Robust Quantitative Comparative Statics for a Multimarket Paradox

We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, where a positive price shock on a monopoly market may actually reduce the monopolist's profit. We use our approach to quantify for the first time the worst case profit reduction for multimarket oligopolies exposed to arbitrary positive price shocks. For markets with affine price functions and firms with convex cost technologies, we show that the relative profit loss of any firm is at most 25% no matter how many firms compete in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on social welfare. We find tight bounds also for these measures showing that total profit and social welfare decreases by at most 25% and 16.6%, respectively. Finally, we show that in our model, mixed, correlated and coarse correlated equilibria are essentially unique, thus, all our bounds apply to these game solutions as well.Comment: 23 pages, 1 figur

A Study of Truck Platooning Incentives Using a Congestion Game

We introduce an atomic congestion game with two types of agents, cars and trucks, to model the traffic flow on a road over various time intervals of the day. Cars maximize their utility by finding a trade-off between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they pay for using the road. In addition to these terms, the trucks have an incentive for using the road at the same time as their peers because they have platooning capabilities, which allow them to save fuel. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm to validate parts of the modeling assumptions and extract reasonable parameters for the simulations. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategy Nash equilibrium of this game. We perform a comprehensive simulation study to understand the influence of various factors, such as the drivers' value of time and the percentage of the trucks that are equipped with platooning devices, on the properties of the Nash equilibrium.Comment: Updated Introduction; Improved Literature Revie

Robust Methods for Influencing Strategic Behavior

Today's world contains many examples of engineered systems that are tightly coupled with their users and customers. In these settings, the strategic and economic behavior of users and customers can have a significant impact on the performance of the overall system, and it may be desirable for an engineer to devise appropriate methods of incentivizing human behavior to improve system performance. This work seeks to understand the fundamental tradeoffs involved in designing behavior-influencing mechanisms for complex interconnected sociotechnical systems. We study several examples and pose them as problems of game design: a planner chooses appropriate ways to select or modify the utility functions of individual agents in order to promote desired behavior. In social systems these modifications take the form of monetary or other incentives, whereas in multiagent engineered systems the modifications may be algorithmic. Here, we ask questions of sensitivity and robustness: for example, if the quality of information available to the planner changes, how can we quantify the impact of this change on the planner's ability to influence behavior? We propose a simple overarching framework for studying this, and then apply it to three distinct domains: incentives for network routing, distributed control design for multiagent engineered systems, and impersonation attacks in networked systems. We ask the following questions:- What features of a behavior-influencing mechanism directly confer robustness?We show weaknesses of several existing methodologies which use pricing for congestion control in transportation networks. In response to these issues, we propose a universal taxation mechanism which can incentivize optimal routing in transportation networks, requiring no information about network structure or user sensitivities, provided that it can charge sufficiently large prices. This suggests that large prices have more robustness than small ones. We also directly compare flow-varying tolls to fixed tolls, and show that a great deal of robustness can be gained by using a flow-varying approach.- How much information does a planner need to be confident that an incentive mechanism will not inadvertently induce pathological behavior?We show that for simple enough transportation networks (symmetric parallel networks are sufficient), a planner can provably avoid perverse incentives by applying a generalized marginal-cost taxation approach. On the other hand, we show that on general networks, perverse incentives are always a risk unless the incentive mechanism is given some information about network structure.- How can robust games be designed for multiagent coordination?We investigate a setting of multiagent coordination in which autonomous agents may suffer from unplanned communication loss events; the planner's task is to program agents with a policy (analogous to an incentive mechanism) for updating their utility functions in response to such events. We show that even when the nominal game is well-behaved and the communication loss is between weakly-coupled agents, there exists no utility update policy which can prevent arbitrarily-poor states from emerging. We also investigate a setting in which an adversary attempts to influence a distributed system in a robust way; here, by understanding susceptibility to adversarial influence, we hope to inform the design of more robust network systems

