Research interests

Coalitional aggregation of renewable power production

A main issue in  integrating renewable generation (wind, solar, PVs) derives from their inherent volatility. This project builds on the widely accepted idea that when independent and geographically sparse wind farm power producers agree to join coalitions and aggregate their production capacities, they reduce the aggregate volatility and end up bidding less conservatively. 

The problem involves a set of independent wind farm producers, which can form coalitions and submit joint bids. A possible configuration is

illustrated in the figure on the left, where we have two coalitions of wind farms (dotted gray), which supply power to the grid. The grid

consists of buses and transmission lines (solid)

and is managed by the independent system operator (ISO). In return, financial flows run from the ISO to the coalitions (dashed). Each coalition is managed by a cooperative designer

who redistribute the revenues among the members of the coalitions.

This project
 deals with the quantitative analysis of the expected benefits of aggregating wind power production. 
 We provide a constructive method to design fair allocation mechanisms in the case where the expected profit is dynamically changing with time. We investigate the sustainability of the program by showing that the coalitions are stable, namely  no producers has incentives to quit the coalition. We answer the above questions within the area of dynamic coalitional game theory and robust control invariance. Finally, we  corroborate our results with numerical studies based on field data from wind farms in UK

Adaptation and coordination in decentralized organizations 

Organizations where the decision making is centralized incur expensive communication, red tape, and bureaucracy. This is due to the fact that one single decision-maker has to extract informative content from big data sets and coordinate multiple actions. Decentralization is one way to overcome the issues related to centralization. Decentralization in turn implies task specialization, by this meaning the decomposition of the whole project into specic tasks which are assigned to different decision-makers. Decentralization and specialization raise issues about adaptation  and coordination  especially if the organization competes in an environment which is dynamic and uncertain. 

Adaption refers to the ability of the organization to respond to market needs, operational conditionsconsumers' requestsSuch a dynamic and uncertain scenario requires that each decision-maker  continuously adapt its task to new instances and coordinate the changes with the other decision-makers. 

This project deals with the analysis of quantitative models simulating a distributed decision making for manufacturing. The model simulates the partitioning of the whole project into specific tasks and assign them to multiple independent decision-makers. 

Case study. A large software project that cannot be developed by a single engineer. The project is decomposed in multiple modules (tasks) and each module is assigned to a different team. If the software project involves the development of a proprietary operating system, we will have a module focusing on the process manager, another module dealing with the network access and so forth. On the one hand, each module needs to be designed based on the  specific needs of the client. On the other hand, all modules will need to be assembled in coherent whole.

Distributed smart manufacturing

Industry  4.0 and the Internet of Things shift the focus from centralized to decentralized and smart manufacturing,  and pose new challenges on i) data acquisition (what data to acquire), ii) data scraping (what data are available on the web), and iii) data analytics (what is the informative content which we can extract from the data).

This project simulates different and parallel manufacturing tasks characterized by different levels of adaptation and coordination, and different communication topologies especially when the industry operates in a changing environment.  In particular, decision-makers are assigned tasks and choose the level of adaptation to a time-varying environment

and the level of coordination among the specialized tasks. A higher level of adaptation implies that the system enables the workers with higher flexibility to adapt their tasks to local information. A higher level of coordination entails an increase in the communication between

workers. Affecting the performance of the organization are two conflicting factors: ii) how well

each task is adapted to specific market conditions, operational conditions, and consumers'

needs and ii) how well all tasks are coordinated with each other.

The figure above [Tarraf and Bauso 2014] displays an assembling process with four final products. The final product AAAB contains three units of A and one of B. Similarly, for AAB, ABB, and ABBB. Each final product is a node. The controlled flows 𝑢  are associated to the arcs (solid). The uncontrolled flows 𝑤  (dashed) are the uncertain demand. Each node is a task, and the controlled flows have to be chosen in coordination between the task managers. The managers adapt to the fluctuating and uncertain demand while guaranteeing a certain level of coordination.

Evolutionary game theory models for the Warburg Effect in cancer cells

The Warburg effect is an aerobic glycolysis, loss of glucose, in the presence of oxigen, which produces ATP (energy). Some scientists conjecture that such an effect is a metabolic strategy used by cancer cells to meet large fluctuations in energy demand observed in tumor environments.

