Risk-Averse Equilibrium Analysis and Computation

An Approximate Solution Method for Large Risk-Averse Markov Decision Processes

Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations. In this paper, we propose and analyze a new method for solving large risk-averse MDPs with hybrid continuous-discrete state spaces and continuous action spaces. The proposed method iteratively improves a bound on the value function using a linearity structure of the MDP. We demonstrate the utility and properties of the method on a portfolio optimization probl…

On-demand or Spot? Selling the cloud to risk-averse customers

In Amazon EC2, cloud resources are sold through a combination of an on-demand market, in which customers buy resources at a fixed price, and a spot market, in which customers bid for an uncertain supply of excess resources. Standard market environments suggest that an optimal design uses just one type of market. We show the prevalence of a dual market system can be explained by heterogeneous risk attitudes of customers. In our stylized model, we consider unit demand risk-averse bidders. We show the model admits a unique equilibrium, with higher revenue and higher welfare than using only spot m…

Risk-Averse No-Regret Learning in Online Convex Games

We consider an online stochastic game with risk-averse agents whose goal is to learn optimal decisions that minimize the risk of incurring significantly high costs. Specifically, we use the Conditional Value at Risk (CVaR) as a risk measure that the agents can estimate using bandit feedback in the form of the cost values of only their selected actions. Since the distributions of the cost functions depend on the actions of all agents that are generally unobservable, they are themselves unknown and, therefore, the CVaR values of the costs are difficult to compute. To address this challenge, we p…

Robust Mechanisms for Risk-Averse Sellers

The existing literature on optimal auctions focuses on optimizing the expected revenue of the seller, and is appropriate for risk-neutral sellers. In this paper, we identify good mechanisms for risk-averse sellers. As is standard in the economics literature, we model the risk-aversion of a seller by endowing the seller with a monotone concave utility function. We then seek robust mechanisms that are approximately optimal for all sellers, no matter what their levels of risk-aversion are. We have two main results for multi-unit auctions with unit-demand bidders whose valuations are drawn i.i.d. …

超越名义均衡：风险规避的多群体平均场博弈

Beyond Nominal Equilibria: Risk-Averse Multi-Population Mean-Field Games

本文提出风险规避多群体平均场博弈范式，在模糊集上优化最坏情况奖励，证明均衡存在性与收缩性，并设计风险规避虚拟博弈方案，数值实验验证收敛性。

Mechanisms for Risk Averse Agents, Without Loss

Auctions in which agents' payoffs are random variables have received increased attention in recent years. In particular, recent work in algorithmic mechanism design has produced mechanisms employing internal randomization, partly in response to limitations on deterministic mechanisms imposed by computational complexity. For many of these mechanisms, which are often referred to as truthful-in-expectation, incentive compatibility is contingent on the assumption that agents are risk-neutral. These mechanisms have been criticized on the grounds that this assumption is too strong, because "real" ag…

Asymptotically tight bounds for inefficiency in risk-averse selfish routing

We consider a nonatomic selfish routing model with independent stochastic travel times, represented by mean and variance latency functions for each edge that depend on their flows. In an effort to decouple the effect of risk-averse player preferences from selfish behavior on the degradation of system performance, Nikolova and Stier- Moses [16] defined the concept of the price of risk aversion as the worst-case ratio of the cost of an equilibrium with risk-averse players and that of an equilibrium with risk-neutral users. For risk-averse users who seek to minimize the mean plus variance of trav…

A Zeroth-Order Momentum Method for Risk-Averse Online Convex Games

We consider risk-averse learning in repeated unknown games where the goal of the agents is to minimize their individual risk of incurring significantly high cost. Specifically, the agents use the conditional value at risk (CVaR) as a risk measure and rely on bandit feedback in the form of the cost values of the selected actions at every episode to estimate their CVaR values and update their actions. A major challenge in using bandit feedback to estimate CVaR is that the agents can only access their own cost values, which, however, depend on the actions of all agents. To address this challenge,…

Evaluating Attacker Risk Behavior in an Internet of Things Ecosystem

In cybersecurity, attackers range from brash, unsophisticated script kiddies and cybercriminals to stealthy, patient advanced persistent threats. When modeling these attackers, we can observe that they demonstrate different risk-seeking and risk-averse behaviors. This work explores how an attacker's risk seeking or risk averse behavior affects their operations against detection-optimizing defenders in an Internet of Things ecosystem. Using an evaluation framework which uses real, parametrizable malware, we develop a game that is played by a defender against attackers with a suite of malware th…