We introduce -Rank, a principled evolutionary dynamics methodology for the evaluation and ranking of agents in large-scale multi-agent interactions, grounded in a novel dynamical game-theoretic solution concept called Markov-Conley chains (MCCs). The approach leverages continuous- and discrete-time evolutionary dynamical systems applied to empirical games, and scales tractably in the number of agents, the type of interactions, and the type of empirical games (symmetric and asymmetric). Current models are fundamentally limited in one or more of these dimensions and are not guaranteed to converge to the desired game-theoretic solution concept (typically the Nash equilibrium). -Rank provides a ranking over the set of agents under evaluation and provides insights into their strengths, weaknesses, and long-term dynamics. This is a consequence of the links we establish to the MCC solution concept when the underlying evolutionary model's ranking-intensity parameter, , is chosen to be large, which exactly forms the basis of -Rank. In contrast to the Nash equilibrium, which is a static concept based on fixed points, MCCs are a dynamical solution concept based on the Markov chain formalism, Conley's Fundamental Theorem of Dynamical Systems, and the core ingredients of dynamical systems: fixed points, recurrent sets, periodic orbits, and limit cycles. -Rank runs in polynomial time with respect to the total number of pure strategy profiles, whereas computing a Nash equilibrium for a general-sum game is known to be intractable. We introduce proofs that not only provide a unifying perspective of existing continuous- and discrete-time evolutionary evaluation models, but also reveal the formal underpinnings of the -Rank methodology. We empirically validate the method in several domains including AlphaGo, AlphaZero, MuJoCo Soccer, and Poker.
The purpose of the first applications of EGTA was to reduce the complexity of large economic problems in electronic commerce, such as continuous double auctions, supply chain management, market games, and automated trading @cite_53 @cite_28 @cite_70 @cite_5 . While these complex economic problems continue to be a primary application area of these methods @cite_32 @cite_30 @cite_2 @cite_44 , the general techniques have been applied in many different settings. These include analysis of interactions among heuristic meta-strategies in poker @cite_40 , network protocol compliance @cite_59 , collision avoidance in robotics @cite_14 , and security games @cite_79 @cite_46 @cite_8 .
@cite_30 @cite_14 @cite_8 @cite_28 @cite_70 @cite_53 @cite_32 @cite_44 @cite_79 @cite_40 @cite_59 @cite_2 @cite_5 @cite_46
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Empirical game-theoretic analysis (EGTA) has recently been applied successfully to analyze the behavior of large numbers of competing traders in a continuous double auction market. Multiagent simulation methods like EGTA are useful for studying complex strategic environments like a stock market, where it is not feasible to solve analytically for the rational behavior of each agent. A weakness of simulation-based methods in strategic settings, however, is that it is typically impossible to prove that the strategy profile assigned to the simulated agents is stable, as in a Nash equilibrium. I propose using reinforcement learning to analyze the regret of supposed Nash-equilibrium strategy profiles found by EGTA. I have developed a new library of reinforcement learning tools, which I have integrated into an extended version of the market simulator from our prior work. I provide evidence for the effectiveness of our library methods, both on a suite of benchmark problems from the literature, and on non-equilibrium strategy profiles in our market environment. Finally, I use our new reinforcement learning tools to provide evidence that the equilibria found by EGTA in our recent continuous double auction study are likely to have only negligible regret, even with respect to an extended strategy space. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. This paper explains when and how communication and computational lower bounds for algorithms for an optimization problem translate to lower bounds on the worst-case quality of equilibria in games derived from the problem. We give three families of lower bounds on the quality of equilibria, each motivated by a different set of problems: congestion, scheduling, and distributed welfare games, welfare-maximization in combinatorial auctions with "black-box" bidder valuations, and welfare-maximization in combinatorial auctions with succinctly described valuations. The most straightforward use of our lower bound framework is to harness an existing computational or communication lower bound to derive a lower bound on the worst-case price of anarchy (POA) in a class of games. This is a new approach to POA lower bounds, which relies on reductions in lieu of explicit constructions. More generally, the POA lower bounds implied by our framework apply to all classes of games that share the same underlying optimization problem, independent of the details of players' utility functions. For this reason, our lower bounds are particularly significant for problems of game design--ranging from the design of simple combinatorial auctions to the computation of tolls for routing networks--where the goal is to design a game that has only near-optimal equilibria. For example, our results imply that the simultaneous first-price auction format is optimal among all "simple combinatorial auctions" in several settings. In the field of infrastructures’ surveillance and protection, it is important to make decisions based on activities occurring in the environment and its local context and conditions. In this paper we use an active rule based event processing architecture in order to make sense of situations from the combination of different signals received by the rule engine. However obtaining some high level information automatically is not without risks, especially in sensitive environments, and detection mistakes can happen for various reasons: the signal’s source can be defective, whether it is human—miss-interpretation of the signal—or computed—material malfunction; the aggregation rules can be wrong syntaxically, for example when a rule will never be triggered or a situation never detected; the interpretation given to the combination of signals does not correspond to the reality on the field—because the knowledge of the rule designer is subjective or because the environment evolves over-time—the rules are therefore incorrect semantically. In this paper, a new approach is proposed to avoid the third kind of error sources. We present a hybrid machine learning technique adapted to the complexity of the rules’ representation, in order to create a system more conform to reality. The proposed approach uses a combination of an Association Rule Mining algorithm and Inductive Logic Programming for rule induction. Empirical studies on simulated datasets demonstrate how our method can contribute to sensible systems such as the security of a public or semi-public place.