The dynamics of social interaction with agents’ heterogeneity

We analyze a class of binary dynamic models inspired by [4] on agents’ choices and social interaction. The main feature of our analysis is that agents are heterogeneous, in particular their attitude to interact with the choices of the other agents changes over time endogenously. Although dynamic approaches to the study of models with heterogeneous agents have been already applied in different fields, to our knowledge a complete study of an endogenously varying population of agents has not yet been pursued. As observed in [3], the main problem is given by the fact that with heterogeneous agents the system may be non reversible. We address these problems, we describe the (possible multiple) steady states of the processes involved, we analyze local and global stability and we discuss the similarities and the differences with respect to the literature. Applications are also provided.heterogeneous agent models, intensity-based models, mean field interactions, random utilities, social interactions.

Identity, reputation and social interaction with an application to sequential voting

We analyze binary choices in a random utility model assuming that the agent's preferences are affected by conformism (with respect to the behavior of the society) and coherence (with respect to his identity). We apply the analysis to sequential voting when voters like to win.identity; reputation; social interaction; random utility models; voting system.

Large portfolio losses: A dynamic contagion model

Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the "Central Limit Theorem" useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.Comment: Published in at http://dx.doi.org/10.1214/08-AAP544 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Endogenous equilibria in liquid markets with frictions and boundedly rational agents

In this paper we propose a simple binary mean field game, where N agents may decide whether to trade or not a share of a risky asset in a liquid market. The asset's returns are endogenously determined taking into account demand and transaction costs. Agents' utility depends on the aggregate demand, which is determined by all agents' observed and forecasted actions. Agents are boundedly rational in the sense that they can go wrong choosing their optimal strategy. The explicit dependence on past actions generates endogenous dynamics of the system. We, firstly, study under a rather general setting (risk attitudes, pricing rules and noises) the aggregate demand for the asset, the emerging returns and the structure of the equilibria of the asymptotic game. It is shown that multiple Nash equilibria may arise. Stability conditions are characterized, in particular boom and crash cycles are detected. Then we precisely analyze properties of equilibria under significant examples, performing comparative statics exercises and showing the stabilizing property of exogenous transaction costs.Endogenous dynamics; Nash equilibria; Bounded rationality; Transaction costs; Mean field games; Random utility

Heterogeneous credit portfolios and the dynamics of the aggregate losses

We study the impact of contagion in a network of firms facing credit risk. We describe an intensity based model where the homogeneity assumption is broken by introducing a random environment that makes it possible to take into account the idiosyncratic characteristics of the firms. We shall see that our model goes behind the identification of groups of firms that can be considered basically exchangeable. Despite this heterogeneity assumption our model has the advantage of being totally tractable. The aim is to quantify the losses that a bank may suffer in a large credit portfolio. Relying on a large deviation principle on the trajectory space of the process, we state a suitable law of large number and a central limit theorem useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.Comment: 35 pages, 3 figure

A data-driven and risk-based prudential approach to validate the DDMRP planning and control system

In this paper, we study the single-item dynamic lot-sizing problem in an environment characterized by stochastic demand and lead times. A recent heuristic called Demand Driven MRP, widely implemented using modern ERP systems, proposes an algorithm that is will effectively tackle this problem. Our primary goal is to propose a theoretical foundation for such a heuristic approach. To this aim, we develop an optimization model inspired by the main principles behind the heuristic algorithm. Specifically, controls are of the type (s(t), S(t)) with time varying thresholds that react to short-run real orders; in this respect, control is risk-based and data-driven. We also consider service levels derived as tail risk measures to ensure fulfillment of realized demand with a predetermined probability; in this respect, our approach is prudential. Finally, we use our model as a benchmark to theoretically validate and contextualize the aforementioned heuristic

Polarization and coherence in mean field games driven by private and social utility

We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority (conformism) and the aspiration of sticking with the own type (stubbornness). We also consider a quadratic cost related to the rate at which a change in the state happens: changing opinion may be a costly operation. Depending on the parameters of the model, the game may have more than one Nash equilibrium, even though the corresponding N-player game does not. Moreover, it exhibits a very rich phase diagram, where polarized/unpolarized, coherent/incoherent equilibria may coexist, except for T small, where the equilibrium is always unique. We fully describe such phase diagram in closed form and provide a detailed numerical analysis of the N-player counterpart of the mean field game. In this finite dimensional setting, the equilibrium selected by the population of players is always coherent (favoring the subpopulation whose type is aligned with the initial condition), but it does not necessarily minimize the cost functional. Rather, it seems that, among the coherent ones, the equilibrium prevailing is the one that most benefits the underdog subpopulation forced to change opinion

Polarization and coherence in mean field games driven by private and social utility

We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority (conformism) and the aspiration of sticking with the own type (stubbornness). We also consider a quadratic cost related to the rate at which a change in the state happens: changing opinion may be a costly operation. Depending on the parameters of the model, the game may have more than one Nash equilibrium, even though the corresponding N-player game does not. Moreover, it exhibits a very rich phase diagram, where polarized/unpolarized, coherent/incoherent equilibria may coexist, except for T small, where the equilibrium is always unique. We fully describe such phase diagram in closed form and provide a detailed numerical analysis of the N-player counterpart of the mean field game. In this finite dimensional setting, the equilibrium selected by the population of players is always coherent (favoring the subpopulation whose type is aligned with the initial condition), but it does not necessarily minimize the cost functional. Rather, it seems that, among the coherent ones, the equilibrium prevailing is the one that most benefits the underdog subpopulation forced to change opinion

Hotelling-Bertrand duopoly competition under firrm-specific network e effects

When dealing with consumer choices, social pressure plays a crucial role; also in the context of market competition, the impact of network/social effects has been largely recognized. However, the effects of firm-specific social recognition on market equilibria has never been addressed so far. In this paper, we consider a duopoly where competing firms are differentiated solely by the level of social (or network) externality they induce on consumers’ perceived utility. We fully characterize the subgame perfect Nash equilibria in locations, prices and market shares. Under a scenario of weak social externality, the firms opt for maximal differentiation and the one with the highest social recognition has a relative advantage in terms of profits. Surprisingly, this outcome is not persistent; excessive social recognition may lead to adverse coordination of consumers: the strongest firm can eventually be thrown out of the market with positive probability. This scenario is related to a Pareto inefficient trap of no differentiation