Ashish R. Hota — Page 3

arXiv2016

Fragility of the Commons under Prospect-Theoretic Risk Attitudes

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player's risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.

cs.GT↗

arXiv2015

Multi-Agent Decentralized Network Interdiction Games

In this work, we introduce decentralized network interdiction games, which model the interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on decentralized shortest path interdiction (DSPI) games, where multiple interdictors try to increase the shortest path lengths of their own adversaries, who all attempt to traverse a common network. We first establish results regarding the existence of equilibria for DSPI games under both discrete and continuous interdiction strategies. To compute such an equilibrium, we present a reformulation of the DSPI games, which leads to a generalized Nash equilibrium problem (GNEP) with non-shared constraints. While such a problem is computationally challenging in general, we show that under continuous interdiction actions, a DSPI game can be formulated as a linear complementarity problem and solved by Lemke's algorithm. In addition, we present decentralized heuristic algorithms based on best response dynamics for games under both continuous and discrete interdiction strategies. Finally, we establish theoretical bounds on the worst-case efficiency loss of equilibria in DSPI games, with such loss caused by the lack of coordination among noncooperative interdictors, and use the decentralized algorithms to empirically study the average-case efficiency loss.

math.OC↗