We study the properties of Braess's paradox in the context of the model of congestion games with flow over time introduced by Koch and Skutella. We compare them to the well known properties of Braess's paradox for Wardrop's model of games with static flows. We show that there are networks which do not admit Braess's paradox in Wardrop's model, but which admit it in the model with flow over time. Moreover, there is a topology that admits a much more severe Braess's ratio for this model. Further, despite its symmetry for games with static flow, we show that Braess's paradox is not symmetric for flows over time. We illustrate that there are network topologies which exhibit Braess's paradox, but for which the transpose does not. Finally, we conjecture a necessary and sufficient condition of existence of Braess's paradox in a network, and prove the condition of existence of the paradox either in the network or in its transpose.
Internet and graphs are very much related. The graphical structure of internet has been studied extensively to provide efficient solutions to routing and other problems. But most of these studies assume a central authority which controls and manages the internet. In the recent years game theoretic models have been proposed which do not require a central authority and the users are assumed to be routing their flows selfishly. The existence of Nash Equilibria, congestion and the amount of inefficiency caused by this selfish routing is a major concern in this field. A type of paradox in the selfi…
The classical network configuration introduced by Braess in 1968 is of fundamental significance because Valiant and Roughgarden showed in 2006 that `the "global" behaviour of an equilibrium flow in a large random network is similar to that in Braess' original four-node example'. In this paper, a natural generalisation of Braess' network is introduced and conditions for the occurrence of Braess' paradox are formulated for the generalised network. The Braess' paradox has been studied mainly in the context of the classical problem introduced by Braess and his colleagues, assuming a certain type o…
The famous Braess paradox describes the following phenomenon: It might happen that the improvement of resources, like building a new street within a congested network, may in fact lead to larger costs for the players in an equilibrium. In this paper we consider general nonatomic congestion games and give a characterization of the maximal combinatorial property of strategy spaces for which Braess paradox does not occur. In a nutshell, bases of matroids are exactly this maximal structure. We prove our characterization by two novel sensitivity results for convex separable optimization problems ov…
To systematically study the implications of additional information about routes provided to certain users (e.g., via GPS-based route guidance systems), we introduce a new class of congestion games in which users have differing information sets about the available edges and can only use routes consisting of edges in their information set. After defining the notion of Information Constrained Wardrop Equilibrium (ICWE) for this class of congestion games and studying its basic properties, we turn to our main focus: whether additional information can be harmful (in the sense of generating greater e…
When comparing new wireless technologies, it is common to consider the effect that they have on the capacity of the network (defined as the maximum number of simultaneously satisfiable links). For example, it has been shown that giving receivers the ability to do interference cancellation, or allowing transmitters to use power control, never decreases the capacity and can in certain cases increase it by $Ω(\log (Δ\cdot P_{\max}))$, where $Δ$ is the ratio of the longest link length to the smallest transmitter-receiver distance and $P_{\max}$ is the maximum transmission power. But there is no re…
The Nash equilibrium point of the transmission probabilities in a slotted ALOHA system with selfish nodes is analyzed. The system consists of a finite number of heterogeneous nodes, each trying to minimize its average transmission probability (or power investment) selfishly while meeting its average throughput demand over the shared wireless channel to a common base station (BS). We use a game-theoretic approach to analyze the network under two reception models: one is called power capture, the other is called signal to interference plus noise ratio (SINR) capture. It is shown that, in some si…
The Braess paradox is a counter-intuitive phenomenon whereby adding roads to a network results in higher travel time at equilibrium. In this paper we present an algorithm to detect the occurrence of this paradox in real-world networks with the help of an improved graph representation accounting for queues. The addition of queues to the network representation enables a closer match with real data. Moreover, we search for routes causing this phenomenon ("Braess routes") rather than links, and advocate removing such routes virtually from navigation systems so that the associated links can continu…
The well-known Braess paradox in congestion games states that adding an additional road to a transportation network may increase the total travel time, and consequently decrease the overall efficiency. Motivated by this, this paper presents a paradox in a similar spirit emerging from another distributed resource allocation game on networks, namely the power allocation game between countries developed in \cite{allocation}. The paradox is that by having additional friends may actually decrease a country's total welfare in equilibrium. Conditions for this paradox to occur as well as some price of…
In routing games, the network performance at equilibrium can be significantly improved if we remove some edges from the network. This counterintuitive fact, widely known as Braess's paradox, gives rise to the (selfish) network design problem, where we seek to recognize routing games suffering from the paradox, and to improve the equilibrium performance by edge removal. In this work, we investigate the computational complexity and the approximability of the network design problem for non-atomic bottleneck routing games, where the individual cost of each player is the bottleneck cost of her path…
