It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems kn...It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.展开更多
We study the effects of the planarity and heterogeneity of networks on evolutionary two-player symmetric games by considering four different kinds of networks, including two types of heterogeneous networks: the weight...We study the effects of the planarity and heterogeneity of networks on evolutionary two-player symmetric games by considering four different kinds of networks, including two types of heterogeneous networks: the weighted planar stochastic lattice(a planar scale-free network) and the random uncorrelated scale-free network with the same degree distribution as the weighted planar stochastic lattice; and two types of homogeneous networks: the hexagonal lattice and the random regular network with the same degree k_0= 6 as the hexagonal lattice. Using extensive computer simulations, we found that both the planarity and heterogeneity of the network have a significant influence on the evolution of cooperation, either promotion or inhibition, depending not only on the specific kind of game(the Harmony, Snowdrift, Stag Hunt or Prisoner's Dilemma games), but also on the update rule(the Fermi, replicator or unconditional imitation rules).展开更多
在“30*60”目标背景下,低碳政策和低碳技术成为能源系统节能与减排新的出发点和落脚点,电转气(power to gas,P2G)作为一种新型能源转换方式为消纳新能源和降低碳排放提供了新的途径。文中首先将电转气精细化为电解制氢和氢气制甲烷两...在“30*60”目标背景下,低碳政策和低碳技术成为能源系统节能与减排新的出发点和落脚点,电转气(power to gas,P2G)作为一种新型能源转换方式为消纳新能源和降低碳排放提供了新的途径。文中首先将电转气精细化为电解制氢和氢气制甲烷两个阶段,构建两阶段P2G、碳捕集、微型燃气轮机掺氢、燃气锅炉掺氢相互协同的运行框架。其次考虑P2G反应热的利用,以及能源运营商和能源用户两主体阶梯碳交易机制对系统碳排放的约束。最后建立考虑两阶段P2G和燃气掺氢的综合能源系统日前双层优化调度模型,上层模型以能源商运营收益最大为目标,下层模型以能源用户的用能效用与购能成本之差最大为目标。通过不同场景下的仿真,验证了所提模型的有效性,并分析了掺氢比和碳交易基价对综合能源系统低碳经济的影响。展开更多
文摘It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575072 and 11475074)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2017-172)
文摘We study the effects of the planarity and heterogeneity of networks on evolutionary two-player symmetric games by considering four different kinds of networks, including two types of heterogeneous networks: the weighted planar stochastic lattice(a planar scale-free network) and the random uncorrelated scale-free network with the same degree distribution as the weighted planar stochastic lattice; and two types of homogeneous networks: the hexagonal lattice and the random regular network with the same degree k_0= 6 as the hexagonal lattice. Using extensive computer simulations, we found that both the planarity and heterogeneity of the network have a significant influence on the evolution of cooperation, either promotion or inhibition, depending not only on the specific kind of game(the Harmony, Snowdrift, Stag Hunt or Prisoner's Dilemma games), but also on the update rule(the Fermi, replicator or unconditional imitation rules).
文摘在“30*60”目标背景下,低碳政策和低碳技术成为能源系统节能与减排新的出发点和落脚点,电转气(power to gas,P2G)作为一种新型能源转换方式为消纳新能源和降低碳排放提供了新的途径。文中首先将电转气精细化为电解制氢和氢气制甲烷两个阶段,构建两阶段P2G、碳捕集、微型燃气轮机掺氢、燃气锅炉掺氢相互协同的运行框架。其次考虑P2G反应热的利用,以及能源运营商和能源用户两主体阶梯碳交易机制对系统碳排放的约束。最后建立考虑两阶段P2G和燃气掺氢的综合能源系统日前双层优化调度模型,上层模型以能源商运营收益最大为目标,下层模型以能源用户的用能效用与购能成本之差最大为目标。通过不同场景下的仿真,验证了所提模型的有效性,并分析了掺氢比和碳交易基价对综合能源系统低碳经济的影响。
