Optimal Leader Research Articles

Hierarchic control for a coupled parabolic system

In this paper we study a Stackelberg–Nash strategy to control systems of coupled linear parabolic partial differential equations. We assume that we can act on the system through several controls called followers , intended to solve a Nash multi-objective equilibrium, and a single leader control satisfying a null controllability objective. We obtain the existence and uniqueness of the Nash equilibrium, its characterization and the optimal leader control satisfying the null controllability problem.

Leader selection for fast consensus in networks

This paper considers a leader-follower system with the aim to select an optimal leader so as to drive the remaining nodes to reach the desired consensus with the fastest convergence speed. An index called consensus centrality (CC) is proposed to quantify how fast a leader could guide the network to achieve the desired consensus. The experiment results explored the big similarities between the distributions of CC and degree in the network, which suggest that the suboptimal leader selected by the maximum degree can approximately approach the optimal leader in heterogeneous networks. Combining the degree-based k-shell decomposition with consensus centrality, a leader selection algorithm is proposed to reduce the computational complexity in large-scale networks. Finally, the convergence time of an equivalent discrete-time model is given to illustrate the properties of the suboptimal solutions.

Optimal Machine Strategies to Commit to in Two-Person Repeated Games

The problem of computing optimal strategy to commit to in various games has attracted intense research interests and has important real-world applications such as security (attacker-defender) games. In this paper, we consider the problem of computing optimal leader’s machine to commit to in two-person repeated game, where the follower also plays a machine strategy. Machine strategy is the generalized notion of automaton strategy, where the number of states in the automaton can be possibly infinite. We begin with the simple case where both players are confined to automata strategies, and then extend to general (possibly randomized) machine strategies. We first give a concise linear program to compute the optimal leader’s strategy and give two efficient implementations of the linear program: one via enumeration of a convex hull and the other via randomization. We then investigate the case where two machines have different levels of intelligence in the sense that one machine is able to record more history information than the other. We show that an intellectually superior leader, sometimes considered being exploited by the follower, can figure out the follower’s machine by brute-force and exploit the follower in return.

Key leaders in social networks

This paper examines optimal targeting and sequencing strategies in the setup proposed by Ballester et al. [3]. The setup features payoff externalities and strategic complementarity among players, who non-cooperatively determine their contributions. We first analyze a two-stage game in which players in the leader group make contributions before the follower group. We construct an exact index to identify the (single) key leader, and demonstrate that the key leader can differ substantially from the key player who most influences the network in the simultaneous-move game. Using Taylor expansions on the strength of network effects, we establish an isomorphism between the optimal leader group selection (targeting) strategy and the classical weighted maximum-cut problem. This approach leads to some design principles for unweighted complete graphs and bipartite graphs.We then allow for an arbitrary sequence of players' moves. If we refine any sequence by making some groups of simultaneous movers act in sequence, their aggregate contribution increases. Consequently, the optimal sequence is a chain structure. When players have homogeneous intrinsic valuations, any chain, arbitrarily ordered, maximizes the aggregate contribution. We further consider the possibility of shrinking the number of stages needed for the optimal sequence. In general, our results hold when the network game exhibits strategic substitutes.

The Benefit of Sequentiality in Social Networks

This paper examines optimal targeting and sequencing strategies in the setup proposed by Ballester et al. (2006). The setup features payoff externalities and strategic complementarity among players, who non-cooperatively determine their contributions. We first analyze a two-stage game in which players in the leader group make contributions before the follower group. We construct an exact index to identify the (single) key leader, and demonstrate that the key leader can differ substantially from the key player who most influences the network in the simultaneous-move game. Using Taylor expansions on the strength of network effects, we establish an isomorphism between the optimal leader group selection (targeting) strategy and the classical weighted maximum-cut problem. This approach leads to some design principles for unweighted complete graphs and bipartite graphs.We then allow for an arbitrary sequence of players' moves. If we refine any sequence by making some groups of simultaneous movers act in sequence, their aggregate contribution increases. Consequently, the optimal sequence is a chain structure. When players have homogeneous intrinsic valuations, any chain, arbitrarily ordered, maximizes the aggregate contribution. We further consider the possibility of shrinking the number of stages needed for the optimal sequence. In general, our results hold when the network game exhibits strategic substitutes.

Leadership: is bad stronger than good?

