Fuzzy restrictions and an application to cooperative games with restricted cooperation

The concept of restriction, which is an extension of that of interior operator, was introduced to model limited cooperation in cooperative game theory. In this paper, a fuzzy version of restrictions is presented. We show that these new operators, called fuzzy restrictions, can be characterized by the transitivity of the fuzzy dependence relations that they induce. As an application, we introduce cooperative games with fuzzy restriction, which are used to model cooperative situations in which each player in a coalition has a level of cooperation within the coalition. A value for these games is defined and characterized.     

Nonlinear dynamics of continuous-variable quantum games with bounded rationality

We investigate the dynamics of a quantum duopoly game where the players use bounded rationality to adjust own decision. The stability conditions of the equilibrium points are analyzed. Furthermore, we present the numerical simulations to show the nonlinear behaviors: bifurcations, strange attractors, stability region.     

Soft cooperation systems and games

A cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation. In order to obtain this allocation, a characteristic function is known. It establishes the profit of each coalition of agents if this coalition decides to act alone. Originally players are considered symmetric and then the allocation only depends on the characteristic function; this paper is about cooperative games with an asymmetric set of agents. We introduced cooperative games with a soft set of agents which explains those parameters determining the asymmetry among them in the cooperation. Now the characteristic function is defined not over the coalitions but over the soft coalitions, namely the profit depends not only on the formed coalition but also on the attributes considered for the players in the coalition. The best known of the allocation rules for cooperative games is the Shapley value. We propose a Shapley kind solution for soft games.     

gain bounds for systems with sector bounded and slope‐restricted nonlinearities

This paper proposes a new method for calculating a bound on the gain of a system comprising a linear time invariant part and a static nonlinear part, which is odd, bounded, zero at zero and has a restriction on its slope. The nonlinear part is also assumed to be sector bounded, with the sector bound being (possibly) different from that implied by the slope restriction. The computation of the gain bound is found by solving a set of linear matrix inequalities, which arise from an integral quadratic constraint formulation of a multiplier problem involving both Zames‐Falb and Popov multipliers. Examples illustrate the effectiveness of the results, and comparisons are made against the state‐of‐the‐art. Copyright © 2011 John Wiley & Sons, Ltd.     

Acquaintance-based trust model for the evolution of cooperation in business games

Reputation systems have been popular in several online market places involving anonymous players as it can provide crucial information on the trustworthiness of an object or individual player to combat selfish and deceptive behaviors from peers. Individual feedbacks on the quality of past association are the fundamental building blocks of reputation systems. Careful consideration in aggregating feedbacks from different sources is in fact very important in computing a reliable value for trust worthiness to facilitate decision making in a social dilemma situation like that of online market places. In this paper, we are considering a possible improvement to a reputation model like that of eBay, with our interest lying on investigating how the cooperativeness and population of cooperators would evolve if the weight of the feedback source was assigned on the basis of past association between players. We categorize the feedback sources into different types to define an aggregation method for trustworthiness assessment that considers applying a dynamically computed weight to each source of feedback. Our results show that breaking feedback sources on the basis of acquaintance and assigning weight accordingly favor the evolution of cooperativeness in the player society when compared to models which do not classify the feedback sources.     

Buyer-supplier games: Optimization over the core

In a buyer-supplier game, a special type of assignment game, a distinguished player, called the buyer, wishes to purchase some combinatorial structure. A set of players, called suppliers, offer various components of the structure for sale. Any combinatorial minimization problem can be transformed into a buyer-supplier game. While most previous work has been concerned with characterizing the core of buyer-supplier games, in this paper we study optimization over the set of core vectors. We give a polynomial time algorithm for optimizing over the core of any buyer-supplier game for which the underlying minimization problem is solvable in polynomial time. In addition, we show that it is hard to determine whether a given vector belongs to the core if the base minimization problem is not solvable in polynomial time. Finally, we introduce and study the concept of focus point price, which answers the question: If we are constrained to play in equilibrium, how much can we lose by playing the wrong equilibrium?     

The unwind property for programs with bounded memory

For programs that can access unbounded memory (e.g., flowchart programs with recursion on simple variable parameters), the ‘unwind property’ is equivalent to the ‘truth-table property’. For programs restricted to bounded memory (e.g., flowchart programs with parameterless recursion), the two properties are not equivalent in general. We recapitulate all known results, give new results, and establish conditions under which the two properties are equivalent for program with bounded memory.     

Promoting cooperation by setting a ceiling payoff for defectors under three-strategy public good games

The puzzle of altruistic behaviours among multi-agent systems poses a dilemma, which has been an overlapping topic that covers many subjects. The public goods game can be regarded as a paradigm for modelling and exploring it. In the traditional definition of public goods game, the equally divided benefit among all participants leads to the dominance of defection. Much effort has been made to explain the evolution of cooperation, including the model in which the payoff ceilings for defectors are introduced. Further, we study a three-strategy evolutionary public goods game by providing the role of being loners. The payoff ceilings will take effect when the number of cooperators exceeds some threshold. Analysis results by following the replicator dynamics indicate that lower values of the payoff ceilings can better promote levels of public cooperation. Importantly, a remarkable cyclic route has been found: when receiving relative lower benefits, loners act as catalysts, helping the population to escape from mutual defection to cooperation. And, the stable equilibrium points from cooperation to isolation can be realised by improving the fixed payoffs of loners. Finally, broader ceilings also for cooperators provide us more hints about how to suppress the spreading of defectors under certain conditions.     