We propose a model of discrete time dynamic congestion games with atomic players and a single source-destination pair. The latencies of edges are composed by free-flow transit times and possible queuing time due to capacity constraints. We give a precise description of the dynamics induced by the individual strategies of players and of the corresponding costs, either when the traffic is controlled by a planner, or when players act selfishly. In parallel networks, optimal and equilibrium behavior eventually coincides, but the selfish behavior of the first players has consequences that cannot be…
We seek to understand when heterogeneity in user preferences yields improved outcomes in terms of overall cost. That this might be hoped for is based on the common belief that diversity is advantageous in many settings. We investigate this in the context of routing. Our main result is a sharp characterization of the network settings in which diversity always helps, versus those in which it is sometimes harmful. Specifically, we consider routing games, where diversity arises in the way that users trade-off two criteria (such as time and money, or, in the case of stochastic delays, expectation a…
Recently, Apt and Markakis introduced a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives (products). To analyze these networks we introduce social network games in which product adoption is obligatory. We show that when the underlying graph is a simple cycle, there is a polynomial time algorithm allowing us to determine whether the game has a Nash equilibrium. In contrast, in the arbitrary case this problem is NP-complete. We also show that the problem of determining whether the gam…
We study traffic networks with multiple origin-destination pairs, relaxing the simplifying assumption of agents having complete knowledge of the network structure. We identify a ubiquitous class of networks, i.e., rings, for which we can safely increase the agents' knowledge without affecting their own overall performance -- known as immunity to Informational Braess' Paradox -- closing a gap in the literature. We also extend our performance measure to include the welfare of all agents, showing that under this measure IBP is a widespread phenomenon and no network is immune to it.
We model the interaction of several radio devices aiming to obtain wireless connectivity by using a set of base stations (BS) as a non-cooperative game. Each radio device aims to maximize its own spectral efficiency (SE) in two different scenarios: First, we let each player to use a unique BS (BS selection) and second, we let them to simultaneously use several BSs (BS Sharing). In both cases, we show that the resulting game is an exact potential game. We found that the BS selection game posses multiple Nash equilibria (NE) while the BS sharing game posses a unique one. We provide fully decentr…
Flows over time enable a mathematical modeling of traffic that changes as time progresses. In order to evaluate these dynamic flows from a game theoretical perspective we consider the price of anarchy (PoA). In this paper we study the impact of spillback effects on the PoA, which turn out to be substantial. It is known that, in general, the PoA is unbounded in the spillback setting. We extend this by showing that it is still unbounded even when considering networks with unit edge capacities and that the Braess ratio can be arbitrarily large. In contrast to that, we show that on a fixed network…
Traffic congestion games abstract away from the costs of junctions in transport networks, yet, in urban environments, these often impact journey times significantly. In this paper we equip congestion games with traffic lights, modelled as junction-based waiting cycles, therefore enabling more realistic route planning strategies. Using the SUMO simulator, we show that our modelling choices coincide with realistic routing behaviours, in particular, that drivers' decisions about route choices are based on the proportion of red light time for their direction of travel. Drawing upon the experimenta…
The fast-growing market of autonomous vehicles, unmanned aerial vehicles, and fleets in general necessitates the design of smart and automatic navigation systems considering the stochastic latency along different paths in the traffic network. The longstanding shortest path problem in a deterministic network, whose counterpart in a congestion game setting is Wardrop equilibrium, has been studied extensively, but it is well known that finding the notion of an optimal path is challenging in a traffic network with stochastic arc delays. In this work, we propose three classes of risk-averse equilib…
In this paper, we study the decentralized parallel multiple access channel (MAC) when transmitters selfishly maximize their individual spectral efficiency by selecting a single channel to transmit. More specifically, we investigate the set of Nash equilibria (NE) of decentralized networks comprising several transmitters communicating with a single receiver that implements single user decoding. This scenario is modeled as a one-shot game where the players (the transmitters) have discrete action sets (the channels). We show that the corresponding game has always at least one NE in pure strategie…
We consider a market in which capacity-constrained generators compete in scalar-parameterized supply functions to serve an inelastic demand spread throughout a transmission constrained power network. The market clears according to a locational marginal pricing mechanism, in which the independent system operator (ISO) determines the generators' production quantities to minimize the revealed cost of meeting demand, while ensuring that network transmission and generator capacity constraints are met. Under the stylizing assumption that both the ISO and generators choose their strategies simultaneo…
A decentralized network of cognitive and non-cognitive transmitters where each transmitter aims at maximizing his energy-efficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their non-cognitive counterparts and the former have a cost for sensing. The Stackelberg equilibrium analysis of this $2-$level hierarchical game is conducted, which allows us to better understand the effects of cognition on energy-efficiency. In particular, it is proven that the network energy-efficiency is maximized when only a given fraction of terminals are cognitiv…
