INTERVENTIONS AND MECHANISM DESIGN IN PUBLIC GOOD NETWORKS
Gruppi di ricerca Analisi e controllo di sistemi dinamici
Descrizione Public good problems are quite common in the society. Individuals and economic organizations commonly purchase goods whose benefits are shared with others. When a firm provides training for its employees, benefits accrue not only to the firm itself, but to the employees and their future employers. If a family renovates their façade, they provide a nicer view for their neighbors. This class of goods, characterized by the inability of the funder to restrict benefits to others, are referred to as public goods. In economics, public good situations are go-to examples of how individually rational action may lead to outcomes that are collectively irrational; when agents disregard the benefits that their actions confer on others, the resulting outcomes are suboptimal not only for the group as an entity, but for each individual agent. A large number of interventions have been put forward to alleviate this failure of cooperation, often based on rewarding agents that take action to benefit others, or creating structures for enforceable agreements.
Network modeling and game theory have been proposed as a tool to understand public goods whose benefits are local to some social or geographical environment. We talk about network games when the strategic interactions among players are described by a graph so that each player only interacts with its neighboring players. In particular, public good games model situations where players exert some costly effort, and benefit from all effort exerted in their neighborhood [1,2]. E.g., in public good games with binary actions, players have to choose between action 1 and action 0. The former is costy and whenever a player undertakes action 1, it automatically gives a direct benefit to its neighbors. For this reason, it is no longer convenient for a player to play 1 when some of its 'friends' are already playing it. Such games also model plenty of interesting socio-economic phenomena: for instance action 1 could correspond to buying an item that can be easily lended (e.g a book, a tool, a subscription to a movie streaming service) or to become depositary of some knowledge or some capability that can be useful to others (e.g. emergency protocols).
Several optimal intervention problems can be formulated in this context. An external planner may want to push the system towards:
- a Nash equilibrium where the number of active players (namely playing action 1) is minimum thus optimizing the global social cost;
- a Nash equilibrium where the number of active players is instead maximum thus optimizing the spread of a certain item;
- a configuration that is not a Nash equilibrium in the original graph and that exhibits certain resilience properties (for instance every player has interaction with at least two active players).
The way the external planner can possibly control the system to reach such goals are various. As in the previous case, we can imagine a setting where certain nodes are, by authority, forced to a certain state. More interestingly, we can consider a setting where the utility functions are altered adding an exogenous term that can model incentives that the planner can give to certain players. Initial studies in this sense are [3,4]. The way exactly to formulate the problem will here be part of the thesis project.
 Y. Bramoullé and R. Kranton, "Public goods in networks," Journal of Economic Theory, 135, pp. 478-494, 2007.
 N. Allouch, "On the private provision of public goods on networks,” Journal of Economic Theory, 157, pp. 527-552, 2015.
 T. Grinshpoun A. Meisels V. Levit, and Z. Komarovsky, "Incentive-based search for efficient equilibria of the public goods game", Artificial Intelligence, 262, pp. 142-162, 2018.
 D. Kempe, S. Yu, and Y. Vorobeychik,"Inducing equilibria in networked public goods games through network
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