A utility-based analysis of equilibria in multi-objective normal form games

Example application domains include urban and air traffic control (Mannion et al., 2016a; Yliniemi et al., 2015), autonomous vehicles (R adulescu et al., 2018; Talpert et al., 2019) and energy systems (Walraven and Spaan, 2016; Mannion et al., 2016b; Reymond et al., 2018). Although many such problems feature multiple conflicting objectives to optimise, most MAS research focuses on agents maximising their return w.r.t. a single objective. By contrast, in multi-objective multi-agent systems (MOMAS), agents explicitly consider the possible tradeoffs between conflicting objective functions. Agents in a MOMAS receive vector-valued payoffs for their actions, where each component of a payoff vector represents the performance on a different objective. Following the utility-based approach (Roijers et al., 2013), we assume that each agent has a utility function which maps vector-valued payoffs to scalar utility values. Compromises between competing objectives are then considered on the the basis of the utility that these tradeoffs have for the users of a MOMAS. The utility-based approach naturally leads to two different optimisation criteria for agents in a MOMAS: expected scalarised returns (ESR) and scalarised expected returns (SER). To date, the differences between the SER and ESR approaches have received little attention in multi-agent settings, despite having received some attention in single-agent settings (see e.g.