Purpose– The purpose of this paper is to investigate if the thesis “bad is stronger than good” also holds true for a number of leadership issues, more specifically: trust in the immediate leader, emotional exhaustion, work atmosphere and propensity to leave.Design/methodology/approach– Questionnaire responses were obtained from military personnel in Estonia, Sweden, Switzerland and the Netherlands (n=625).Findings– Multiple regression analyses revealed a certain pattern. Constructive leadership behaviours showed stronger positive associations with trust in the immediate supervisor and work atmosphere, than destructive leadership behaviours showed negative associations. On the other hand, destructive leadership behaviours showed stronger positive associations with emotional exhaustion and propensity to leave, than constructive leadership behaviours showed negative associations. This suggests that constructive leadership behaviours possibly have a greater impact on positive phenomenon and/or phenomenon associated with work-related relationships. On the other hand, destructive leadership behaviours appear to have a greater impact on negative phenomena with a stronger personal meaning. The results also show that the passive forms of destructive leadership are the behaviours that had the strongest impact on the investigated dependent variables.Research limitations/implications– Limitations related to item construction, common method variance, response set tendencies, translation of the instruments, and lack of response rate are discussed.Practical implications– The results emphasize the importance of focusing on both constructive and destructive leadership at the selection stage, as well as during training of military leaders. Focusing on them separately obstructs optimal leader development and prevents leaders from gaining authentic self-knowledge. The results also point at the importance of including both aspects of leadership in leader evaluation processes.Originality/value– The use of both constructive and destructive leadership behaviours with respondents from multiple nations in the same analysis.

On Systematic Computation of Optimal Nonlinear Solutions for the Reverse Stackelberg Game

In control of large-scale intelligent infrastructures, multilevel optimization can serve as a useful framework to deal with overall complex problems, especially in networks that already exhibit a natural hierarchy of decision makers with different objectives. In particular, solution methods from the hierarchical game theory can be adopted. Here, we focus on solving problems that belong to the specific class of reverse Stackelberg games. In this game, a follower player acts subsequent to the leader's revelation of her so-called leader function, which maps the leader decision space to the follower decision space. In general, the problem of finding a leader function such that the leader's objective function is optimized while taking into account a follower decision that is optimal for the follower, is difficult to solve. We provide a structured solution approach for the class of nonlinear leader functions and make a comparison with the evolutionary approaches proposed in the literature. In particular, a continuous multilevel optimization approach and a gridding approach are proposed to compute an optimal leader function based on basis functions. Also, leader functions derived by interpolation are discussed. All approaches are illustrated and compared in a worked example, in which the required computation times and deviation from the desired solution are considered.

Minimizing Convergence Error in Multi-Agent Systems Via Leader Selection: A Supermodular Optimization Approach

In a leader-follower multi-agent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are determined by the choice of leader agents. In this paper, we study leader selection in order to minimize convergence errors experienced by the follower agents, which we define as a norm of the distance between the follower agents' intermediate states and the convex hull of the leader agent states. By introducing a novel connection to random walks on the network graph, we show that the convergence error has an inherent supermodular structure as a function of the leader set. Supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set, provide provable performance guarantees, and do not rely on continuous relaxations. We formulate two leader selection problems within the supermodular optimization framework, namely, the problem of selecting a fixed number of leader agents in order to minimize the convergence error, as well as the problem of selecting the minimum-size set of leader agents to achieve a given bound on the convergence error. We introduce algorithms for approximating the optimal solution to both problems in static networks, dynamic networks with known topology distributions, and dynamic networks with unknown and unpredictable topology distributions. Our approach is shown to provide significantly lower convergence errors than existing random and degree-based leader selection methods in a numerical study.

Targeted Information Release in Social Networks

As a common practice, various firms initially make information and access to their products/services scarce within a social network; identifying influential players that facilitate information dissemination emerges as a pivotal step for their success. In this paper, we tackle this problem using a stylized model that features payoff externalities and local network effects, and the network designer is allowed to release information to only a subset of players (leaders); these targeted players make their contributions first and the rest followers move subsequently after observing the leaders' decisions. In the presence of incomplete information, the signaling incentive drives the optimal selection of leaders and can lead to a first-order materialistic effect on the equilibrium outcomes. We propose a novel index for the key leader selection (i.e., a single player to provide information to) that can be substantially different from the key player index in Ballester et al. (2006) and the key leader index with complete information proposed in Zhou and Chen (2013). We also show that in undirected graphs, the optimal leader group identified in Zhou and Chen (2013) is exactly the optimal follower group when signaling is present. The pecking order in complete graphs suggests that the leader should be selected by the ascending order of intrinsic valuations. We also examine the out-tree hierarchical structure that describes a typical economic organization. The key leader turns out to be the one that stays in the middle, and it is not necessarily exactly the central player in the network.

