Congestion Games with Complementarities

We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in modern networked environments. Our model is inspired by utility functions with constant elasticity of substitution (CES) which is a well-studied model in economics. We consider congestion games with different aggregation functions. In particular, we study $L_p$ norms and analyze the existence and complexity of (approximate) pure Nash equilibria. Additionally, we give an almost tight characterization based on monotonicity properties to describe the set of aggregation functions that guarantee the existence of pure Nash equilibria.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-57586-5_1

The cutting power of preparation

In a strategic game, a curb set [Basu and Weibull, Econ. Letters 36 (1991) 141] is a product set of pure strategies containing all best responses ro every possible belief restricted to this set. Prep sets [Voorneveld, Games Econ. Behav. 48 (2004) 403] relax this condition by only requiring the presence of at least one best response to such a belief. The purpose of this paper is to provide economically interesting classes of games in which minimal prep sets give sharp predictions, whereas in relevant subclasses of these games, minimal curb sets have no cutting power whatsoever and simply consist of the entire strategy space. These classes include potential games, congestion games with player-specific payoffs, and supermodular games.curb sets; prep sets; potential games; congestion games; supermodular games

The Cutting Power of Preparation

In a strategic game, a curb set [Basu and Weibull, Econ.Letters 36 (1991) 141-146] is a product set of pure strategies containing all best responses to every possible belief restricted to this set.Prep sets [Voorneveld, Games Econ. Behav. 48 (2004) 403-414] relax this condition by only requiring the presence of at least one best response to such a belief.The purpose of this paper is to provide sufficient conditions under which minimal prep sets give sharp predictions.These conditions are satisfied in many economically relevant classes of games, including supermodular games, potential games, and congestion games with player-specific payoffs.In these classes, minimal curb sets generically have a large cutting power as well, although it is shown that there are relevant subclasses of coordination games and congestion games where minimal curb sets have no cutting power at all and simply consist of the entire strategy space.curb sets;prep sets;supermodular games;potential games;congestion games

Strategic complementarities and nested potential games

This note shows that every finite game of strategic complementarities is a nested pseudo-potential game defined in Uno (2007, Economics Bulletin 3 (17)) if the action set of each player is one-dimensional, except possibly for one playerStrategic complementarities, potential games, existence of a pure strategy Nash equilibrium

Equilibrium Computation in Resource Allocation Games

We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and player-specific affine cost functions, we devise the first polynomial time algorithm computing a pure Nash equilibrium. Our algorithm is combinatorial and computes the exact equilibrium assuming rational input. The idea is to compute an equilibrium for an associated integrally-splittable singleton congestion game in which the players can only split their demands in integral multiples of a common packet size. While integral games have been considered in the literature before, no polynomial time algorithm computing an equilibrium was known. Also for this class, we devise the first polynomial time algorithm and use it as a building block for our main algorithm. We then develop a polynomial time computable transformation mapping a multimarket Cournot competition game with firm-specific affine price functions and quadratic costs to an associated atomic splittable congestion game as described above. The transformation preserves equilibria in either games and, thus, leads -- via our first algorithm -- to a polynomial time algorithm computing Cournot equilibria. Finally, our analysis for integrally-splittable games implies new bounds on the difference between real and integral Cournot equilibria. The bounds can be seen as a generalization of the recent bounds for single market oligopolies obtained by Todd [2016].Comment: This version contains some typo corrections onl

Controlled Matching Game for Resource Allocation and User Association in WLANs

In multi-rate IEEE 802.11 WLANs, the traditional user association based on the strongest received signal and the well known anomaly of the MAC protocol can lead to overloaded Access Points (APs), and poor or heterogeneous performance. Our goal is to propose an alternative game-theoretic approach for association. We model the joint resource allocation and user association as a matching game with complementarities and peer effects consisting of selfish players solely interested in their individual throughputs. Using recent game-theoretic results we first show that various resource sharing protocols actually fall in the scope of the set of stability-inducing resource allocation schemes. The game makes an extensive use of the Nash bargaining and some of its related properties that allow to control the incentives of the players. We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as its MAC anomaly. The mechanism can be implemented as a virtual connectivity management layer to achieve efficient APs-user associations without modification of the MAC layer

Heterogeneous Tiebout communities with private production and anonymous crowding

his paper examines, in the context of a multiple types of consumers, a set of necessary and sufficient conditions under which equilibrium and optimum exist, and involve mixing types of consumers in jurisdictions. Pricing includes visa permits for entry. Following Berglas (1976), we assume anonymous crowding and complementarities in production. For a large economy, we prove existence of equilibrium and the first and second welfare theorems. Our simultaneous optimization approach provides a new technique for showing existence of equilibrium in local public good economies with local production and a continuum of agents.Local public goods, Collaborative production, Wages, Anonymous crowding, Visa permits, Societal stratification, Heterogeneous Tiebout communities, Generalized game

Cultural Identity and Knowledge Creation in Cosmopolitan Cities

We study how the city system is affected by the possibility for the members of the same cultural diaspora to interact across different cities. In so doing, we propose a simple two- city model with two mobile cultural groups. A localized externality fosters the productivity of individuals when groups interact in a city. At the same time, such interaction dilutes cultural identities and reduces the consumption of culture-specific goods and services. We show that the two groups segregate in different cities when diaspora members find it hard to communicate at distance whereas they integrate in multicultural cities when communication is easy. The model generates situations in which segregation is an equilibrium but is Pareto dominated by integration.Cultural Identity, Cosmopolitan City, Productiviy

Social Interactions and Spillovers

The aim of this paper is to provide a tractable model where both socialization (or network formation) and productive efforts can be analyzed simultaneously. This permits a full-fledged equilibrium/welfare analysis of network formation with endogenous productive efforts and heterogeneous agents. We show that there exist two stable interior equilibria, which we can Pareto rank. The socially efficient outcome lies between these two equilibria. When the intrinsic returns to production and socialization increase, all equilibrium actions decrease at the Pareto-superior equilibrium, while they increase at the Pareto-inferior equilibrium. In both cases, the percentage change in socialization effort is higher (in absolute value) than that of the productive effort.Peer effects; network formation; welfare