Efficiency of Restricted Tolls in Non-atomic Network Routing Games

An effective means to reduce the inefficiency of Nash flows in non- atomic network routing games is to impose tolls on the arcs of the network. It is a well-known fact that marginal cost tolls induce a Nash flow that corresponds to a minimum cost flow. However, despite their effectiveness, marginal cost tolls suffer from two major drawbacks, namely (i) that potentially every arc of the network is tolled, and (ii) that the imposed tolls can be arbitrarily large. In this paper, we study the restricted network toll problem in which tolls can be imposed on the arcs of the network but are restricted to not exceed a predefined threshold for every arc. We show that optimal restricted tolls can be computed efficiently for parallel-arc networks and affine latency functions. This generalizes a previous work on taxing subnetworks to arbitrary restrictions. Our algorithm is quite simple, but relies on solving several convex programs. The key to our approach is a characterization of the flows that are inducible by restricted tolls for single-commodity networks. We also derive bounds on the efficiency of restricted tolls for multi-commodity networks and polynomial latency functions. These bounds are tight even for parallel-arc networks. Our bounds show that restricted tolls can significantly reduce the price of anarchy if the restrictions imposed on arcs with high-degree polynomials are not too severe. Our proof is constructive. We define tolls respecting the given thresholds and show that these tolls lead to a reduced price of anarchy by using a (\lambda,\mu)-smoothness approach

The Anarchy-Stability Tradeoff in Congestion Games

This work focuses on the design of incentive mechanisms in congestion games, a commonly studied model for competitive resource sharing. While the majority of the existing literature on this topic focuses on unilaterally optimizing the worst case performance (i.e., price of anarchy), in this manuscript we investigate whether optimizing for the worst case has consequences on the best case performance (i.e., price of stability). Perhaps surprisingly, our results show that there is a fundamental tradeoff between these two measures of performance. Our main result provides a characterization of this tradeoff in terms of upper and lower bounds on the Pareto frontier between the price of anarchy and the price of stability. Interestingly, we demonstrate that the mechanism that optimizes the price of anarchy inherits a matching price of stability, thereby implying that the best equilibrium is not necessarily any better than the worst equilibrium for such a design choice. Our results also establish that, in several well-studied cases, the unincentivized setting does not even lie on the Pareto frontier, and that any incentive with price of stability equal to 1 incurs a much higher price of anarchy.Comment: 27 pages, 1 figure, 1 tabl

Uncertainty in Multi-Commodity Routing Networks: When does it help?

We study the equilibrium behavior in a multi-commodity selfish routing game with many types of uncertain users where each user over- or under-estimates their congestion costs by a multiplicative factor. Surprisingly, we find that uncertainties in different directions have qualitatively distinct impacts on equilibria. Namely, contrary to the usual notion that uncertainty increases inefficiencies, network congestion actually decreases when users over-estimate their costs. On the other hand, under-estimation of costs leads to increased congestion. We apply these results to urban transportation networks, where drivers have different estimates about the cost of congestion. In light of the dynamic pricing policies aimed at tackling congestion, our results indicate that users' perception of these prices can significantly impact the policy's efficacy, and "caution in the face of uncertainty" leads to favorable network conditions.Comment: Currently under revie

Demand-Independent Optimal Tolls

3sìWardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time. Network tolls are a prominent and popular way to induce an optimum flow in equilibrium. The classical approach to find such tolls is marginal cost pricing which requires the exact knowledge of the demand on the network. In this paper, we investigate under which conditions demand-independent optimum tolls exist that induce the system optimum flow for any travel demand in the network. We give several characterizations for the existence of such tolls both in terms of the cost structure and the network structure of the game. Specifically we show that demand-independent optimum tolls exist if and only if the edge cost functions are shifted monomials as used by the Bureau of Public Roads. Moreover, non-negative demand-independent optimum tolls exist when the network is a directed acyclic multi-graph. Finally, we show that any network with a single origin-destination pair admits demand-independent optimum tolls that, although not necessarily non-negative, satisfy a budget constraint.openopenRiccardo Colini-Baldeschi; Max Klimm; Marco ScarsiniCOLINI BALDESCHI, Riccardo; Klimm, Max; Scarsini, Marc