflect key aspects of the OSS phenomenon. Apart from extrinsic motives (namely signaling), the present model also contains intrinsic motives of OSS programmers, such as play value or homo ludens payoff, userprogrammers’ and gift culture benefits. Such intrinsic motives feature extensively in the wider OSS literature and contribute new insights to the economic analysisopen source software; public goods; homo ludens; war of attrition

Mean Field Equilibrium in Dynamic Games with Complementarities

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical distribution of the states of other players. Such games can be used to model a diverse set of applications, including network security models, recommender systems, and dynamic search in markets. Stochastic games are generally difficult to analyze, and these difficulties are only exacerbated when the number of players is large (as might be the case in the preceding examples). We consider an approximation methodology called mean field equilibrium to study these games. In such an equilibrium, each player reacts to only the long run average state of other players. We find necessary conditions for the existence of a mean field equilibrium in such games. Furthermore, as a simple consequence of this existence theorem, we obtain several natural monotonicity properties. We show that there exist a "largest" and a "smallest" equilibrium among all those where the equilibrium strategy used by a player is nondecreasing, and we also show that players converge to each of these equilibria via natural myopic learning dynamics; as we argue, these dynamics are more reasonable than the standard best response dynamics. We also provide sensitivity results, where we quantify how the equilibria of such games move in response to changes in parameters of the game (e.g., the introduction of incentives to players).Comment: 56 pages, 5 figure