Optimal leader allocation in UAV formation pairs ensuring cooperation

This paper considers the problem of optimally allocating the leader task between pairs of selfish unmanned aerial vehicles (UAVs) flying in formation. The UAV that follows the other achieves a fuel benefit. The noncooperative nature of the agents makes it necessary to arbitrate leader-allocation mechanisms that induce collaboration so that the fuel consumption benefits of flying in formation can be realized. Formulated as a nonlinear program, our problem poses two distinct challenges: on the one hand, given a fixed number of leader switches, determine the optimal leader allocation and, on the other, find the optimal number of leader switches. Even though the first problem is nonconvex, we identify a suitable restriction of its feasible set that makes it convex while maintaining the same optimal value. Regarding the second problem, our analysis of the optimal value of the problem as a function of the number of switches allows us to design a search algorithm which is guaranteed to find the solution in logarithmic time. Several simulations illustrate our results.

REQUEST+: A framework for efficient processing of region-based queries in sensor networks

In wireless sensor networks, individual sensing values are not reliable due to node failures. The effect of these failures can be reduced by using aggregated values for groups of sensor nodes instead of the individual sensing values. However, most existing works have focused on computing the aggregation of all the nodes without grouping. Only a few approaches dealt with the processing of grouped aggregate queries. However, since groups in their approaches are disjoint, some areas which are not covered by groups cannot be considered, even if the areas are relevant to the user’s interest. In this paper, we propose a new type of queries, region-based queries, and a framework to process region-based queries, called REQUEST+. A region in REQUEST+ is defined as a maximal set of nodes located within a circle having a diameter specified in the query. To efficiently construct a large number of regions covering the entire monitoring area, we build the SEC (Smallest Enclosing Circle) index. Moreover, in order to process a region-based query, we adapt a clustering-based aggregation method, in which there is a leader node for each region. To minimize the communication cost, we formulate an optimal leader selection problem and prove that it is NP-hard. In addition, we transform the problem into the weighted set-cover problem to utilize the algorithm devised for the problem. Finally, we construct a query-initiated routing tree for the communication between the leader and non-leader nodes. In the experimental results, we show that the result of our region-based query is more reliable than that of the query which is based on individual nodes, and our processing method is more energy-efficient than existing methods for processing grouped aggregate queries.

Achieving System-Optimal Splitting Rates in a Freeway Network Using a Reverse Stackelberg Approach

A game-theoretical method is proposed to achieve a system-optimal distribution of traffic over a freeway network. In particular, the road authority is represented by a leader player and each follower player embodies a group of drivers with the same value of time that plan to travel between a given origin and destination. In the proposed reverse Stackelberg approach, the leader presents a function to each follower that maps a vector of splitting rates over possibles routes to a monetary incentive. The follower then decides upon a splitting rate and the associated monetary incentive that yield the minimum weighted measure of travel time and monetary fees. In this manner, the road authority can compose an optimal leader function under which the followers will behave as desired, i.e., to achieve the system-optimal splitting rates.

Joint sensor localisation and target tracking in sensor networks

The authors propose a sequential quasi-Monte Carlo (SQMC)-based algorithm for joint estimation of sensor-node locations and target trajectory in a wireless sensor network. The sensor nodes are randomly deployed with no prior knowledge about their positions. A predictive entropy-based information utility is used to select the leader node at each stage, and all other nodes are kept in standby mode to save power. The Bayesian estimates required to track the systems's non-linear dynamics are computed using the powerful SQMC method, which naturally integrates sensor collaboration with optimal leader node selection. Extensions of the algorithm to other interesting scenarios such as missing observations and non-Gaussian noise are also presented, which are very relevant to the unreliable environments encountered in hostile territories. The authors demonstrate through simulations that even with a very small fraction of the total number of nodes acting as beacon nodes, the proposed method can not only track the moving target, but can also obtain fairly accurate estimates of the (unknown) locatp(z(t)|z(i(j))(t − 1))ions of the sensor nodes.

Conformational change in the Bacillus subtilis RNase P holoenzyme–pre-tRNA complex enhances substrate affinity and limits cleavage rate

