Thesis Summary Empirical Game-Theoretic Methods for Strategy Design and Analysis in Complex

孙诗婕 SUN Shijie 李栋宁 LI Dongning 江南大学，江苏无锡 214122 （Jiangnan University，214122 Wuxi Jiangsu）14摘要：剧情类游戏作为电子游戏的一大类别，旨在向玩家进行故事讲述并与玩家互动，即游戏设计者预设游戏世界，玩家介入、亲历并反馈游戏世界。

其叙事目标的设计，需要从游戏设计师和游戏玩家两者需求出发，从而完成游戏叙事。

结合戴维•赫尔曼（David Herman）的“CAPA 解释模式”，对剧情类游戏的叙事目标进行设计研究，藉由游戏故事“解释的语境”、游戏中的“何时、何地”、人物的维度及游戏叙事归因4要素，提出构建游戏世界观、搭建游戏时空规则、创建玩家游戏“化身”、探寻游戏叙事意图归属4种叙事目标，希图为剧情类游戏的叙事目标设计提供理论参考。

关键词：剧情类游戏；游戏叙事； 戴维•赫尔曼； CAPA解释模式Abstract: As a large category of video games, plot games are designed to tell the story and interact with the players, i.e., the game designer sets up the game world, and the players step in, experience and give feedback on the game world. The design of its narrative target needs to start from the needs of both the game designer and the game players in order to complete the narrative of the game. In this paper, the narrative objectives of plot games are designed and studied with David Herman’s “CAPA Interpretation Model”, through the four elements of the game story “The context of explanation”, “When and where”in the game, the dimension of the characters and the narrative attribution in the game, this paper puts forward four kinds of narrative targets: the Blueprint of the game world, the rules of time and space of the game, the avatar of the game, and the attribution of the narrative intention of the game.Key words: plot games ； game narrative ； David Herman ； CAPA interpretation model中图分类号：J0 文献标识码：A doi：10.3963/j.issn.2095-0705.2022.02.014赫尔曼解释模式下的剧情类游戏叙事目标设计On Narrative Goal Design of Plot Games Based on Herman’s Interpretation Model收稿日期：2022-02-14作者简介：孙诗婕（1995—），女，江南大学设计学院硕士研究生，研究方向为数字媒体艺术设计及理论；李栋宁（1971—），男，博士，江南大学设计学院教授，研究方向为影视艺术理论、数字媒体艺术设计及理论。

for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871) 2 (School of Information Science and Engineering, Central South University, Changsha 410075) (E-mail: xhnian@) Abstract The suboptimal control program via memoryless state feedback strategies for LQ differential games with multiple players is studied in this paper. Sufficient conditions for the existence of the suboptimal strategies for LQ differential games are presented. It is shown that the suboptimal strategies of LQ differential games are associated with a coupled algebraic Riccati inequality. Furthermore, the problem of designing suboptimal strategies is considered. A non-convex optimization problem with BMI constrains is formulated to design the suboptimal strategies which minimizes the performance indices of the closed-loop LQ differential games and can be solved by using LMI Toolbox of MATLAB. An example is given to illustrate the proposed results. Key words Differential game, suboptimal control, Nash equilibrium, bilinear matrix inequalities