This project deals with the development of cell models describing both the efficient but slow responding aerobic metabolism and the inefficient but fast responding glycolytic metabolism.  

The model simulates different tradeoffs between efficiency and speed of metabolic pahtways for the upregulation of ATP. We answer the above questions in the context of evolutionary game theory to shed light on the Darwinian dynamics and the “survival of the fittest” rules governing carcinogenesis. 

This project originates from a brainstorm with Dr. Katerina Stankova (Maastricht University), expert of Systems and Evolutionary Biology (

Robust Control of Production/Distribution/Transportation Networks

Production networks  describe production processes and/or activities necessary to turn raw materials into intermediate products and eventually into final products. Thus, the nodes of the networks represent raw materials and intermediate/final products. The buffer at each single node i models the amount of material or product of type “i” stored or produced up to the current time. Hyperarcs describe the materials or products consumed (tail nodes) and produced (head nodes) in each activity or process. So, at a given time, the flow on a hyperarc defines the amount of materials and products consumed and produced. Only part of the flows are controlled by the supplier, whereas the rest of the flows are controlled by the market and as such they are uncertain to the supplier and subject to fluctuations. At each production stage, the supplier establishes which processes or activities to execute and the quantity of materials/products involved and this just by selecting a specific flow on each controlled hyperarc. A high level of stored materials/products usually induces high storage costs whereas a low level may cause shortages in case of unforseen demand. So, typically the aim of the supplier is to stabilize the amount of stored materials and products to a fixed target level. The above figure depicts a case study with 6 products/nodes, 12 processes (variable u's) and 3 demand flows (variables w's).

The figure on the right depicts an hypothetical time plot of a buffer level after a robust stabilizing control policy is implemented. The level of the buffer is steered to zero within a tolerance epsilon after some time T.
Challenges include the possibility of i) decentralizing  controls, i.e., arcs belong to different owners (decision-makers) who select the corresponding flow; ii) distributing information (local information), i.e., the flow on a single arc depends on the buffer levels of corresponding nodes; iii) distributing objectives (local objective functions), i.e., each Decision Maker is assigned an objective which he/she will try to maximize or minimize.   
The same approach can be used to study distribution networks like power grids, and transportation networks. 

Social Networks and Consensus

In social networks one often observes herd behaviors or crowd-seeking attitudes in that certain individuals or social groups tend to mimic the behavior of other individuals or social groups. Behaviors may involve political opinions (left, right), and or social interactions  like aggressive/non-aggressive or cooperative/non-cooperative. 
Mimicry can also be observed in financial markets under the name of ``stock market bubbles'', which sees investors to emulate other investors. Crowd-seeking or crowd-averse attitudes are the consequence of the interactions among the agents and  can be described through so-called averaging processes and algorithms.
In the above figure, nodes corresponds to individuals i=1…n. The individual i is characterized by behavior/state x_i that evolves depending on his/her neighbors' behaviors. Here links connect neighbors. 

Challenges include convergence analysis under the influence of external manipulators, malicious agents, stubborn agents, or zealots. 

The figure on the right depicts a typical consensus dynamics where, all states converge to a unique value, consensus or agreement value, and this despite of the influence of malicious nodes 

(see peaks in the plot).

Mean field games in engineering, economics, and social sciences

n everyday decision making, an individual makes decisions on the basis of the observed population behavior around him. At the same time, if one extends this to all individuals of a population then one observes a consequent time evolution of the population behavior.

We observe this, for instance, in agricultural markets, where a large number of independent producers choose an optimal production rate based on an aggregate description of how much the competitors will produce (total  produced quantity of a given product). Each producer tries to maximize the production rate when the forecasted demand is high, and total produced quantity by others is low so that the sale price can be increased.

Another application domain is "herd behaviors" in social networks. This is linked to imitation phenomena in mass behaviors, which explains current tendencies in society, fashion, or markets.   

Mean field games capture this mutual interaction between a population and its individuals. A new equilibrium concept called mean field equilibrium replaces the classical Nash equilibrium in game theory. In a mean field equilibrium each individual responds optimally to the population behavior. In other words, no individuals have incentives to deviate from their current strategies. 

