1,324 research outputs found
On Binary Networked Public Goods Game with Altruism
In the classical Binary Networked Public Goods (BNPG) game, a player can
either invest in a public project or decide not to invest. Based on the
decisions of all the players, each player receives a reward as per his/her
utility function. However, classical models of BNPG game do not consider
altruism which players often exhibit and can significantly affect equilibrium
behavior. Yu et al. (2021) extended the classical BNPG game to capture the
altruistic aspect of the players. We, in this paper, first study the problem of
deciding the existence of a Pure Strategy Nash Equilibrium (PSNE) in a BNPG
game with altruism. This problem is already known to be NP-Complete. We
complement this hardness result by showing that the problem admits efficient
algorithms when the input network is either a tree or a complete graph. We
further study the Altruistic Network Modification problem, where the task is to
compute if a target strategy profile can be made a PSNE by adding or deleting a
few edges. This problem is also known to be NP-Complete. We strengthen this
hardness result by exhibiting intractability results even for trees. A perhaps
surprising finding of our work is that the above problem remains NP-Hard even
for bounded degree graphs when the altruism network is undirected but becomes
polynomial-time solvable when the altruism network is directed. We also show
some results on computing an MSNE and some parameterized complexity results. In
summary, our results show that it is much easier to predict how the players in
a BNPG game will behave compared to how the players in a BNPG game can be made
to behave in a desirable way.Comment: 26 page
Solving Graph-based Public Good Games with Tree Search and Imitation Learning
Public goods games represent insightful settings for studying incentives for individual agents to make contributions that, while costly for each of them, benefit the wider society. In this work, we adopt the perspective of a central planner with a global view of a network of self-interested agents and the goal of maximizing some desired property in the context of a best-shot public goods game. Existing algorithms for this known NP-complete problem find solutions that are sub-optimal and cannot optimize for criteria other than social welfare.In order to efficiently solve public goods games, our proposed method directly exploits the correspondence between equilibria and the Maximal Independent Set (mIS) structural property of graphs. In particular, we define a Markov Decision Process which incrementally generates an mIS, and adopt a planning method to search for equilibria, outperforming existing methods. Furthermore, we devise a graph imitation learning technique that uses demonstrations of the search to obtain a graph neural network parametrized policy which quickly generalizes to unseen game instances. Our evaluation results show that this policy is able to reach 99.5\% of the performance of the planning method while being three orders of magnitude faster to evaluate on the largest graphs tested. The methods presented in this work can be applied to a large class of public goods games of potentially high societal impact and more broadly to other graph combinatorial optimization problems
Tight inapproximability of Nash equilibria in public goods games
We study public goods games, a type of game where every player has to decide whether or not to produce a good which is public, i.e., neighboring players can also benefit from it. Specifically, we consider a setting where the good is indivisible and where the neighborhood structure is represented by a directed graph, with the players being the nodes. Papadimitriou and Peng (2023) recently showed that in this setting computing mixed Nash equilibria is PPAD-hard, and that this remains the case even for ε-well-supported approximate equilibria for some sufficiently small constant ε. In this work, we strengthen this inapproximability result by showing that the problem remains PPAD-hard for any non-trivial approximation parameter ε
Statics and dynamics of selfish interactions in distributed service systems
We study a class of games which model the competition among agents to access
some service provided by distributed service units and which exhibit congestion
and frustration phenomena when service units have limited capacity. We propose
a technique, based on the cavity method of statistical physics, to characterize
the full spectrum of Nash equilibria of the game. The analysis reveals a large
variety of equilibria, with very different statistical properties. Natural
selfish dynamics, such as best-response, usually tend to large-utility
equilibria, even though those of smaller utility are exponentially more
numerous. Interestingly, the latter actually can be reached by selecting the
initial conditions of the best-response dynamics close to the saturation limit
of the service unit capacities. We also study a more realistic stochastic
variant of the game by means of a simple and effective approximation of the
average over the random parameters, showing that the properties of the
average-case Nash equilibria are qualitatively similar to the deterministic
ones.Comment: 30 pages, 10 figure
Design and Analysis of Strategic Behavior in Networks
Networks permeate every aspect of our social and professional life.A networked system with strategic individuals can represent a variety of real-world scenarios with socioeconomic origins. In such a system, the individuals\u27 utilities are interdependent---one individual\u27s decision influences the decisions of others and vice versa. In order to gain insights into the system, the highly complicated interactions necessitate some level of abstraction. To capture the otherwise complex interactions, I use a game theoretic model called Networked Public Goods (NPG) game. I develop a computational framework based on NPGs to understand strategic individuals\u27 behavior in networked systems. The framework consists of three components that represent different but complementary angles to the understanding. The first part is learning, which aims to produce quantitative and interpretable models of individuals\u27 behavior. The second part focuses on analyzing the individuals\u27 equilibrium behavior, providing guidance on what a rational individual would do when facing other individuals\u27 strategic behavior. The individuals\u27 equilibrium behavior may not be socially preferable, motivating the third part to investigate designing their behavior through network modifications
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