Economic Games as Estimators

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Validation of cognitive models for collaborative hybrid systems with discrete human input

We present a method to validate a cognitive model, based on the cognitive architecture ACT-R, in dynamic humanautomation systems with discrete human input. We are inspired by the general problem of K-choice games as a proxy for many decision making applications in dynamical systems. We model the human as a Markovian controller based on gathered experimental data, that is, a non-deterministic control input with known likelihoods of control actions associated with certain configurations of the state-space. We use reachability analysis to predict the outcome of the resulting discrete-time stochastic hybrid system, in which the outcome is defined as a function of the system trajectory. We suggest that the resulting expected outcomes can be used to validate the cognitive model against actual human subject data. We apply our method to a twochoice game in which the human is tasked with maximizing net coverage of a robotic swarm that can operate under rendezvous or deployment dynamics. We validate the corresponding ACTR cognitive model generated with the data from eight human subjects. The novelty of this work is 1) a method to compute expected outcome in a hybrid dynamical system with a Markov chain model of the human's discrete choice, and 2) application of this method to validation of cognitive models with a database of actual human subject data

O-Minimal Hybrid Reachability Games

In this paper, we consider reachability games over general hybrid systems, and distinguish between two possible observation frameworks for those games: either the precise dynamics of the system is seen by the players (this is the perfect observation framework), or only the starting point and the delays are known by the players (this is the partial observation framework). In the first more classical framework, we show that time-abstract bisimulation is not adequate for solving this problem, although it is sufficient in the case of timed automata . That is why we consider an other equivalence, namely the suffix equivalence based on the encoding of trajectories through words. We show that this suffix equivalence is in general a correct abstraction for games. We apply this result to o-minimal hybrid systems, and get decidability and computability results in this framework. For the second framework which assumes a partial observation of the dynamics of the system, we propose another abstraction, called the superword encoding, which is suitable to solve the games under that assumption. In that framework, we also provide decidability and computability results

Time-varying partitioning for predictive control design: density-games approach

The design of distributed optimization-based controllers for large-scale systems (LSSs) implies every time new challenges. The fact that LSSs are generally located throughout large geographical areas makes dicult the recollection of measurements and their transmission. In this regard, the communication network that is required for a centralized control approach might have high associated economic costs. Furthermore, the computation of a large amount of data implies a high computational burden to manage, process and use them in order to make decisions over the system operation. A plausible solution to mitigate the aforementioned issues associated with the control of LSSs consists in dividing this type of systems into smaller sub-systems able to be handled by independent local controllers. This paper studies two fundamental components of the design of distributed optimization-based controllers for LSSs, i.e., the system partitioning and distributed optimization algorithms. The design of distributed model predictive control (DMPC) strategies with a system partitioning and by using density-dependent population games (DDPG) is presented.Peer ReviewedPostprint (author's final draft

CHARDA: Causal Hybrid Automata Recovery via Dynamic Analysis

We propose and evaluate a new technique for learning hybrid automata automatically by observing the runtime behavior of a dynamical system. Working from a sequence of continuous state values and predicates about the environment, CHARDA recovers the distinct dynamic modes, learns a model for each mode from a given set of templates, and postulates causal guard conditions which trigger transitions between modes. Our main contribution is the use of information-theoretic measures (1)~as a cost function for data segmentation and model selection to penalize over-fitting and (2)~to determine the likely causes of each transition. CHARDA is easily extended with different classes of model templates, fitting methods, or predicates. In our experiments on a complex videogame character, CHARDA successfully discovers a reasonable over-approximation of the character's true behaviors. Our results also compare favorably against recent work in automatically learning probabilistic timed automata in an aircraft domain: CHARDA exactly learns the modes of these simpler automata.Comment: 7 pages, 2 figures. Accepted for IJCAI 201