Ribonuclease P (RNase P) is a ribonucleoprotein complex that catalyzes the 5' maturation of precursor tRNAs. To investigate the mechanism of substrate recognition in this enzyme, we characterize the thermodynamics and kinetics of Bacillus subtilis pre-tRNA(Asp) binding to B. subtilis RNase P holoenzyme using fluorescence techniques. Time courses for fluorescein-labeled pre-tRNA binding to RNase P are biphasic in the presence of both Ca(II) and Mg(II), requiring a minimal two-step association mechanism. In the first step, the apparent bimolecular rate constant for pre-tRNA associating with RNase P has a value that is near the diffusion limit and is independent of the length of the pre-tRNA leader. Following formation of the initial enzyme-substrate complex, a unimolecular step enhances the overall affinity of pre-tRNA by eight- to 300-fold as the length of the leader sequence increases from 2 to 5 nucleotides. This increase in affinity is due to a decrease in the reverse rate constant for the conformational change that correlates with the formation of an optimal leader-protein interaction in the RNase P holoenzyme-pre-tRNA complex. Furthermore, the forward rate constant for the conformational change becomes rate limiting for cleavage under single-turnover conditions at high pH, explaining the origin of the observed apparent pK(a) in the RNase P-catalyzed cleavage reaction. These data suggest that a conformational change in the RNase P*pre-tRNA complex is coupled to the interactions between the 5' leader and P protein and aligns essential functional groups at the cleavage active site to enhance efficient cleavage of pre-tRNA.

Optimally computing all solutions of Stackelberg with parametric prices and of general monotonous gain functions on a tree

This paper considers Hotelling's duopoly model on a tree with parametric service prices. Two competitors, the leader and the follower, sequentially place a server in a network. Users decide for a server according to the sum of distance and server price. The goal of the competitors is to maximize their profit induced by the total demand served. García and Pelegrín (2003) develop an algorithm with O ( n 3 log n ) running time to compute the Stackelberg set, i.e., the set of all optimal leader positions. In this paper we first provide an algorithm to compute the Stackelberg set and the relaxed Simpson set with worst case running time O ( n ) . Second we suggest an algorithm to compute the optimal set for general monotonous gain functions. Its running time is O ( n log n ) and we prove that this bound is tight even for computing the security set.

The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions

Let M be a single s – t network of parallel links with load dependent latency functions shared by an infinite number of selfish users. This may yield a Nash equilibrium with unbounded Coordination Ratio [E. Koutsoupias, C. Papadimitriou, Worst-case equilibria, in: 16th Annual Symposium on Theoretical Aspects of Computer Science, STACS, vol. 1563, 1999, pp. 404–413; T. Roughgarden, É. Tardos, How bad is selfish routing? in: 41st IEEE Annual Symposium of Foundations of Computer Science, FOCS, 2000, pp. 93–102]. A Leader can decrease the coordination ratio by assigning flow α r on M , and then all Followers assign selfishly the ( 1 − α ) r remaining flow. This is a Stackelberg Scheduling Instance ( M , r , α ) , 0 ≤ α ≤ 1 . It was shown [T. Roughgarden, Stackelberg scheduling strategies, in: 33rd Annual Symposium on Theory of Computing, STOC, 2001, pp. 104–113] that it is weakly NP-hard to compute the optimal Leader’s strategy. For any such network M we efficiently compute the minimum portion β M of flow r > 0 needed by a Leader to induce M ’s optimum cost, as well as her optimal strategy. This shows that the optimal Leader’s strategy on instances ( M , r , α ≥ β M ) is in P . Unfortunately, Stackelberg routing in more general nets can be arbitrarily hard. Roughgarden presented a modification of Braess’s Paradox graph, such that no strategy controlling α r flow can induce ≤ 1 α times the optimum cost. However, we show that our main result also applies to any s – t net G . We take care of the Braess’s graph explicitly, as a convincing example. Finally, we extend this result to k commodities. A conference version of this paper has appeared in [A. Kaporis, P. Spirakis, The price of optimum in stackelberg games on arbitrary single commodity networks and latency functions, in: 18th annual ACM symposium on Parallelism in Algorithms and Architectures, SPAA, 2006, pp. 19–28]. Some preliminary results have also appeared as technical report in [A.C. Kaporis, E. Politopoulou, P.G. Spirakis, The price of optimum in stackelberg games, in: Electronic Colloquium on Computational Complexity, ECCC, (056), 2005].

Randomized self-stabilizing and space optimal leader election under arbitrary scheduler on rings

We present a randomized self-stabilizing leader election protocol and a randomized self-stabilizing token circulation protocol under an arbitrary scheduler on anonymous and unidirectional rings of any size. These protocols are space optimal. We also give a formal and complete proof of these protocols. To this end, we develop a complete model for probabilistic self-stabilizing distributed systems which clearly separates the non deterministic behavior of the scheduler from the randomized behavior of the protocol. This framework includes all the necessary tools for proving the self- stabilization of a randomized distributed system: definition of a probabilistic space and definition of the self-stabilization of a randomized protocol. We also propose a new technique of scheduler management through a self-stabilizing protocol composition (cross-over composition). Roughly speaking, we force all computations to have a fairness property under any scheduler, even under an unfair one.