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.Comment: Accepted for publication in Games and Economic Behavior, 201

On the Existence of Pure Strategy Nash Equilibria in Integer-Splittable Weighted Congestion Games

We study the existence of pure strategy Nash equilibria (PSNE) in integer–splittable weighted congestion games (ISWCGs), where agents can strategically assign different amounts of demand to different resources, but must distribute this demand in fixed-size parts. Such scenarios arise in a wide range of application domains, including job scheduling and network routing, where agents have to allocate multiple tasks and can assign a number of tasks to a particular selected resource. Specifically, in an ISWCG, an agent has a certain total demand (aka weight) that it needs to satisfy, and can do so by requesting one or more integer units of each resource from an element of a given collection of feasible subsets. Each resource is associated with a unit–cost function of its level of congestion; as such, the cost to an agent for using a particular resource is the product of the resource unit–cost and the number of units the agent requests.While general ISWCGs do not admit PSNE [(Rosenthal, 1973b)], the restricted subclass of these games with linear unit–cost functions has been shown to possess a potential function [(Meyers, 2006)], and hence, PSNE. However, the linearity of costs may not be necessary for the existence of equilibria in pure strategies. Thus, in this paper we prove that PSNE always exist for a larger class of convex and monotonically increasing unit–costs. On the other hand, our result is accompanied by a limiting assumption on the structure of agents’ strategy sets: specifically, each agent is associated with its set of accessible resources, and can distribute its demand across any subset of these resources.Importantly, we show that neither monotonicity nor convexity on its own guarantees this result. Moreover, we give a counterexample with monotone and semi–convex cost functions, thus distinguishing ISWCGs from the class of infinitely–splittable congestion games for which the conditions of monotonicity and semi–convexity have been shown to be sufficient for PSNE existence [(Rosen, 1965)]. Furthermore, we demonstrate that the finite improvement path property (FIP) does not hold for convex increasing ISWCGs. Thus, in contrast to the case with linear costs, a potential function argument cannot be used to prove our result. Instead, we provide a procedure that converges to an equilibrium from an arbitrary initial strategy profile, and in doing so show that ISWCGs with convex increasing unit–cost functions are weakly acyclic

Different Policy Objectives of the Road Pricing Problem – a Game Theory Approach

Using game theory we investigate a new approach to formulate and solve optimal tolls with a focus on different policy objectives of the road authority. The aim is to gain more insight into determining optimal tolls as well as into the behavior of users after tolls have been imposed on the network. The problem of determining optimal tolls is stated and defined using utility maximization theory, including elastic demand on the travelers’ side and different objectives for the road authority. Game theory notions are adopted regarding different games and players, rules and outcomes of the games played between travelers on the one hand and the road authority on the other. Different game concepts (Cournot, Stackelberg and monopoly game) are mathematically formulated and the relationship between players, their payoff functions and rules of the games are defined for very simplistic cases. The games are solved for different scenarios and different objectives for the road authority, using the Nash equilibrium concept. Using the Stackelberg game concept as being most realistic for road pricing, a few experiments are presented illustrating the optimal toll design problem subject to different pricing policies considering different objectives of the road authority. Results show different outcomes both in terms of optimal tolls as well as in payoffs for travelers. There exist multiple optimal solutions and objective function may have a non- continuous shape. The main contribution is the two-level separation between of the users from the road authority in terms of their objectives and influences.

A decentralized approach for self-coexistence among heterogeneous networks in TVWS

IEEE This paper focuses on coexistence and self- coexistence challenges between secondary heterogeneous wireless networks/users sharing TV Whitespace spectrum. The coexistence problems arise from having several primary and secondary networks of different technologies cohabiting the same licensed spectrum simultaneously. The self- coexistence problems arise from many secondary systems /users coexisting at the same place while using identical or different technologies. In particular, fair distribution of available spectrum becomes a serious issue. In this work we use a game theoretic approach to model the self-coexistence problem as a competitive game between secondary networks. We show that our game belongs to the class of congestion-averse games which are known to posses pure Nash Equilibria. This leads us to a decentralized approach for spectrum sharing among systems with different PHY/MAC characteristics. We show that our proposal outperforms other centralized algorithms in terms of user fairness and per-user theoretical data rates

Traveller Behaviour: Decision making in an unpredictable world

This paper discusses the nature and consequences of uncertainty in transport systems. Drawing on work from a number of fields, it addresses travellers’ abilities to predict variable phenomena, their perception of uncertainty, their attitude to risk and the various strategies they might adopt in response to uncertainty. It is argued that despite the increased interest in the representation of uncertainty in transport systems, most models treat uncertainty as a purely statistical issue and ignore the psychological aspects of response to uncertainty. The principle theories and models currently used to predict travellers’ response to uncertainty are presented and number of alternative modelling approaches are outlined. It is argued that the current generation of predictive models do not provide an adequate basis for forecasting response to changes in the degree of uncertainty or for predicting the likely effect of providing additional information. A number of alternative modelling approaches are identified to deal with travellers’ acquisition of information, the definition of their choice set and their choice between the available options. The use of heuristic approaches is recommended as an alternative to more conventional probabilistic methods

A Game-theory Analysis of Charging Stations Selection by EV Drivers

We address the problem of Electric Vehicle (EV) drivers' assistance through Intelligent Transportation System (ITS). Drivers of EVs that are low in battery may ask a navigation service for advice on which charging station to use and which route to take. A rational driver will follow the received advice, provided there is no better choice i.e., in game-theory terms, if such advice corresponds to a Nash-equilibrium strategy. Thus, we model the problem as a game: first we propose a congestion game, then a game with congestion-averse utilities, both admitting at least one pure-strategy Nash equilibrium. The former represents a practical scenario with a high level of realism, although at a high computational price. The latter neglects some features of the real-world scenario but it exhibits very low complexity, and is shown to provide results that, on average, differ by 16% from those obtained with the former approach. Furthermore, when drivers value the trip time most, the average per-EV performance yielded by the Nash equilibria and the one attained by solving a centralized optimization problem that minimizes the EV trip time differ by 15% at most. This is an important result, as minimizing this quantity implies reduced road traffic congestion and energy consumption, as well as higher user satisfaction