The promotion of cooperation and fair competition is one of the key questions in economics and management science. Most of previous studies in this field applied game theory method. These studies often designed management mechanism based on the Nash equilibrium analysis. However, people in reality are boundedly rational and often deviate from the Nash equilibrium. In recent years, data driven analysis for human cooperation and competition behaviors becomes one of the mainstream directions of economics and management science. This paper provides a survey of this field. We first introduce some theoretical and data driven methods for analyzing human behavior and mechanism design, including Nash equilibrium analysis, evolutionary game theory, cooperative game theory, behavioral economics, experimental economics, psychology, and neuroscience methods. Then we discuss internal factors, external factors, and institutional factors that may affect human cooperation and competition. For internal factors, we focus on prosocial preferences, such as altruism, reciprocity, fairness, and trust. We summarize related empirical results and discuss the neural and evolutionary mechanisms of these prosocial preferences. For external factors, we focus on the influences of social norm, network structure, and information structure on cooperation and competition. For institutional factors, we discuss the effects of different types of reputation mechanisms and incentive mechanisms. Finally, some challenging questions in this field are discussed.

Due to the scarcity of information, the uncertainty of the service system and the limited cognitive ability of customers, it is difficult for customers to estimate the expected utility after receiving the service accurately, and then make rational decisions. In this paper, the Logit choice model is used to describe the strategic behavior of boundedly rational customers, based on queueing game theory, the customer equilibrium strategy, revenue and social welfare is analyzed under almost unobservable case and fully unobservable case, the influence of customer boundedly rationality on the optimal revenue and optimal social welfare under the two information levels is compared through numerical case. The results show that, under the two information levels, the equilibrium strategy of boundedly rational customers exists and is unique; There is a unique optimal price that maximizes the revenue; There is a unique optimal price that maximizes the social welfare; As the average vacation time decreases, customers prefer to enter the system, revenue increases and so does social welfare. In addition, under the fully unobservable case, the variation of social welfare with respect to the bounded rationality level of customers depends on the service price and is a unimodal function of the bounded rationality level of customers; There exists a specific bounded rationality level such that revenue and social welfare are simultaneously maximized.

A generalized mixed quasi-variational inequality (GMQVI) is a generalization of the variational inequality. Variational inequalities and their generalization are widely used, for instance, economics, transportation and optimal control. Based on the intrinsic properties of the generalized projection operator, under certain assumptions of monotonicity and compactness, this paper gives the regularized gap function for generalized mixed quasi-variational inequality problems in reflexive Banach spaces, which in turn induces the D-gap function for GMQVI by the difference of two regularized gap functions. And using these gap functions, the local error bound described by the regularized gap function and the global error bound characterized by the D-gap function and the regularization term are obtained.

This paper innovatively integrates facility location games with the bin packing problem, defining a novel class of facility location bin packing games (FLBPG). Departing from classical models, we are the first to analyze a scenario in which items require further service after visiting a facility. Our optimization objective is to minimize the total access distances of all items to the facilities, as well as the overall number of bins required for this subsequent service. In this model, items act as strategic agents, each possessing information about their location and size. First, we study the scenario in which item size is private information, and the item cost is determined by sharing the bin packing cost. For the resulting pure bin packing game and facility location bin packing game, we design strategy-proof mechanisms with approximation ratios bounded within [1.691, 2] and [5/3, 7/4], respectively. Second, we address a more complex scenario in which both item size and location are private, correlated pieces of information, and the item cost is defined as the actual access distance to the assigned facility. In this context, we design three distinct strategy-proof mechanisms. We rigorously establish their approximation ratio bounds: the first mechanism achieves bounds of [47/35, 11/8], the second [45/34, 1.7], and the third [11/9, 10/9]. This work expands the theoretical framework of facility location games. The proposed mechanism design methodology effectively addresses the integrated optimization of facility location and bin packing within a complex strategic environment. Our mechanisms offer robust solutions by ensuring both strategy-proofness and demonstrable approximation efficiency.

This paper considers single machine scheduling with carbon emission cost and piece rate maintenance. A maintenance activity is required after processing a number of jobs. During the processing of jobs and maintenance activities, the corresponding carbon emissions will be generated. For both minimizing the maximum completion time and total completion time, we establish a scheduling model of minimizing the total cost of processing and carbon emission, respectively. It is shown that this problem can be transformed into an assignment problem and a polynomial time algorithm with time complexity of $O(n^4)$ is given.

In this paper, we consider a class of nonconvex composite optimization problems, whose objective function is the sum of a continuous differentiable bifunction of the entire variables, and two proper lower semi-continuous nonconvex function of their private variables. We propose a new golden ratio proximal alternating linearized algorithm to solve this problem. Under the assumption of Kurdyka-Lojasiewicz (in short: KL) property, we prove the iterative sequence generated by the algorithm converges to the critical point of the problem. Finally, numerical results on sparse signal recovery illustrate the efficiency and superiority of the proposed algorithm.

