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Cumulative Prospect Theory (CPT) is a modeling tool widely used in behavioral economics and cognitive psychology that captures subjective decision making of individuals under risk or uncertainty. In this paper, we propose a dynamic pricing strategy for Shared Mobility on Demand Services (SMoDSs) using a passenger behavioral model based on CPT. This dynamic pricing strategy together with dynamic routing via a constrained optimization algorithm that we have developed earlier, provide a complete solution customized for SMoDS of multi-passenger transportation. The basic principles of CPT and the derivation of the passenger behavioral model in the SMoDS context are described in detail. The implications of CPT on dynamic pricing of the SMoDS are delineated using computational experiments involving passenger preferences. These implications include interpretation of the classic fourfold pattern of risk attitudes, strong risk aversion over mixed prospects, and behavioral preferences of self reference. Overall, it is argued that the use of the CPT framework corresponds to a crucial building block in designing socio-technical systems by allowing quantification of subjective decision making under risk or uncertainty that is perceived to be otherwise qualitative.our earlier work in [13] and [5], and offer a solution based on Cumulative Prospect Theory for determining dynamic tariffs.The results of [13] correspond to designing dynamic routes for passengers who request the SMoDS, based upon the requested pickup, drop-off locations, and a pre-specified bound on the walking distance by each passenger. An Alternating Minimization (AltMin) based algorithm was presented that optimizes a relevant time cost. The SMoDS server then offered pickup and drop-off locations as well as walking, waiting and riding times to each passenger derived via the AltMin algorithm. The notion of Transactive Control in [5] was introduced to enable the SMoDS to offer a dynamic tariff to the passenger which can serve as an incentive for the decision on the offer. A passenger behavioral model based on Utility Theory [22] was derived, with the utility of the passenger being a function of both travel times and tariff. The resulting socio-technical model that combines the passenger behavioral model and the optimization of dynamic routes was used to derive a desired probability of acceptance that led to the average estimated waiting time of passengers on the SMoDS platform being regulated around a desired value. The derivation of the actual dynamic tariffs was however not addressed and assumed to be such that the desired probability of acceptance from each passenger was realized.The results mentioned above have two deficiencies. The first is that the passenger behavioral model is significantly more complex than that considered in [5]. Strategic decision making, adjustments based upon framing effect, loss aversion, and probability distortion are several key features related to subjective decision making of individuals when facing uncertainty, which makes classic ...

Travel time in urban centers is a significant contributor to the quality of living of its citizens. Mobility on Demand (MoD) services such as Uber and Lyft have revolutionized the transportation infrastructure, enabling new solutions for passengers. Shared MoD services have shown that a continuum of solutions can be provided between the traditional private transport for an individual and the public mass transit based transport, by making use of the underlying cyber-physical substrate that provides advanced, distributed, and networked computational and communicational support. In this paper, we propose a novel shared mobility service using a dynamic framework. This framework generates a dynamic route for multi-passenger transport, optimized to reduce time costs for both the shuttle and the passengers and is designed using a new concept of a space window. This concept introduces a degree of freedom that helps reduce the cost of the system involved in designing the optimal route. A specific algorithm based on the Alternating Minimization approach is proposed. Its analytical properties are characterized. Detailed computational experiments are carried out to demonstrate the advantages of the proposed approach and are shown to result in an order of magnitude improvement in the computational efficiency with minimal optimality gap when compared to a standard Mixed Integer Quadratically Constrained Programming based algorithm.

This work proposes a dynamic and adversarial resource allocation problem in a graph environment, which is referred to as the dynamic Defender-Attacker Blotto (dDAB) game. A team of defender robots is tasked to ensure numerical advantage at every node in the graph against a team of attacker robots. The engagement is formulated as a discrete-time dynamic game, where the two teams reallocate their robots in sequence and each robot can move at most one hop at each time step. The game terminates with the attacker's victory if any node has more attacker robots than defender robots. Our goal is to identify the necessary and sufficient number of defender robots to guarantee defense. Through a reachability analysis, we first solve the problem for the case where the attacker team stays as a single group. The results are then generalized to the case where the attacker team can freely split and merge into subteams. Crucially, our analysis indicates that there is no incentive for the attacker team to split, which significantly reduces the search space for the attacker's winning strategies and also enables us to design defender counter-strategies using superposition. We also present an efficient numerical algorithm to identify the necessary and sufficient number of defender robots to defend a given graph. Finally, we present illustrative examples to verify the efficacy of the proposed framework.