Marco Tolotti

Trade-In Programs in the Context of Technological Innovation with Herding

We study optimal pricing strategies and consequent market shares’ dynamics in a transition from an old and established technology to a new one. We simulate an agent-based model, in which a large population of possible buyers decide whether to adopt or not depending on prices, private signals and herding behavior. The firm, on its part, sets prices to maximize revenues. We show that trade-in programs, in practice comparable to very aggressive discounts, are supported by a rational attitude.

Opinion Dynamics and Stubbornness Via Multi-Population Mean-Field Games

This paper studies opinion dynamics for a set of heterogeneous populations of individuals pursuing two conflicting goals: to seek consensus and to be coherent with their initial opinions. The multi-population game under investigation is characterized by (i) rational agents who behave strategically, (ii) heterogeneous populations, and (iii) opinions evolving in response to local interactions. The main contribution of this paper is to encompass all of these aspects under the unified framework of mean-field game theory. We show that, assuming initial Gaussian density functions and affine control policies, the Fokker–Planck–Kolmogorov equation preserves Gaussianity over time. This fact is then used to explicitly derive expressions for the optimal control strategies when the players are myopic. We then explore consensus formation depending on the stubbornness of the involved populations: We identify conditions that lead to some elementary patterns, such as consensus, polarization, or plurality of opinions. Finally, under the baseline example of the presence of a stubborn population and a most gregarious one, we study the behavior of the model with a finite number of players, describing the dynamics of the average opinion, which is now a stochastic process. We also provide numerical simulations to show how the parameters impact the equilibrium formation.

Strategic Interaction in Interacting Particle Systems

In the last decades, models inspired by statistical mechanics have been vastly used in the context of social sciences to model the behavior of interacting economic actors. In particular, parallel updating models such as Probabilistic Cellular Automata have been proved to be very useful to represent rational agents aiming at maximize their utility in the presence of social externalities. What PCA do not account for is strategic interaction, i.e., the fact that, when deciding, agents forecast the action of other agents. In this contribution, we compare models that differ in the presence of strategic interaction and memory of past actions. We will show that the emergent equilibria can be very different: Fixed points, cycles of period 2, and chaotic behavior may appear and, possibly, coexist for some values of the parameters, of the model.

Optimality of a Two-Tier Rate Structure for a Transaction Tax in an Artificial Market

In this paper we discuss the effects of a Transaction Tax on an artificial market with varying liquidity where a large number of agents can trade a share of a risky asset. A market maker is in charge to optimally set the level of taxation in order to obtain a desired mixture of activity and volatility. We show that, depending on the liquidity of the market, two possible regimes of optimal taxation emerge: a non-negligible level of taxation for highly liquid markets and low (close to zero) levels of taxation for low liquidity markets. This outcome resembles the two-tier rate structure discussed by Spahn in his famous contributions (see [1]).

MEASURING BRAND AWARENESS IN A RANDOM UTILITY MODEL

Brand awareness is recognized to be an important determinant in shaping the success of durables [13, 16], yet it is very difficult to be quantified. This is exactly the main goal of this paper: propose a suitable model where brand awareness of two competing firms is modeled and, eventually, estimated. To this aim, we build a random utility model for a duopoly where each competitor is characterized by different pricing strategies and brand awareness. As a result, different levels of market shares will emerge at the equilibrium. As a case study, we calibrate the model with real data from the smartphone industry obtaining an estimate of the value of the brand awareness of two leading brands.

How the Innovation Diffusion Models from the Past can Help us to Explain Marketing in the New Media Era

Even if the rhetoric of the Internet and the new digital media seems to have radically changed our technological environment, historical recurrences are relevant tools in order to analyze the future marketing. We propose a new multi-stage model able to bridge two different approaches, namely the adoption models a la Bass and the recent line of research concerning agent-based innovation diffusion models. Our technology allows us to find a closed form equation for awareness and adoption, taking into account heterogeneous population.

OPTIMAL POLICIES IN TWO-STEP BINARY GAMES UNDER SOCIAL PRESSURE AND LIMITED RESOURCES

In this paper, we propose a model where binary games with many players are implemented at two subsequent dates. An external authority sets incentives to maximize the gain deriving from the project. We show that the interplay between the optimal participation shares at the two subsequent dates makes the optimal strategy nontrivial and, to some extent, unexpected. As an application, in the context of an insurgence muting into an armed rebellion, we study the emergence of escalation effects when many actors interact taking into account social recognition.