A proper k-coloring of a graph G is a vertex k-coloring such that adjacent vertices have different colors. A polychromatic k-coloring of a plane graph G is a vertex k-coloring such that every face meets all k colors. The degree of a face f of G is the number of vertices incident with f and is denoted by $g(f)$. Let $g(G)=\min\{g(f)|f\in F(G)\}$, where $F(G)$ is the face set of plane graph G. Obviously, if a plane graph G has a polychromatic k-coloring, then $k\leq g(G)$. In 2012, Horev et al. showed that every simple cubic bipartite plane graph is proper polychromatic 4-colorable (2012). In this paper, we extend the above result, and show that every subcubic bipartite plane graph G with $g(G)\geq 5$ has a proper polychromatic 4-coloring. The condition that $g(G)\geq 5$ is tight, because there exists (non-cubic) subcubic bipartite plane graph G which has $g(G)=4$ but has no proper polychromatic 4-coloring.

For a spanning tree T of graph G, the centroid of T is a vertex v for which the largest component of $T-v$ has as few vertices as possible. The number of vertices of this component is called the centroid branch weight of T. The minimum branch spanning tree problem is to find a spanning tree T of G such that the centroid branch weight is minimized. This minimum value is called the branch index of G. In application to design of communication networks, the loads of all branches leading from the switch center (centroid) should be as balanced as possible. In 2022, we proposed this new type of location problem and presented basic theoretic results. This paper is devoted to deepen the study on theory and algorithms. We first prove that the weighted version of the problem is NP-hard even for planar graphs. Then, we determine the exact formulas of branch indices for several important graph families, such as polyhedral graphs, hypercubes, and graph product $K_m\times K_n$, co-bipartite graphs, and establish a heuristic algorithm.

Based on the background of the manufacturing system, this paper proposes an M/G/1 queuing model with maintenance strategy and different arrival rates, in which the server begins its service under the control of $N$-policy. Firstly, using the renewal process theory, total probability decomposition technique and Laplace transform, we study the transient properties of the queue length at any time $t$, and obtain the expressions of the Laplace transform of the transient queue size distribution with respect to time $t$. Then, on the basis of the transient analysis, the recursive formulas of the steady-state queue-length distribution are presented by employing L'Hospital's rule. Finally, applying the renewal reward theory, the explicit expression of the long-run expected cost per unit time of the system is obtained under a given cost structure, and numerical examples are provided to discuss the optimal control policy that the server begins its service and optimal maintenance strategy.

The problem of hypergraph balanced bipartitioning has become a vital part of very large scale integration circuit physical design. Iterative methods such as Kernighan-Lin and Fiduccia-Mattheyses heuristics have been used to solve this NP-hard problem and perform well. However, these methods have some disadvantages as follows. First, an initial solution of poor quality will easily get trapped in bad local optima. Second, the movement of vertices is restricted to balanced partition. To resolve these issues, we transform the hypergraph bi-partitioning problem into a 0-1 programming. Then an iterative algorithm is designed to solve the problem, which overcomes the shortcomings of traditional iterative algorithms. Our algorithm performs better than Fiduccia-Mattheyses on the ISPD98 hypergraph partitioning benchmarks. Our results have an average improvement of 13.2% over Fiduccia-Mattheyses. If taking our results as initial solutions of the Fiduccia-Mattheyses heuristic, the average cut count is reduced by 30.1%. Moreover, our algorithm can be incorporated into a multilevel partitioning framework, and the partition result has an average improvement of 3.6%.

The filled function method is a kind of deterministic method, which is adopted to find the global optimal solution for the unconstrained optimization problem. The core technique of this method is to construct the filled function, which is such that the iterative process of the algorithm constantly jump out of the current local minimizer. Currently, the filled function generally contains parameters, and the selection of parameters has a great influence on the computation effect of the algorithm. In this paper, a new non parameter-filled function is constructed by using the definition of filled function, and a new global optimization method is developed. Numerical experiments illustrate that this method is feasible and effective, and has better global optimization ability.

Sparsity regularization model is widely used in inverse problems such as signal and image processing. This paper mainly focuses on the linear least squares $\ell_0$ minimization problem coming from linear inverse problems. Extrapolation forward-backward splitting algorithm is one of the most popular solving methods. If the iteration number is sufficiently large, the non-zero index set of iteration point remains unchanged. Then extrapolation forward-backward splitting algorithm methods is equivalent to solving the problem $\min\limits_{x\in C} f(x)$ where $C$ is some linear subspace related to iteration points. On the other hand, variable metric type method can reach fast performance in practice. Encouraged by these, we employ the fast convergent quasi Newton method into the extrapolation step, and then propose a block variable metric extrapolation algorithm. Meanwhile, its convergence, linear convergence rate and superlinear convergence rate are studied. Finally, numerical experiments show the effectiveness and fast-speed of the proposed algorithm.