Package‘GameTheoryAllocation’October12,2022Type PackageTitle Tools for Calculating Allocations in Game TheoryVersion1.0Date2016-07-20Author Alejandro Saavedra-NievesMaintainer Alejandro Saavedra-Nieves<***********************************>Depends R(>=2.15.0),e1071,lpSolveAPIDescription Many situations can be modeled as game theoretic situations.Some procedures are in-cluded in this package to calculate the most important allocations rules in Game Theory:Shap-ley value,Owen value or nucleolus,among other.First,we must define as an argu-ment the value of the unions of the envolved agents with the characteristic function.License GPL-2LazyLoad yesNeedsCompilation noRepository CRANDate/Publication2016-07-2417:25:09R topics documented:GameTheoryAllocation-package (2)coalitions (3)EPM_allocation (4)isinthecore (5)nucleolus (6)Owen_value (7)Shapley_value (8)Index912GameTheoryAllocation-package GameTheoryAllocation-packageTools for Calculating Allocations in Game TheoryDescriptionMany situations can be modeled as game theoretic situations.Some procedures are included in this package to calculate the most important allocations rules in Game Theory:Shapley value,Owen value or nucleolus,among other.First,we must define as an argument the value of the unions of the envolved agents with the characteristic function.Author(s)A.Saavedra-NievesMaintainer:A.Saavedra-Nieves(***********************************)ReferencesFrisk,M.,Gothe-Lundgren,M.,Jornsten,K.,Ronnqvist,M.(2010).Cost allocation in collaborative forest transportation.European Journal of Operational Research,V ol.205,pp.448-458.Gillies,D.B.(1953).Some theorems on n-person games.PhD thesis,Princeton University.Owen,G.(1977).Values of games with a priori unions.Mathematical Economics and Game Theory:Essays in Honor of Oskar Morgenstern(Eds.:O.Moeschlin R.Hein).Springer,New York.Shapley,L.S.(1953).A value por n-person games.In H.Kuhn y A.Tucker(eds),Contributions to the theory of games II,V ol.28,Annals of Mathematics Studies.Princeton University Press.Schmeidler,D.(1969).The nucleolus of a characteristic function game,SIAM Journal of Applied Mathematics,vol.17,pp.1163-1170.Examples#Example1characteristic_function<-c(0,0.538,0.761,1.742,0.554,0.137,0.293,0.343)isinthecore(characteristic_function,allocation=c(0.1,0.2,0.043),game="cost")#[1]"The allocation is not in the core"#NULLisinthecore(characteristic_function,allocation=c(0.05,0.206,0.087),game="cost")#[1]"The allocation is in the core"#NULLnucleolus(characteristic_function,game="cost")#[1]"Nucleolus"#123#0.1370.2060#Example2coalitions3characteristic_function<-c(1,1,2,1,2,2,2)Owen_value(characteristic_function,union=list(c(1,2),c(3)),game="cost")#[1]"Owen Value"#123#0.250.251.5coalitions coalitionsDescriptionThis function gives all the coalitions in a binary mode and usual way.Usagecoalitions(n)Argumentsn Number of the involved playersValueA list with the following components:Binary A matrix where each row indicates a binary representation of the coalition in a binary mode.The second one,the usual way.Classic A vector with the associated representation of the coalitions.Author(s)A.Saavedra-NievesExamplescoalitions(3)#$Binary#[,1][,2][,3]#[1,]000#[2,]100#[3,]010#[4,]001#[5,]110#[6,]101#[7,]011#[8,]111##$Classic#[1]"0"" {1} "" {2} "" {3} "" {1,2} "#[6]" {1,3} "" {2,3} "" {1,2,3}4EPM_allocation EPM_allocation Equal Profit Method allocationDescriptionThis function gives the Equal Profit Method allocation described in Frisk et al.(2010).UsageEPM_allocation(characteristic_function,r=NA,info=NA,game=c("profit","cost"))Argumentscharacteristic_functionA vector with the characteristic function v(S)(or c(S),if we work with a costgame),according to the order of coalitions shown in coalitions function.r Incremental step for calculating the EPM-allocation.If no solution is found,weincrease iteratively in r units the allowed excess to get an epsilon-core alloca-tion.Procedure stops when a solution is found.info For knowing information about the resolution,make info=1game Characters to indicate if the game is a cost or profit game.The possibles valuesare"cost"or"profit".ValueA vector with the allocation that EPM method proposes.Author(s)A.Saavedra-NievesReferencesFrisk,M.,Gothe-Lundgren,M.,Jornsten,K.,Ronnqvist,M.(2010).Cost allocation in collaborative forest transportation.European Journal of Operational Research,V ol.205,pp.448-458.Examplescharacteristic_function<-c(0,0.538,0.761,1.742,0.554,0.137,0.293,0.343)EPM_allocation(characteristic_function,r=0.01,info=1,game="cost")#[1]"EPM_allocation"#[1]"The cost game has a non-empty core"#123#0.050.2060.087isinthecore5 isinthecore Isinthecore(core allocations)DescriptionThis function checks if the allocation belongs to the core of the TU game.Usageisinthecore(characteristic_function,allocation,game=c("profit","cost"))Argumentscharacteristic_functionA vector with the characteristic function v(S)(or c(S),if we work with a costgame),according to the order of coalitions shown in coalitions function.allocation A vector with the allocation where each component indicates the part of each agent.game Characters to indicate if the game is a cost or profit game.The possibles values are"cost"or"profit".Author(s)A.Saavedra-NievesReferencesGillies,D.B.