## 1 Introduction  
Under the pressure of environmental protection and global warming, transportation service providers have evolved from providing dedicated rides to offering shared rides for travelers/customers in the sharing economy era. A variety of shared mobility transport models have appeared in the past decade. For transport policy makers and service providers, an important issue is formulating shared mobility transport models that are accepted by users in order to reduce energy consumption and the emission of greenhouse gases. There are several factors influencing the acceptance of shared mobility transport models [1, 2, 3, 4, 5]. These include economic factors such as cost savings and non-economic factors such as safety and trust. As transportation costs constitute a large part of industry and daily-life expenses, savings on transportation costs provide an important incentive for shared mobility models in smart cities. In a ridesharing system, the ridesharing participantsinclude drivers and passengers. If a driver travels alone without ridesharing, the travel cost will be paid by the driver. Similarly, a passenger traveling alone without ridesharing also has to pay the travel cost by him/herself. Suppose the itineraries of a driver and a set of passengers are spatially and temporarily similar: the driver may share the ride with the set of passengers. If the overall costs of the shared ride are less than the overall travel costs of the driver and the set of passengers, cost savings are achieved. Based on the above reasoning, most studies on ridesharing attempt to maximize the overall cost savings. Therefore, the problem of maximizing coast savings has been extensively studied in the ridesharing literature [6; 7]. Most studies on ridesharing focus on the maximization of the overall savings on transportation costs. However, the maximization of the overall savings on transportation costs may not lead to the satisfaction of users' expectation for cost savings. Ridesharing is attractive for drivers and passengers only if the portion of cost savings allocated to each of them is no lower than their expectations. In this study, to describe drivers' and passengers' expectations of cost savings, we used \"minimal expected cost savings discount\" to refer to the reduction in costs expected by drivers and passengers. If drivers' and passengers' minimal expected cost savings discounts are not met, ridesharing is not attractive. Therefore, ridesharing models must satisfy participants' minimal expected cost savings discounts, as they are directly related to participants' acceptance of and satisfaction with ridesharing. For people to adopt ridesharing as a means to reduce costs, a minimal expected cost savings discount must be offered. There is obviously a gap between the existing studies and the real problems faced by service providers. This calls for the development of a decision model to formulate a ridesharing system that meets users' expectations for cost savings. In this paper, we introduce the concept of the minimal expected cost savings discount and formulate a discount-guaranteed ridesharing model that maximizes the overall cost savings under the constraint that the cost savings discount for users cannot be lower than the minimal expected cost savings discount. As a ridesharing system typically consist of drivers, passengers, and a service provider, it can be modeled as a multi-agent system (MAS) [8; 9]. In a MAS, an agent is a cooperative, autonomous, and intelligent entity working to achieve certain goals. MASs have been applied to a variety of complex problems. By representing drivers, passengers, and the service provider as agents, the MAS paradigm can be used to model a ridesharing system. In this paper, we adopted the MAS concept to model a ridesharing system. Our MAS included driver agents, passenger agents, and a service provider agent. The driver agents and passenger agents submit bids to the system, and the service provider agent must determine the winning bids.