Modified static anti‐windup for saturated systems with sector‐bounded and slope‐restricted nonlinearities

This paper proposes modified static anti‐windup techniques for saturated systems with sector‐bounded and slope‐restricted nonlinearities by augmenting the pre‐designed controller with the so‐called differential compensator to process the slope restriction. By using a purely quadratic Lyapunov function and with a modified sector condition dealing with actuator saturation, LMI‐based synthesis conditions are presented to address the problems of the estimates of the region of attraction and performance analysis of the closed‐loop system. Numerical examples illustrate the effectiveness of the proposed approaches. Copyright © 2016 John Wiley & Sons, Ltd.     

Identification for systems with bounded noise

In this paper, we present a set-membership identification algorithm for systems with unknown but bounded disturbance. The algorithm contains a weighting factor which is selected according to whether the new observed data contains sufficient information. The proposed approach ensures that the estimation error is bounded and nonincreasing. Furthermore, it is shown that the parameter estimates provided by the algorithm will converge to a region containing the true parameters, and its upper bound is also given     

Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties.     

The dynamic programming equations for stochastic games with discrete actions

We consider the quasi-variational inequalities associated with a stochastic game with discrete actions and switching costs. We obtain an analytical uniqueness result, and, for a particular case, a regurality estimate.     

具有可行联盟的合作对策的最小二乘解

最小二乘解是基于最小平方优化方法得到的使联盟中局中人的分配值之和与联盟收益的期望偏差最小的分配方案.为了拓展最小二乘解的适用范围,构建可行联盟集合限制下最小二乘解的最优化模型,根据凸规划理论探讨该最小二乘解的存在性及唯一性条件,进而利用拉格朗日乘子法给出求解最小二乘解的矩阵方程,并基于此探讨解的具体表达式和一些重要性质.同时,基于不可分开的局中人获得相同分配值这一分配准则,在最小二乘解的基础上提出对称最小二乘解,并讨论其唯一性条件及相关性质.值得指出的是,当且仅当其可行联盟集合为非奇异时,具有可行联盟的合作对策存在唯一的最小二乘解.所提出的最小二乘解可为局中人合作具有限制时的收益分配问题提供理论依据和决策参考.     

Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition

How do we build algorithms for agent interactions with human adversaries? Stackelberg games are natural models for many important applications that involve human interaction, such as oligopolistic markets and security domains. In Stackelberg games, one player, the leader, commits to a strategy and the follower makes her decision with knowledge of the leader's commitment. Existing algorithms for Stackelberg games efficiently find optimal solutions (leader strategy), but they critically assume that the follower plays optimally. Unfortunately, in many applications, agents face human followers (adversaries) who — because of their bounded rationality and limited observation of the leader strategy — may deviate from their expected optimal response. In other words, human adversaries' decisions are biased due to their bounded rationality and limited observations. Not taking into account these likely deviations when dealing with human adversaries may cause an unacceptable degradation in the leader's reward, particularly in security applications where these algorithms have seen deployment. The objective of this paper therefore is to investigate how to build algorithms for agent interactions with human adversaries.To address this crucial problem, this paper introduces a new mixed-integer linear program (MILP) for Stackelberg games to consider human adversaries, incorporating: (i) novel anchoring theories on human perception of probability distributions and (ii) robustness approaches for MILPs to address human imprecision. Since this new approach considers human adversaries, traditional proofs of correctness or optimality are insufficient; instead, it is necessary to rely on empirical validation. To that end, this paper considers four settings based on real deployed security systems at Los Angeles International Airport (Pita et al., 2008 [35]), and compares 6 different approaches (three based on our new approach and three previous approaches), in 4 different observability conditions, involving 218 human subjects playing 2960 games in total. The final conclusion is that a model which incorporates both the ideas of robustness and anchoring achieves statistically significant higher rewards and also maintains equivalent or faster solution speeds compared to existing approaches.     

基于演化博弈惩罚机制的多智能体协作稳定性研究

针对复杂、动态环境中多Agent协作的稳定性问题,提出了一种基于博弈论及惩罚机制的协作方法,通过效用函数来选择最优策略,实现均衡协作;为了提高协作的稳定性与成功率,引入惩罚机制,通过不断调整惩罚系数来维护多Agent协作的稳定性,并在形成协作团队时,充分考虑参与协作的Agent的信誉值。仿真结果表明,该方法能有效地降低任务完成时间,避免Agent在动态协作中随意退出,提高协作效率及协作稳定性。     

Adaptive control for systems with bounded disturbances

The authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum- and nonminimum-phase systems subject to bounded disturbances. The parameter estimation scheme is a least-squares algorithm with dead zone. The dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates. In the minimum-phase case, the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value. The projection procedure can also be used to avoid pole-zero cancellations in an adaptive pole-placement algorithm     

The symmetric Banzhaf value for fuzzy games with a coalition structure

In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.     

The Borel measure of sequences with bounded run-length

Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure. Such sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus, large scale simulation, and cryptology. They are basic objects of study in ergodic theory.