Probabilistic Disclosure: Maximisation vs. Minimisation

We consider opacity questions where an observation function provides to an external attacker a view of the states along executions and secret executions are those visiting some state from a fixed subset. Disclosure occurs when the observer can deduce from a finite observation that the execution is secret, the epsilon-disclosure variant corresponding to the execution being secret with probability greater than 1 - epsilon. In a probabilistic and non deterministic setting, where an internal agent can choose between actions, there are two points of view, depending on the status of this agent: the successive choices can either help the attacker trying to disclose the secret, if the system has been corrupted, or they can prevent disclosure as much as possible if these choices are part of the system design. In the former situation, corresponding to a worst case, the disclosure value is the supremum over the strategies of the probability to disclose the secret (maximisation), whereas in the latter case, the disclosure is the infimum (minimisation). We address quantitative problems (comparing the optimal value with a threshold) and qualitative ones (when the threshold is zero or one) related to both forms of disclosure for a fixed or finite horizon. For all problems, we characterise their decidability status and their complexity. We discover a surprising asymmetry: on the one hand optimal strategies may be chosen among deterministic ones in maximisation problems, while it is not the case for minimisation. On the other hand, for the questions addressed here, more minimisation problems than maximisation ones are decidable

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach

Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization and Information Disclosure

This paper examines the problem of how to design incentive-compatible mechanisms in environments in which the agents' private information evolves stochastically over time and in which decisions have to be made in each period. The environments we consider are fairly general in that the agents' types are allowed to evolve in a non-Markov way, decisions are allowed to affect the type distributions and payoffs are not restricted to be separable over time. Our first result is the characterization of a dynamic payoff formula that describes the evolution of the agents' equilibrium payoffs in an incentive-compatible mechanism. The formula summarizes all local first-order conditions taking into account how current information affects the dynamics of expected payoffs. The formula generalizes the familiar envelope condition from static mechanism design: the key difference is that a variation in the current types now impacts payoffs in all subsequent periods both directly and through the effect on the distributions of future types. First, we identify assumptions on the primitive environment that guarantee that our dynamic payoff formula is a necessary condition for incentive compatibility. Next, we specialize this formula to quasi-linear environments and show how it permits one to establish a dynamic "revenue-equivalence" result and to construct a formula for dynamic virtual surplus which is instrumental for the design of optimal mechanisms. We then turn to the characterization of sufficient conditions for incentive compatibility. Lastly, we show how our results can be put to work in a variety of applications that include the design of profit-maximizing dynamic auctions with AR(k) values and the provision of experience goods.dynamic mechanisms, asymmetric information, stochastic processes, incentives

Graph Attention Multi-Agent Fleet Autonomy for Advanced Air Mobility

Autonomous mobility is emerging as a new mode of urban transportation for moving cargo and passengers. However, such fleet coordination schemes face significant challenges in scaling to accommodate fast-growing fleet sizes that vary in their operational range, capacity, and communication capabilities. We introduce the concept of partially observable advanced air mobility games to coordinate a fleet of aerial vehicle agents accounting for their heterogeneity and self-interest inherent to commercial mobility fleets. We propose a novel heterogeneous graph attention-based encoder-decoder (HetGAT Enc-Dec) neural network to construct a generalizable stochastic policy stemming from the inter- and intra-agent relations within the mobility system. We train our policy by leveraging deep multi-agent reinforcement learning, allowing decentralized decision-making for the agents using their local observations. Through extensive experimentation, we show that the fleets operating under the HetGAT Enc-Dec policy outperform other state-of-the-art graph neural network-based policies by achieving the highest fleet reward and fulfillment ratios in an on-demand mobility network.Comment: 12 pages, 12 figures, 3 table