(1953).Some theorems on n-person games.PhD thesis,Princeton University. Examplescharacteristic_function<-c(0,0.538,0.761,1.742,0.554,0.137,0.293,0.343)isinthecore(characteristic_function,allocation=c(0.1,0.2,0.043),game="cost")#[1]"The allocation is not in the core"#NULLisinthecore(characteristic_function,allocation=c(0.05,0.206,0.087),game="cost")#[1]"The allocation is in the core"#NULL6nucleolus nucleolus NucleolusDescriptionThis function gives the nucleolus described in Schmeidler(1969).Usagenucleolus(characteristic_function,game=c("profit","cost"))Argumentscharacteristic_functionA vector with the characteristic function v(S)(or c(S),if we work with a costgame),according to the order of coalitions shown in coalitions function.game Characters to indicate if the game is a cost or profit game.The possibles values are"cost"or"profit".ValueA vector with the allocation that nucleolus proposes.Author(s)A.Saavedra-NievesReferencesSchmeidler,D.(1969).The nucleolus of a characteristic function game,SIAM Journal of Applied Mathematics,vol.17,pp.1163-1170.Examplescharacteristic_function<-c(0,0.538,0.761,1.742,0.554,0.137,0.293,0.343)nucleolus(characteristic_function,game="cost")#[1]"Nucleolus"#123#0.1370.2060Owen_value7 Owen_value Owen_value(Owen value)DescriptionThis function gives the Owen value described in Owen(1977).UsageOwen_value(characteristic_function,union,game=c("profit","cost"))Argumentscharacteristic_functionA vector with the characteristic function v(S)(or c(S),if we work with a costgame),according to the order of coalitions shown in coalitions function.union A list with a partition of the players set.Each element of this list is a union a priori,following the proposal of Owen.game Characters to indicate if the game is a cost or profit game.The possibles values are"cost"or"profit".ValueA vector with the allocation that Owen value(Owen,1977)proposes.Author(s)A.Saavedra-NievesReferencesOwen,G.(1977).Values of games with a priori unions.Mathematical Economics and Game Theory:Essays in Honor of Oskar Morgenstern(Eds.:O.Moeschlin R.Hein).Springer,New York.Examplescharacteristic_function<-c(1,1,2,1,2,2,2)Owen_value(characteristic_function,union=list(c(1,2),c(3)),game="cost")#[1]"Owen Value"#123#0.250.251.5Shapley_value(characteristic_function,game="cost")#[1]"Shapley Value"#123#0.33333330.33333331.3333338Shapley_value Shapley_value Shapley_value(Shapley Value)DescriptionThis function gives the Shapley value introduced in Shapley(1953).UsageShapley_value(characteristic_function,game=c("profit","cost"))Argumentscharacteristic_functionA vector with the characteristic function v(S)(or c(S),if we work with a costgame),according to the order of coalitions shown in coalitions function.game Characters to indicate if the game is a cost or profit game.The possibles values are"cost"or"profit".ValueA vector with the allocation that Shapley value(Shapley,1953)proposes.Author(s)A.Saavedra-NievesReferencesShapley,L.S.(1953).A value por n-person games.In H.Kuhn y A.Tucker(eds),Contributions to the theory of games II,V ol.28,Annals of Mathematics Studies.Princeton University Press.Examplescharacteristic_function<-c(1,1,2,1,2,2,2)Shapley_value(characteristic_function,game="cost")#[1]"Shapley Value"#123#0.33333330.33333331.333333IndexShapley_value,8∗EPM_allocationEPM_allocation,4∗EPMEPM_allocation,4∗GameTheoryGameTheoryAllocation-package,2∗coalitioncoalitions,3∗coacoalitions,3∗core_allocationsisinthecore,5∗coreisinthecore,5∗nucleolusgtnucleolus,6∗nucleolusnucleolus,6∗owen_valueOwen_value,7∗owenOwen_value,7∗shapley_valueShapley_value,8∗shapleyShapley_value,8coalitions,3EPM_allocation,4GameTheoryAllocation(GameTheoryAllocation-package),2GameTheoryAllocation-package,2isinthecore,5nucleolus,6Owen_value,79。

Character relationships
Characters: The story features a diverse cast of characters with different backgrounds and experiences.
Summary: The characters' relationships and interactions contribute to the overall narrative and provide insights into the theme.
Details: The characters support and encourage each other in their language learning journey, demonstrating the power of community and collaboration in learning. Their individual experiences and perspectives add depth to the theme, making it more relatable and meaningful to learners.
Determining tense and voice
Tense indicates when the action took place (past, present or future), and voice indicates whether the subject is performing the action (active voice) or receiving it (passive voice).
Understanding sentence complexity