英文标题：
《On the Resource Allocation for Political Campaigns》
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作者：
Sebasti\\\'an Morales, Charles Thraves
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最新提交年份：
2020
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英文摘要：
  In an election campaign, candidates must decide how to optimally allocate their efforts/resources optimally among the regions of a country. As a result, the outcome of the election will depend on the players\' strategies and the voters\' preferences. In this work, we present a zero-sum game where two candidates decide how to invest a fixed resource in a set of regions, while considering their sizes and biases. We explore the Majority System (MS) as well as the Electoral College (EC) voting systems. We prove equilibrium existence and uniqueness under MS in a deterministic model; in addition, their closed form expressions are provided when fixing the subset of regions and relaxing the non-negative investing constraint. For the stochastic case, we use Monte Carlo simulations to compute the players\' payoffs, together with its gradient and hessian. For the EC, given the lack of Equilibrium in pure strategies, we propose an iterative algorithm to find Equilibrium in mixed strategies in a subset of the simplex lattice. We illustrate numerical instances under both election systems, and contrast players\' equilibrium strategies. Finally, we show that polarization induces candidates to focus on larger regions with negative biases under MS, whereas candidates concentrate on swing states under EC.
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中文摘要：
在竞选活动中，候选人必须决定如何在一个国家的各个地区之间以最佳方式分配他们的努力/资源。因此，选举结果将取决于参与者的策略和选民的偏好。在这项工作中，我们提出了一个零和博弈，其中两个候选人决定如何在一组地区投资固定资源，同时考虑他们的规模和偏见。我们探讨了多数票制度（MS）以及选举团（EC）投票制度。在确定性模型中，证明了MS下平衡点的存在唯一性；此外，在确定区域子集和放松非负投资约束时，给出了它们的闭式表达式。对于随机情况，我们使用蒙特卡罗模拟来计算参与者的收益，以及它的梯度和黑森分布。对于EC，考虑到纯策略中缺乏均衡，我们提出了一个迭代算法来寻找单纯形格子集中混合策略中的均衡。我们举例说明了两种选举制度下的数值例子，并对比了参与者的均衡策略。最后，我们表明，极化诱导候选者在MS下关注具有负偏差的更大区域，而在EC下，候选者关注摇摆状态。
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Computer Science and Game Theory        计算机科学与博弈论
分类描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵盖计算机科学和博弈论交叉的所有理论和应用方面，包括机制设计的工作，游戏中的学习（可能与学习重叠），游戏中的agent建模的基础（可能与多agent系统重叠），非合作计算环境的协调、规范和形式化方法。该领域还涉及博弈论在电子商务等领域的应用。
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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