Scalarization method is one of the basic research subjects for multi-objective optimization problems. In this paper, we first study the properties of generalized Tchebycheff norm, and obtain some strict monotonicity results on the non-negative quadrant. Furthermore, two kinds of scalarization results of weakly efficient solutions, efficient solutions, strictly efficient solutions and properly efficient solutions of multi-objective optimization problems are studied by using the properties of the generalized Tchebycheff norm. Moreover, we point out that under the assumption of convexity of the objective function, the scalarization studied in this paper is equivalent to the weighted scalarization.

In this paper, two-agent serial batching problems are studied on a single machine. Each batch has a capacity constraint on the processing time. And there is batching cost for each batch which is a constant. The preemption of jobs is not allowed. We consider two problems: One problem is to minimize the sum of the total completion time and the batching cost of one agent under the condition that the sum of the makespan and the batching cost of the other agent does not exceed a threshold value. The other is to minimize the sum of the total completion time and the batching cost of one agent under the condition that the sum of the total completion time and the batching cost of the other agent does not exceed a threshold value. Both problems are NP-hard. A (2, 3/2)-approximation algorithm is provided for the first problem and for the second problem, we design a (2, 2)-asymptotic approximation algorithm.

Let A and B be two sets, the symmetry difference of A and B is a set consisting of all elements not belonging to $A\cap B$ in $A\cup B$, denoted by $A\Delta B$. A hypergraph is called a cancellative hypergraph, if it contains no three distinct edges A, B, and C, such that $A\Delta B\subset C$. In fact, a cancellative3-uniform hypergraph contains neither $F_4=\{abc, abd, bcd\}$ nor $F_5=\{abc, abd, cde\}$ as its subgraphs. Bollobás (1974) determined the maximum number of edges in a cancellative3-uniform hypergraph, and got that only the balanced complete3-partite3-uniform hypergraph achieved the maximum number of edges in a cancellative3-uniform hypergraph. Furthermore, Keevash and Mubayi (2004) determined that only the balanced complete3-partite3-uniform hypergraph achieved the maximum number of edges in a3-uniform hypergraph containing no copy of $F_5$. Let $\mathcal{H}$ be a hypergraph, and W be a nonempty subset of $V(\mathcal{H})$. If every edge in $\mathcal{H}$ contains exactly one vertex in W, then we call W an independent transversal of $\mathcal{H}$. In this paper, we determine the maximump-spectral radius of a cancellative3-uniform hypergraph with an independent transversal. Furthermore, if $p>2$, we get that only the balanced complete3-partite3-uniform hypergraph achieved the maximump-spectral radius of a cancellative3-uniform hypergraph with an independent transversal.

The purpose of this paper is to study an approximation theorem and generic convergence of the generalized weakly-mixed vector quasi-equilibrium problem. Firstly, we give an existence theorem for the solution of generalized weakly-mixed vector quasi-equilibrium problems by using the Fan-Knaster-Kuratowski-Mazurkiewicz (Fan-KKM) lemma. Then, based on Simon's bounded rationality theory, we give an approximation theorem for generalized weakly-mixed vector quasi-equilibrium problems in a very general case. Finally, by using Fort's theorem, we obtain a generic convergence result for the solution of generalized weakly-mixed vector quasi-equilibrium problems in the sense of Baire classification.

Since the filled function algorithm is proposed, parameters have been regarded as the main factor restricting the efficiency of the algorithm. So it is particularly important to construct a filled function without parameters. In order to improve the efficiency and accuracy of the algorithm, a new class of parameter-free filled tunnel functions is constructed in this paper. Some properties of the new class of filled tunnel functions are analyzed. Based on the filled tunnel functions, a new global optimization algorithm is proposed, and numerical experiments are carried out on the algorithm. The numerical experiment results show that the algorithm is feasible and effective.

Let $\mathcal{H}$ be a family of graphs. The planar Turán number of $\mathcal{H}$, denoted by ex$_{\mathcal{P}}(n,\mathcal{H})$, is the maximum number of edges over all planar graphs on n vertices that do not contain any $H\in\mathcal{H}$ as a subgraph. In this paper, we partition the graph into some specific subgraphs called as triangle blocks. Based on the partition, we calculate the contribution of each triangle block to the vertex, edge and face to graph G, respectively. Considered the structure of plane graph and by double-counting techniques and induction on the order of G, we obtained the following result: Let G be a connected $\{C_5,C_6\}$-free plane graph on n vertices, if $n\geq14$, then $e(G)\leq\frac{30n-84}{13}$. We also give infinitely many graphs which attain these bounds.

In this paper, we introduce a new vacation strategy. We consider an queueing-inventory system with lost sales and (s, S) strategy under the vacation strategy. When inventory level is zero, the server goes to a working vacation in which if the replenishment is successful, the server immediately begins to serve the customer normally. When the working vacation is over, if the inventory level is still zero, the server will take multiple vacations, otherwise he/she will return to the normal working state. We analyze the stationary distributions of the queueing-inventory system under the vacation strategy by using Markov process method. On this basis, some performance indices and average cost function are obtained. Finally, the optimal inventory policy and the optimal expected cost are also discussed by numerical examples.