The figure shows the mean field and its time evolution of the stocks of a population of producers. The x-axis represents stock levels and the y-axis the density mass of producers with that stock. Initial stocks are extracted from a Gaussian distribution with mean 70 (the blue bell) and increasing variance (from top to bottom). While all producers produce at their own rate, the mean stock decreases as resources are exhaustible. If producers with higher stocks produce at a higher rate then the variance of the mean field decreases with time until all stocks reach zero. Challenges include the analysisand computation based on fixed point techniques of mean field equilibria, with or without external disturbances (robust mean field equilibria). 

Coalitional  games with transferable utilities (TU games)

A paradigmatic problem in communication networks is "rate allocation in a multiple access channel". Here, one can observe a bargaining process that involves the users who aim at obtaining a fair allocation of the total transmission rate available. If a user, or coalition of users receives an unfair allocation, it will adopt a selfish behavior thus reducing the efficiency of the global network. Other applications arise in receivers and transmitters cooperation, or packet forwarding ad hoc networks.

Bargaining among competing players or coalitions arise in many other areas, like politics, supply chains, social science. In supply chains, retailers may benefit from coordinating (coalizing) with other retailers in order to place joint orders to the warehouse thus reducing transportation costs. 

In all the above situations, one has a number of players, a set of possible coalitions, and for each coalition a value representing the total reward of the coalition. The value of the coalition captures the benefit of "acting together", of pursuing "joint strategies". 

Once a coalition is formed, the member need to agree on the way how to divide the reward of the coalition among them. This is known as (reward) allocation policy of the coalition. 

A main issue concerns the stability of allocations. In other words, one wishes to investigate the existence of allocations policies that make the coalition stable, i.e., no sub-coalitions would benefit from splitting from the grand-coalition.  

The above figure depicts the time plot of the allocation vectors corresponding to the 3 players/retailers in a supply chain case study. Eventually all retailers agree to divide the reward 10 K EUR deriving from joint reorders (in 1 year) according to: 7 K EUR to player 1, 3 K EUR to player 2, and 0 K EUR to player 3. For the case study, and corresponding coalition values this allocation vector was shown to be stable.    

Challenges include the stability of allocations in dynamic environments where coalitions values vary with time according to exogenous or endogenous factors. 

Approachability/Attainability in repeated games with vector payoffs

Consider a scenario where  an  employee  happen to negotiate with his/her employer on a number of non-interchangeable factors, like salary, annual leave, career opportunities etc. Assume that this negotiation occurs periodically every time the employment contract expires. 

We can look at this as a two player game (player 1 is the employee and players 2 the employer), where the result of the interactions between the two players at each stage is a payoff vector, each payoff component representing one of the above factors.

Then, the employee may wish to look at strategies that on the long run provide him with an acceptable/desirable cumulative or average payoff vector. 

Approachability and attainability are game theoretic modeling frameworks that capture the strategic thinking in repeated interactions  between two players. 

A main question involves the existence and computation of strategies for Player 1 such that the payoff vectors may converge arbitrarily close to a pre-defined set, called approachable/attainable set, whatever the opponent does. 

Challenges include cases where the approachable/attainable set varies with time following exogenous or endogenous rules; the payoff is discounted (1 EUR today is better than 1 EUR tomorrow);

the interaction involves a population of players; knowledge about the current payoff is imperfect. 

The figure on the right shows an inventory applications where a single retailer controls the flows f1, f2, and f3  of goods to and from two different stores (nodes)  in order to  stabilize  the stock of the goods in the two  stores and this despite of the influence of an uncertain demand w1 and w2. 

 shows that 
by selecting an opportune strategy for the flows f1, f2, and f3 (black arrows) the retailer succeeds in stabilizing the stock levels (blue and green rectangles)  arbitrarily close to pre-assigned values (top-right) in the presence of uncertain demand (red arrows).

In this youtube video Eilon (Solan) talks about attainability for the 20th Anniversary of the Center for the Study of Rationality, Jerusalem, 28-30 December 2011.
Pagine secondarie (1): Grantham Project