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

Mean Field Equilibrium in Dynamic Games with Strategic 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 (for example, the introduction of incentives to players)

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

Mechanisms of Endogenous Institutional Change

This paper proposes an analytical-cum-conceptual framework for understanding the nature of institutions as well as their changes. In doing so, it attempts to achieve two things: First, it proposes a way to reconcile an equilibrium (endogenous) view of institutions with the notion of agents’ bounded rationality by introducing such concepts as a summary representation of equilibrium as common knowledge of agents. Second, it specifies some generic mechanisms of institutional coherence and change -- overlapping social embededdness, Schumpeterian innovation in bundling games and dynamic institutional complementarities -- useful for understanding the dynamic interactions of economic, political, social and organizational factors.

Co-Management Strategy for the Sustainable use of Coral Reef Resources in the National Natural Park "Corales del Rosario y San Bernardo" in Colombia

The National Natural Park "Corales del Rosario y San Bernardo", located in the Caribbean Sea, is one of the most important parks in Colombia since it hosts high biological biodiversity, receives more tourists than any other natural park in the country and provides sustenance to several communities settled in and around it. However, lack of governance and incompatibility of incentives among authorities, communities and visitors threaten its conservation and sustainability. Using experimental economic games with fisherman communities, we tested different rules related with the management of natural resources in the protected area. In addition to standard rules of communication and external regulation, we tested a rule called co-management, in which we explored the complementarities between repeated communication and external non-coercive authority intervention. We also tested inter temporal effects where over extraction (by the group) in a round reduces the availability of resource for next round and, in consequence, increases effort and reduces benefits for fishers. Results confirmed the effectiveness of communication and, to some extent, external regulation. More important than that, co-management treatment exhibit no matter the location of the communities with respect to the park- the best results in terms of sustainable use of the resource. Participants incorporated dynamic implications in their decisions when information asymmetries were overcome, through internal communication or external guidance. These results highlight the importance of resource management designs that recognize communities as key actors in decision making for the sustainable use and conservation of common pool resources in protected areas.Resource /Energy Economics and Policy,

Diffusion of Behavior and Equilibrium Properties in Network Games

Situations in which agents’ choices depend on choices of those in close proximity, be it social or geographic, are ubiquitous. Selecting a new computer platform, signing a political petition, or even catching the flu are examples in which social interactions have a significant role. While some behaviors or states propagate and explode within the population (e.g., Windows OS, the HIV virus) others do not (e.g., certain computer viruses). Our goal in this paper is twofold. First, we provide a general dynamic model in which agents’ choices depend on the underlying social network of connections. Second, we show the usefulness of the model in determining when a given behavior expands within a population or disappears as a function of the environment’s fundamentals. We study a framework in which agents face a choice between two actions, 0 and 1 (e.g., whether to pursue a certain level of education, switch to Linux OS, etc.). Agents are linked through a social network, and an agent’s payoffs from each action depend on the number of neighbors she has and her neighbors’ choices. The diffusion process is defined so that at each period, each agent best responds to the actions taken by her neighbors in the previous period, assuming that her neighbors follow the population distribution of actions (a mean-field approximation). Steady states correspond to equilibria of the static game. Under some simple conditions, equilibria take one of two forms. Some are stable, so that a slight perturbation to any such equilibrium would lead the diffusion process to converge back to that equilibrium point. Other equilibria are unstable, so that a slight change in the distribution of actions leads to a new distribution of actions and eventually to a stable steady state. We call such equilibria tipping points. We analyze how the environment’s fundamentals (cost distribution, payoffs, and network structure) affect the set of equilibria, and characterize the adoption patterns within the network. The paper relates to recent work on network games and network diffusion, including work by Stephen Morris (2000); Pastor-Satorras and Vespignani (2000); Mark E. J. Newman (2002); Dunia López-Pintado (2004); Jackson and Brian W. Rogers (2007); Jackson and Yariv (2005); and Andrea Galeotti et al. (2005, henceforth GGJVY). Its contribution is in characterizing diffusion of strategic behavior and analyzing the stability properties of equilibria, and employing methods that allow us to make comparisons across general network structures and settings. Given that social networks differ substantially and systematically in structure across settings (e.g., ethnic groups, professions, etc.), understanding the implications of social structure on diffusion is an important undertaking for a diverse set of applications

Dynamic Multi-Arm Bandit Game Based Multi-Agents Spectrum Sharing Strategy Design

For a wireless avionics communication system, a Multi-arm bandit game is mathematically formulated, which includes channel states, strategies, and rewards. The simple case includes only two agents sharing the spectrum which is fully studied in terms of maximizing the cumulative reward over a finite time horizon. An Upper Confidence Bound (UCB) algorithm is used to achieve the optimal solutions for the stochastic Multi-Arm Bandit (MAB) problem. Also, the MAB problem can also be solved from the Markov game framework perspective. Meanwhile, Thompson Sampling (TS) is also used as benchmark to evaluate the proposed approach performance. Numerical results are also provided regarding minimizing the expectation of the regret and choosing the best parameter for the upper confidence bound